Flat-fading channel

classsionna.phy.channel.FlatFadingChannel(num_tx_ant,num_rx_ant,spatial_corr=None,return_channel=False,precision=None,**kwargs)[source]

Applies random channel matrices to a vector input and adds AWGN

This class combinesGenerateFlatFadingChannel andApplyFlatFadingChannel and computes the output ofa flat-fading channel with AWGN.

For a given batch of input vectors\(\mathbf{x}\in\mathbb{C}^{K}\),the output is

\[\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n}\]

where\(\mathbf{H}\in\mathbb{C}^{M\times K}\) are randomly generatedflat-fading channel matrices and\(\mathbf{n}\in\mathbb{C}^{M}\sim\mathcal{CN}(0, N_o\mathbf{I})\)is an AWGN vector that is optionally added.

ASpatialCorrelation can be configured and thechannel realizations optionally returned. This is useful to simulatereceiver algorithms with perfect channel knowledge.

Parameters:

• num_tx_ant (int) – Number of transmit antennas

• num_rx_ant (int) – Number of receive antennas

• spatial_corr (None (default) |SpatialCorrelation) – Spatial correlation to be applied

• return_channel (bool, (defaultFalse)) – Indicates if the channel realizations should be returned

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• x ([batch_size, num_tx_ant],tf.complex) – Tensor of transmit vectors

• no (None (default) | Tensor,tf.float) – (Optional) noise powerno per complex dimension.Will be broadcast to the shape ofy.For more details, seeAWGN.

Output:

• y ([batch_size, num_rx_ant],tf.complex) – Channel output

• h ([batch_size, num_rx_ant, num_tx_ant],tf.complex) – Channel realizations. Will only be returned ifreturn_channel==True.

propertyapply

Calls the internalApplyFlatFadingChannel

propertygenerate

Calls the internalGenerateFlatFadingChannel

propertyspatial_corr

Get/set spatialcorrelation to be applied

Type:

SpatialCorrelation

classsionna.phy.channel.GenerateFlatFadingChannel(num_tx_ant,num_rx_ant,spatial_corr=None,precision=None,**kwargs)[source]

Generates tensors of flat-fading channel realizations

This class generates batches of random flat-fading channel matrices.A spatial correlation can be applied.

Parameters:

• num_tx_ant (int) – Number of transmit antennas

• num_rx_ant (int) – Number of receive antennas

• spatial_corr (None (default) |SpatialCorrelation) – Spatial correlation to be applied

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

batch_size (int) – Number of channel matrices to generate

Output:

h ([batch_size, num_rx_ant, num_tx_ant],tf.complex) – Batch of random flat fading channel matrices

propertyspatial_corr

Get/set spatialcorrelation to be applied

Type:

SpatialCorrelation

classsionna.phy.channel.ApplyFlatFadingChannel(precision=None,**kwargs)[source]

Applies given channel matrices to a vector input and adds AWGN

This class applies a given tensor of flat-fading channel matricesto an input tensor. AWGN noise can be optionally added.Mathematically, for channel matrices\(\mathbf{H}\in\mathbb{C}^{M\times K}\)and input\(\mathbf{x}\in\mathbb{C}^{K}\), the output is

\[\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n}\]

where\(\mathbf{n}\in\mathbb{C}^{M}\sim\mathcal{CN}(0, N_o\mathbf{I})\)is an AWGN vector that is optionally added.

Parameters:

precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• x ([batch_size, num_tx_ant],tf.complex) – Transmit vectors

• h ([batch_size, num_rx_ant, num_tx_ant],tf.complex) – Channel realizations. Will be broadcast to thedimensions ofx if needed.

• no (None (default) | Tensor,tf.float) – (Optional) noise powerno per complex dimension.Will be broadcast to the shape ofy.For more details, seeAWGN.

Output:

y ([batch_size, num_rx_ant],tf.complex) – Channel output

classsionna.phy.channel.SpatialCorrelation(*args,precision=None,**kwargs)[source]

Abstract class that defines an interface for spatial correlation functions

TheFlatFadingChannel model can be configured with aspatial correlation model.

Parameters:

precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

h (tf.complex) – Tensor of arbitrary shape containing spatially uncorrelatedchannel coefficients

Output:

h_corr (tf.complex) – Tensor of the same shape ash containing the spatiallycorrelated channel coefficients

classsionna.phy.channel.KroneckerModel(r_tx=None,r_rx=None,precision=None)[source]

Kronecker model for spatial correlation

Given a batch of matrices\(\mathbf{H}\in\mathbb{C}^{M\times K}\),\(\mathbf{R}_\text{tx}\in\mathbb{C}^{K\times K}\), and\(\mathbf{R}_\text{rx}\in\mathbb{C}^{M\times M}\), this functionwill generate the following output:

\[\mathbf{H}_\text{corr} = \mathbf{R}^{\frac12}_\text{rx} \mathbf{H} \mathbf{R}^{\frac12}_\text{tx}\]

Note that\(\mathbf{R}_\text{tx}\in\mathbb{C}^{K\times K}\) and\(\mathbf{R}_\text{rx}\in\mathbb{C}^{M\times M}\)must be positive semi-definite, such as the ones generated byexp_corr_mat().

Parameters:

• r_tx ([…, K, K],tf.complex) – Transmit correlation matrices. Ifthe rank ofr_tx is smaller than that of the inputh,it will be broadcast.

• r_rx ([…, M, M],tf.complex) – Receive correlation matrices. Ifthe rank ofr_rx is smaller than that of the inputh,it will be broadcast.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

h ([…, M, K],tf.complex) – Spatially uncorrelated channel coeffficients

Output:

h_corr ([…, M, K],tf.complex) – Spatially correlated channel coefficients

propertyr_rx

Get/set receive correlation matrices

Type:

[…, M, M],tf.complex

propertyr_tx

Get/set transmit correlation matrices

Type:

[…, K, K],tf.complex

classsionna.phy.channel.PerColumnModel(r_rx,precision=None)[source]

Per-column model for spatial correlation

Given a batch of matrices\(\mathbf{H}\in\mathbb{C}^{M\times K}\)and correlation matrices\(\mathbf{R}_k\in\mathbb{C}^{M\times M}, k=1,\dots,K\),this function will generate the output\(\mathbf{H}_\text{corr}\in\mathbb{C}^{M\times K}\),with columns

\[\mathbf{h}^\text{corr}_k = \mathbf{R}^{\frac12}_k \mathbf{h}_k,\quad k=1, \dots, K\]

where\(\mathbf{h}_k\) is the kth column of\(\mathbf{H}\).Note that all\(\mathbf{R}_k\in\mathbb{C}^{M\times M}\) mustbe positive semi-definite, such as the ones generatedbyone_ring_corr_mat().

This model is typically used to simulate a MIMO channel between multiplesingle-antenna users and a base station with multiple antennas.The resulting SIMO channel for each user has a different spatial correlation.

Parameters:

• r_rx ([…, M, M],tf.complex) – Receive correlation matrices. Ifthe rank ofr_rx is smaller than that of the inputh,it will be broadcast. For a typically use of this model,r_rxhas shape […, K, M, M], i.e., a different correlation matrix for eachcolumn ofh.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

h ([…, M, K],tf.complex) – Spatially uncorrelated channel coeffficients

Output:

h_corr ([…, M, K], tf.complex) – Spatially correlated channel coefficients

propertyr_rx

Get/set receive correlation matrices

Type:

[…, M, M],tf.complex

Channel model interface

classsionna.phy.channel.ChannelModel(precision=None,**kwargs)[source]

Abstract class that defines an interface for channel models

Any channel model which generates channel impulse responsesmust implement this interface.All the channel models available in Sionna,such asRayleighBlockFadingorTDL, implement this interface.

Remark: Some channel models only require a subset of the input parameters.

Parameters:

precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• batch_size (int) – Batch size

• num_time_steps (int) – Number of time steps

• sampling_frequency (float) – Sampling frequency [Hz]

Output:

• a ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths, num_time_steps],tf.complex) – Path coefficients

• tau ([batch size, num_rx, num_tx, num_paths],tf.float) – Path delays [s]

Time domain channel

The model of the channel in the time domain assumes pulse shaping and receivefiltering are performed using a conventional sinc filter (see, e.g.,[Tse]).Using sinc for transmit and receive filtering, the discrete-time domain receivedsignal at time step\(b\) is

where\(x_{u, k, b}\) is the baseband symbol transmitted by transmitter\(u\) on antenna\(k\) and at time step\(b\),\(w_{v, l, b} \sim \mathcal{CN}\left(0,N_0\right)\) the additive whiteGaussian noise, and\(\bar{h}_{u, k, v, l, b, \ell}\) the channel filter tapat time step\(b\) and for time-lag\(\ell\), which is given by

classsionna.phy.channel.TimeChannel(channel_model,bandwidth,num_time_samples,maximum_delay_spread=3e-06,l_min=None,l_max=None,normalize_channel=False,return_channel=False,precision=None,**kwargs)[source]

Generates channel responses and applies them to channel inputs in the time domain

The channel output consists ofnum_time_samples +l_max -l_mintime samples, as it is the result of filtering the channel input of lengthnum_time_samples with the time-variant channel filter of lengthl_max -l_min + 1. In the case of a single-input single-output link and given a sequence of channelinputs\(x_0,\cdots,x_{N_B}\), where\(N_B\) isnum_time_samples, thislayer outputs

\[y_b = \sum_{\ell = L_{\text{min}}}^{L_{\text{max}}} x_{b-\ell} \bar{h}_{b,\ell} + w_b\]

where\(L_{\text{min}}\) correspondsl_min,\(L_{\text{max}}\) tol_max,\(w_b\) tothe additive noise, and\(\bar{h}_{b,\ell}\) to the\(\ell^{th}\) tap of the\(b^{th}\) channel sample.This layer outputs\(y_b\) for\(b\) ranging from\(L_{\text{min}}\) to\(N_B + L_{\text{max}} - 1\), and\(x_{b}\) is set to 0 for\(b < 0\) or\(b \geq N_B\).The channel taps\(\bar{h}_{b,\ell}\) are computed assuming a sinc filteris used for pulse shaping and receive filtering. Therefore, given a channel impulse response\((a_{m}(t), \tau_{m}), 0 \leq m \leq M-1\), generated by thechannel_model,the channel taps are computed as follows:

\[\bar{h}_{b, \ell}= \sum_{m=0}^{M-1} a_{m}\left(\frac{b}{W}\right) \text{sinc}\left( \ell - W\tau_{m} \right)\]

for\(\ell\) ranging froml_min tol_max, and where\(W\) isthebandwidth.

For multiple-input multiple-output (MIMO) links, the channel output is computed for each antenna of each receiver and by summing over all the antennas of all transmitters.

Parameters:

• channel_model (ChannelModel) – Used channel model

• bandwidth (float) – Bandwidth (\(W\)) [Hz]

• num_time_samples (int) – Number of time samples forming the channel input (\(N_B\))

• maximum_delay_spread (float, (default 3e-6)) – Maximum delay spread [s].Used to compute the default value ofl_max ifl_max is set toNone. If a value is given forl_max, this parameter is not used.It defaults to 3us, which was foundto be large enough to include most significant paths with all channelmodels included in Sionna assuming a nominal delay spread of 100ns.

• l_min (None (default) |int) – Smallest time-lag for the discrete complex baseband channel (\(L_{\text{min}}\)).If set toNone, defaults to the value given bytime_lag_discrete_time_channel().

• l_max (None (default) |int) – Largest time-lag for the discrete complex baseband channel (\(L_{\text{max}}\)).If set toNone, it is computed frombandwidth andmaximum_delay_spreadusingtime_lag_discrete_time_channel(). If it is not set toNone,then the parametermaximum_delay_spread is not used.

• normalize_channel (bool, (defaultFalse)) – If set toTrue, the channel is normalized over the block sizeto ensure unit average energy per time step.

• return_channel (bool, (defaultFalse)) – If set toTrue, the channel response is returned in addition to thechannel output.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• x ([batch size, num_tx, num_tx_ant, num_time_samples],tf.complex) – Channel inputs

• no (None (default) | Tensor,tf.float) – Tensor whose shape can be broadcast to the shape of thechannel outputs: [batch size, num_rx, num_rx_ant, num_time_samples].The (optional) noise powerno is per complex dimension. Ifno is a scalar,noise of the same variance will be added to the outputs.Ifno is a tensor, it must have a shape that can be broadcast tothe shape of the channel outputs. This allows, e.g., adding noise ofdifferent variance to each example in a batch. Ifno has a lowerrank than the channel outputs, thenno will be broadcast to theshape of the channel outputs by adding dummy dimensions after the lastaxis.

Output:

• y ([batch size, num_rx, num_rx_ant, num_time_samples + l_max - l_min],tf.complex) – Channel outputsThe channel output consists ofnum_time_samples +l_max -l_mintime samples, as it is the result of filtering the channel input of lengthnum_time_samples with the time-variant channel filter of lengthl_max -l_min + 1.

• h_time ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_time_samples + l_max - l_min, l_max - l_min + 1],tf.complex) – (Optional) Channel responses. Returned only ifreturn_channelis set toTrue.For each batch example,num_time_samples +l_max -l_min timesteps of the channel realizations are generated to filter the channel input.

classsionna.phy.channel.GenerateTimeChannel(channel_model,bandwidth,num_time_samples,l_min,l_max,normalize_channel=False,precision=None,**kwargs)[source]

Generate channel responses in the time domain

For each batch example,num_time_samples +l_max -l_min time steps of achannel realization are generated by this layer.These can be used to filter a channel input of lengthnum_time_samples using theApplyTimeChannel layer.

The channel taps\(\bar{h}_{b,\ell}\) (h_time) returned by this layerare computed assuming a sinc filter is used for pulse shaping and receive filtering.Therefore, given a channel impulse response\((a_{m}(t), \tau_{m}), 0 \leq m \leq M-1\), generated by thechannel_model,the channel taps are computed as follows:

\[\bar{h}_{b, \ell}= \sum_{m=0}^{M-1} a_{m}\left(\frac{b}{W}\right) \text{sinc}\left( \ell - W\tau_{m} \right)\]

for\(\ell\) ranging froml_min tol_max, and where\(W\) isthebandwidth.

Parameters:

• channel_model (ChannelModel) – Channel model to be used

• bandwidth (float) – Bandwidth (\(W\)) [Hz]

• num_time_samples (int) – Number of time samples forming the channel input (\(N_B\))

• l_min (int) – Smallest time-lag for the discrete complex baseband channel (\(L_{\text{min}}\))

• l_max (int) – Largest time-lag for the discrete complex baseband channel (\(L_{\text{max}}\))

• normalize_channel (bool, (defaultFalse)) – If set toTrue, the channel is normalized over the block sizeto ensure unit average energy per time step.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

batch_size (None (default) |int) – Batch size. Defaults toNone for channel models that do not require this parameter.

Output:

h_time ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_time_samples + l_max - l_min, l_max - l_min + 1],tf.complex) – Channel responses.For each batch example,num_time_samples +l_max -l_min time steps of achannel realization are generated by this layer.These can be used to filter a channel input of lengthnum_time_samples using theApplyTimeChannel layer.

classsionna.phy.channel.ApplyTimeChannel(num_time_samples,l_tot,precision=None,**kwargs)[source]

Apply time domain channel responsesh_time to channel inputsx,by filtering the channel inputs with time-variant channel responses.

For each batch example,num_time_samples +l_tot - 1 time steps of achannel realization are required to filter the channel inputs.

The channel output consists ofnum_time_samples +l_tot - 1time samples, as it is the result of filtering the channel input of lengthnum_time_samples with the time-variant channel filter of lengthl_tot. In the case of a single-input single-output link and given a sequence of channelinputs\(x_0,\cdots,x_{N_B}\), where\(N_B\) isnum_time_samples, thislayer outputs

\[y_b = \sum_{\ell = 0}^{L_{\text{tot}}} x_{b-\ell} \bar{h}_{b,\ell} + w_b\]

where\(L_{\text{tot}}\) correspondsl_tot,\(w_b\) to the additive noise, and\(\bar{h}_{b,\ell}\) to the\(\ell^{th}\) tap of the\(b^{th}\) channel sample.This layer outputs\(y_b\) for\(b\) ranging from 0 to\(N_B + L_{\text{tot}} - 1\), and\(x_{b}\) is set to 0 for\(b \geq N_B\).

For multiple-input multiple-output (MIMO) links, the channel output is computed for each antennaof each receiver and by summing over all the antennas of all transmitters.

Parameters:

• num_time_samples (int) – Number of time samples forming the channel input (\(N_B\))

• l_tot (int) – Length of the channel filter (\(L_{\text{tot}} = L_{\text{max}} - L_{\text{min}} + 1\))

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• x ([batch size, num_tx, num_tx_ant, num_time_samples],tf.complex) – Channel inputs

• h_time ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_time_samples + l_tot - 1, l_tot],tf.complex) – Channel responses.For each batch example,num_time_samples +l_tot - 1 time steps of achannel realization are required to filter the channel inputs.

• no (None (default) | tensor,tf.float) – Scalar or tensor whose shape can be broadcast to the shape of the channel outputs: [batch size, num_rx, num_rx_ant, num_time_samples + l_tot - 1].The (optional) noise powerno is per complex dimension. Ifno is ascalar, noise of the same variance will be added to the outputs.Ifno is a tensor, it must have a shape that can be broadcast tothe shape of the channel outputs. This allows, e.g., adding noise ofdifferent variance to each example in a batch. Ifno has a lowerrank than the channel outputs, thenno will be broadcast to theshape of the channel outputs by adding dummy dimensions after thelast axis.

Output:

y ([batch size, num_rx, num_rx_ant, num_time_samples + l_tot - 1], tf.complex) – Channel outputs.The channel output consists ofnum_time_samples +l_tot - 1time samples, as it is the result of filtering the channel input of lengthnum_time_samples with the time-variant channel filter of lengthl_tot.

sionna.phy.channel.cir_to_time_channel(bandwidth,a,tau,l_min,l_max,normalize=False)[source]

Compute the channel taps forming the discrete complex-basebandrepresentation of the channel from the channel impulse response(a,tau)

This function assumes that a sinc filter is used for pulse shaping and receivefiltering. Therefore, given a channel impulse response\((a_{m}(t), \tau_{m}), 0 \leq m \leq M-1\), the channel tapsare computed as follows:

\[\bar{h}_{b, \ell}= \sum_{m=0}^{M-1} a_{m}\left(\frac{b}{W}\right) \text{sinc}\left( \ell - W\tau_{m} \right)\]

for\(\ell\) ranging froml_min tol_max, and where\(W\) isthebandwidth.

Input:

• bandwidth (float) – Bandwidth [Hz]

• a ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths, num_time_steps],tf.complex) – Path coefficients

• tau ([batch size, num_rx, num_tx, num_paths] or [batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths],tf.float) – Path delays [s]

• l_min (int) – Smallest time-lag for the discrete complex baseband channel (\(L_{\text{min}}\))

• l_max (int) – Largest time-lag for the discrete complex baseband channel (\(L_{\text{max}}\))

• normalize (bool, (defaultFalse)) – If set toTrue, the channel is normalized over the block sizeto ensure unit average energy per time step.

Output:

hm ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_time_steps, l_max - l_min + 1],tf.complex) – Channel taps coefficients

sionna.phy.channel.time_to_ofdm_channel(h_t,rg,l_min)[source]

Compute the channel frequency response from the discrete complex-basebandchannel impulse response

Given a discrete complex-baseband channel impulse response\(\bar{h}_{b,\ell}\), for\(\ell\) ranging from\(L_\text{min}\le 0\)to\(L_\text{max}\), the discrete channel frequency response is computed as

\[\hat{h}_{b,n} = \sum_{k=0}^{L_\text{max}} \bar{h}_{b,k} e^{-j \frac{2\pi kn}{N}} + \sum_{k=L_\text{min}}^{-1} \bar{h}_{b,k} e^{-j \frac{2\pi n(N+k)}{N}}, \quad n=0,\dots,N-1\]

where\(N\) is the FFT size and\(b\) is the time step.

This function only produces one channel frequency response per OFDM symbol, i.e.,only values of\(b\) corresponding to the start of an OFDM symbol (aftercyclic prefix removal) are considered.

Input:

• h_t ([…num_time_steps,l_max-l_min+1],tf.complex) – Tensor of discrete complex-baseband channel impulse responses

• resource_grid (ResourceGrid) – Resource grid

• l_min (int) – Smallest time-lag for the discrete complex basebandchannel impulse response (\(L_{\text{min}}\))

Output:

h_f ([…,num_ofdm_symbols,fft_size],tf.complex) – Tensor of discrete complex-baseband channel frequency responses

Note

Note that the result of this function is generally different from theoutput ofcir_to_ofdm_channel() becausethe discrete complex-baseband channel impulse response is truncated(seecir_to_time_channel()). This effectcan be observed in the example below.

Examples

# Setup resource grid and channel modelsm=StreamManagement(np.array([[1]]),1)rg=ResourceGrid(num_ofdm_symbols=1,fft_size=1024,subcarrier_spacing=15e3)tdl=TDL("A",100e-9,3.5e9)# Generate CIRcir=tdl(batch_size=1,num_time_steps=1,sampling_frequency=rg.bandwidth)# Generate OFDM channel from CIRfrequencies=subcarrier_frequencies(rg.fft_size,rg.subcarrier_spacing)h_freq=tf.squeeze(cir_to_ofdm_channel(frequencies,*cir,normalize=True))# Generate time channel from CIRl_min,l_max=time_lag_discrete_time_channel(rg.bandwidth)h_time=cir_to_time_channel(rg.bandwidth,*cir,l_min=l_min,l_max=l_max,normalize=True)# Generate OFDM channel from time channelh_freq_hat=tf.squeeze(time_to_ofdm_channel(h_time,rg,l_min))# Visualize resultsplt.figure()plt.plot(np.real(h_freq),"-")plt.plot(np.real(h_freq_hat),"--")plt.plot(np.imag(h_freq),"-")plt.plot(np.imag(h_freq_hat),"--")plt.xlabel("Subcarrier index")plt.ylabel(r"Channel frequency response")plt.legend(["OFDM Channel (real)","OFDM Channel from time (real)","OFDM Channel (imag)","OFDM Channel from time (imag)"])

Channel with OFDM waveform

To implement the channel response assuming an OFDM waveform, it is assumed thatthe power delay profiles are invariant over the duration of an OFDM symbol.Moreover, it is assumed that the duration of the cyclic prefix (CP) equals atleast the maximum delay spread. These assumptions are common in the literature, as theyenable modeling of the channel transfer function in the frequency domain as asingle-tap channel.

For every link\((u, k, v, l)\) and resource element\((s,n)\),the frequency channel response is obtained by computing the Fourier transform ofthe channel response at the subcarrier frequencies, i.e.,

where\(s\) is used as time step to indicate that the channel response canchange from one OFDM symbol to the next in the event of mobility, even if it isassumed static over the duration of an OFDM symbol.

For every receive antenna\(l\) of every receiver\(v\), thereceived signal\(y_{v, l, s, n}`\) for resource element\((s, n)\) is computed by

where\(x_{u, k, s, n}\) is the baseband symbol transmitted by transmitter\(u`\) on antenna\(k\) and resource element\((s, n)\), and\(w_{v, l, s, n} \sim \mathcal{CN}\left(0,N_0\right)\) the additive whiteGaussian noise.

classsionna.phy.channel.OFDMChannel(channel_model,resource_grid,normalize_channel=False,return_channel=False,precision=None,**kwargs)[source]

Generate channel frequency responses and apply them to channel inputsassuming an OFDM waveform with no ICI nor ISI

For each OFDM symbol\(s\) and subcarrier\(n\), the channel output is computed as follows:

\[y_{s,n} = \widehat{h}_{s, n} x_{s,n} + w_{s,n}\]

where\(y_{s,n}\) is the channel output computed by this layer,\(\widehat{h}_{s, n}\) the frequency channel response,\(x_{s,n}\) the channel inputx, and\(w_{s,n}\) the additive noise.

For multiple-input multiple-output (MIMO) links, the channel output is computed for each antennaof each receiver and by summing over all the antennas of all transmitters.

The channel frequency response for the\(s^{th}\) OFDM symbol and\(n^{th}\) subcarrier is computed from a given channel impulse response\((a_{m}(t), \tau_{m}), 0 \leq m \leq M-1\) generated by thechannel_modelas follows:

\[\widehat{h}_{s, n} = \sum_{m=0}^{M-1} a_{m}(s) e^{-j2\pi n \Delta_f \tau_{m}}\]

where\(\Delta_f\) is the subcarrier spacing, and\(s\) is used as timestep to indicate that the channel impulse response can change from one OFDM symbol to thenext in the event of mobility, even if it is assumed static over the durationof an OFDM symbol.

Parameters:

• channel_model (ChannelModel) – Used channel model

• resource_grid (ResourceGrid) – Resource grid

• normalize_channel (bool, (defaultFalse)) – If set toTrue, the channel is normalized over the resource gridto ensure unit average energy per resource element.

• return_channel (bool, (defaultFalse)) – If set toTrue, the channel response is returned in addition to thechannel output.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• x ([batch size, num_tx, num_tx_ant, num_ofdm_symbols, fft_size],tf.complex) – Channel inputs

• no (None (default) | tensor,tf.float) – Tensor whose shape can be broadcast to the shape of thechannel outputs:[batch size, num_rx, num_rx_ant, num_ofdm_symbols, fft_size].The (optional) noise powerno is per complex dimension. Ifno isa scalar, noise of the same variance will be added to the outputs.Ifno is a tensor, it must have a shape that can be broadcast tothe shape of the channel outputs. This allows, e.g., adding noise ofdifferent variance to each example in a batch. Ifno has a lowerrank than the channel outputs, thenno will be broadcast to theshape of the channel outputs by adding dummy dimensions after the lastaxis.

Output:

• y ([batch size, num_rx, num_rx_ant, num_ofdm_symbols, fft_size],tf.complex) – Channel outputs

• h_freq ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_ofdm_symbols, fft_size],tf.complex) – (Optional) Channel frequency responses. Returned only ifreturn_channel is set toTrue.

classsionna.phy.channel.GenerateOFDMChannel(channel_model,resource_grid,normalize_channel=False,precision=None,**kwargs)[source]

Generates channel frequency responses

The channel impulse response is constant over the duration of an OFDM symbol.

Given a channel impulse response\((a_{m}(t), \tau_{m}), 0 \leq m \leq M-1\), generated by thechannel_model,the channel frequency response for the\(s^{th}\) OFDM symbol and\(n^{th}\) subcarrier is computed as follows:

\[\widehat{h}_{s, n} = \sum_{m=0}^{M-1} a_{m}(s) e^{-j2\pi n \Delta_f \tau_{m}}\]

where\(\Delta_f\) is the subcarrier spacing, and\(s\) is used as timestep to indicate that the channel impulse response can change from one OFDM symbol to thenext in the event of mobility, even if it is assumed static over the durationof an OFDM symbol.

Parameters:

• channel_model (ChannelModel) – Channel model to be used.

• resource_grid (ResourceGrid) – Resource grid

• normalize_channel (bool, (defaultFalse)) – If set toTrue, the channel is normalized over the resource gridto ensure unit average energy per resource element.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

batch_size (None (default) |int) – Batch size. Defaults toNone for channel models that do not require this parameter.

Output:

h_freq ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_ofdm_symbols, num_subcarriers],tf.complex) – Channel frequency responses

classsionna.phy.channel.ApplyOFDMChannel(precision=None,**kwargs)[source]

Apply single-tap channel frequency responses to channel inputs

For each OFDM symbol\(s\) and subcarrier\(n\), the single-tap channelis applied as follows:

\[y_{s,n} = \widehat{h}_{s, n} x_{s,n} + w_{s,n}\]

where\(y_{s,n}\) is the channel output computed by this layer,\(\widehat{h}_{s, n}\) the frequency channel response (h_freq),\(x_{s,n}\) the channel inputx, and\(w_{s,n}\) the additive noise.

For multiple-input multiple-output (MIMO) links, the channel output is computed for each antennaof each receiver and by summing over all the antennas of all transmitters.

Parameters:

precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• x ([batch size, num_tx, num_tx_ant, num_ofdm_symbols, fft_size],tf.complex) – Channel inputs

• h_freq ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_ofdm_symbols, fft_size],tf.complex) – Channel frequency responses

• no (None (default) | tensor,tf.float) – Tensor whose shape can be broadcast to the shape of thechannel outputs:[batch size, num_rx, num_rx_ant, num_ofdm_symbols, fft_size].The (optional) noise powerno is per complex dimension. Ifno is ascalar, noise of the same variance will be added to the outputs.Ifno is a tensor, it must have a shape that can be broadcast tothe shape of the channel outputs. This allows, e.g., adding noise ofdifferent variance to each example in a batch. Ifno has a lowerrank than the channel outputs, thenno will be broadcast to theshape of the channel outputs by adding dummy dimensions after thelast axis.

Output:

y ([batch size, num_rx, num_rx_ant, num_ofdm_symbols, fft_size],tf.complex) – Channel outputs

sionna.phy.channel.cir_to_ofdm_channel(frequencies,a,tau,normalize=False)[source]

Compute the frequency response of the channel atfrequencies

Given a channel impulse response\((a_{m}, \tau_{m}), 0 \leq m \leq M-1\) (inputsa andtau),the channel frequency response for the frequency\(f\)is computed as follows:

\[\widehat{h}(f) = \sum_{m=0}^{M-1} a_{m} e^{-j2\pi f \tau_{m}}\]

Input:

• frequencies ([fft_size],tf.float) – Frequencies at which to compute the channel response

• a ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths, num_time_steps],tf.complex) – Path coefficients

• tau ([batch size, num_rx, num_tx, num_paths] or [batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths],tf.float) – Path delays

• normalize (bool, (defaultFalse)) – If set toTrue, the channel is normalized over the resource grid

Output:

h_f ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_time_steps, fft_size],tf.complex) – Channel frequency responses atfrequencies

Rayleigh block fading

classsionna.phy.channel.RayleighBlockFading(num_rx,num_rx_ant,num_tx,num_tx_ant,precision=None,**kwargs)[source]

Generates channel impulse responses corresponding to a Rayleigh blockfading channel model

The channel impulse responses generated are formed of a single path withzero delay and a normally distributed fading coefficient.All time steps of a batch example share the same channel coefficient(block fading).

This class can be used in conjunction with the classes that simulate thechannel response in time or frequency domain, i.e.,OFDMChannel,TimeChannel,GenerateOFDMChannel,ApplyOFDMChannel,GenerateTimeChannel,ApplyTimeChannel.

Parameters:

• num_rx (int) – Number of receivers (\(N_R\))

• num_rx_ant (int) – Number of antennas per receiver (\(N_{RA}\))

• num_tx (int) – Number of transmitters (\(N_T\))

• num_tx_ant (int) – Number of antennas per transmitter (\(N_{TA}\))

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• batch_size (int) – Batch size

• num_time_steps (int) – Number of time steps

Output:

• a ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths = 1, num_time_steps],tf.complex) – Path coefficients

• tau ([batch size, num_rx, num_tx, num_paths = 1],tf.float) – Path delays [s]

3GPP 38.901 channel models

The submoduletr38901 implements 3GPP channel models from[TR38901].

TheCDL,UMi,UMa, andRMamodels require setting-up antenna models for the transmitters andreceivers. This is achieved using thePanelArray class.

TheUMi,UMa, andRMa models requiresetting-up a network topology, specifying, e.g., the user terminals (UTs) andbase stations (BSs) locations, the UTs velocities, etc.Utility functions are available to help laying outcomplex topologies or to quickly setup simple but widely used topologies.

classsionna.phy.channel.tr38901.PanelArray(num_rows_per_panel,num_cols_per_panel,polarization,polarization_type,antenna_pattern,carrier_frequency,num_rows=1,num_cols=1,panel_vertical_spacing=None,panel_horizontal_spacing=None,element_vertical_spacing=None,element_horizontal_spacing=None,precision=None)[source]

Antenna panel array following the[TR38901] specification

This class is used to create models of the panel arrays used by thetransmitters and receivers and that need to be specified when using theCDL,UMi,UMa, andRMamodels.

Example

>>>array=PanelArray(num_rows_per_panel=4,...num_cols_per_panel=4,...polarization='dual',...polarization_type='VH',...antenna_pattern='38.901',...carrier_frequency=3.5e9,...num_cols=2,...panel_horizontal_spacing=3.)>>>array.show()

Parameters:

• num_rows_per_panel (int) – Number of rows of elements per panel

• num_cols_per_panel (int) – Number of columns of elements per panel

• polarization ("single" |"dual") – Polarization

• polarization_type ("V" |"H" |"VH" |"cross") – Type of polarization. For single polarization, must be “V” or “H”.For dual polarization, must be “VH” or “cross”.

• antenna_pattern ("omni" |"38.901") – Element radiation pattern

• carrier_frequency (float) – Carrier frequency [Hz]

• num_rows (int,(default 1)) – Number of rows of panels

• num_cols (int,(default 1)) – Number of columns of panels

• panel_vertical_spacing (None (default) |float) – Vertical spacing of panels [multiples of wavelength].Must be greater than the panel width.If set toNone, it is set to the panel width + 0.5.

• panel_horizontal_spacing (None (default) |float) – Horizontal spacing of panels [in multiples of wavelength].Must be greater than the panel height.If set toNone, it is set to the panel height + 0.5.

• element_vertical_spacing (None (default) |float) – Element vertical spacing [multiple of wavelength].Defaults to 0.5 if set toNone.

• element_horizontal_spacing (None (default) |float) – Element horizontal spacing [multiple of wavelength].Defaults to 0.5 if set toNone.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

propertyant_ind_pol1

Indices of antenna elements with the first polarization direction

propertyant_ind_pol2

Indices of antenna elements with the second polarization direction.Only defined with dual polarization.

propertyant_pol1

Field of an antenna element with the first polarization direction

propertyant_pol2

Field of an antenna element with the second polarization direction.Only defined with dual polarization.

propertyant_pos

Positions of the antennas

propertyant_pos_pol1

Positions of the antenna elements with the first polarizationdirection

propertyant_pos_pol2

Positions of antenna elements with the second polarization direction.Only defined with dual polarization.

propertyelement_horizontal_spacing

Horizontal spacing between the antenna elements within a panel[multiple of wavelength]

propertyelement_vertical_spacing

Vertical spacing between the antenna elements within a panel[multiple of wavelength]

propertynum_ant

Total number of antenna elements

propertynum_cols

Number of columns of panels

propertynum_cols_per_panel

Number of columns of elements per panel

propertynum_panels

Number of panels

propertynum_panels_ant

Number of antenna elements per panel

propertynum_rows

Number of rows of panels

propertynum_rows_per_panel

Number of rows of elements per panel

propertypanel_horizontal_spacing

Horizontal spacing between the panels [multiple of wavelength]

propertypanel_vertical_spacing

Vertical spacing between the panels [multiple of wavelength]

propertypolarization

Polarization (“single” or “dual”)

propertypolarization_type

Polarization type. “V” or “H” for single polarization.“VH” or “cross” for dual polarization.

show()[source]

Show the panel array geometry

show_element_radiation_pattern()[source]

Show the radiation field of antenna elements forming the panel

classsionna.phy.channel.tr38901.Antenna(polarization,polarization_type,antenna_pattern,carrier_frequency,precision=None)[source]

Single antenna following the[TR38901] specification

This class is a special case ofPanelArray,and can be used in lieu of it.

Parameters:

• polarization ("single" |"dual") – Polarization

• polarization_type ("V" |"H" |"VH" |"cross") – Type of polarization. For single polarization, must be “V” or “H”.For dual polarization, must be “VH” or “cross”.

• antenna_pattern ("omni" |"38.901") – Element radiation pattern

• carrier_frequency (float) – Carrier frequency [Hz]

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

classsionna.phy.channel.tr38901.AntennaArray(num_rows,num_cols,polarization,polarization_type,antenna_pattern,carrier_frequency,vertical_spacing=None,horizontal_spacing=None,precision=None)[source]

Antenna array following the[TR38901] specification

This class is a special case ofPanelArray,and can used in lieu of it.

Parameters:

• num_rows (int) – Number of rows of elements

• num_cols (int) – Number of columns of elements

• polarization ("single" |"dual") – Polarization

• polarization_type ("V" |"H" |"VH" |"cross") – Type of polarization. For single polarization, must be “V” or “H”.For dual polarization, must be “VH” or “cross”.

• antenna_pattern ("omni" |"38.901") – Element radiation pattern

• carrier_frequency (float) – Carrier frequency [Hz]

• vertical_spacing (None (default) |float) – Element vertical spacing [multiple of wavelength].Defaults to 0.5 if set toNone.

• horizontal_spacing (None (default) |float) – Element horizontal spacing [multiple of wavelength].Defaults to 0.5 if set toNone.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

classsionna.phy.channel.tr38901.TDL(model,delay_spread,carrier_frequency,num_sinusoids=20,los_angle_of_arrival=0.7853981633974483,min_speed=0.0,max_speed=None,num_rx_ant=1,num_tx_ant=1,spatial_corr_mat=None,rx_corr_mat=None,tx_corr_mat=None,precision=None)[source]

Tapped delay line (TDL) channel model from the 3GPP[TR38901] specification

The power delay profiles (PDPs) are normalized to have a total energy of one.

Channel coefficients are generated using a sum-of-sinusoids model[SoS].Channel aging is simulated in the event of mobility.

If a minimum speed and a maximum speed are specified such that themaximum speed is greater than the minimum speed, then speeds are randomlyand uniformly sampled from the specified interval for each link and eachbatch example.

The TDL model only works for systems with a single transmitter and a singlereceiver. The transmitter and receiver can be equipped with multipleantennas. Spatial correlation is simulated through filtering by specifiedcorrelation matrices.

Thespatial_corr_mat parameter can be used to specify an arbitraryspatial correlation matrix. In particular, it can be used to modelcorrelated cross-polarized transmit and receive antennas as follows(see, e.g., Annex G.2.3.2.1[TS38141-1]):

\[\mathbf{R} = \mathbf{R}_{\text{rx}} \otimes \mathbf{\Gamma} \otimes \mathbf{R}_{\text{tx}}\]

where\(\mathbf{R}\) is the spatial correlation matrixspatial_corr_mat,\(\mathbf{R}_{\text{rx}}\) the spatial correlation matrix at the receiverwith same polarization,\(\mathbf{R}_{\text{tx}}\) the spatial correlationmatrix at the transmitter with same polarization, and\(\mathbf{\Gamma}\)the polarization correlation matrix.\(\mathbf{\Gamma}\) is 1x1 for single-polarizedantennas, 2x2 when only the transmit or receive antennas are cross-polarized, and 4x4 whentransmit and receive antennas are cross-polarized.

It is also possible not to specifyspatial_corr_mat, but instead the correlation matricesat the receiver and transmitter, using therx_corr_mat andtx_corr_matparameters, respectively.This can be useful when single polarized antennas are simulated, and it is alsomore computationally efficient.This is equivalent to settingspatial_corr_mat to :

\[\mathbf{R} = \mathbf{R}_{\text{rx}} \otimes \mathbf{R}_{\text{tx}}\]

where\(\mathbf{R}_{\text{rx}}\) is the correlation matrix at the receiverrx_corr_mat and\(\mathbf{R}_{\text{tx}}\) the correlation matrix atthe transmittertx_corr_mat.

Example

The following code snippet shows how to setup a TDL channel model assumingan OFDM waveform:

>>>tdl=TDL(model="A",...delay_spread=300e-9,...carrier_frequency=3.5e9,...min_speed=0.0,...max_speed=3.0)>>>>>>channel=OFDMChannel(channel_model=tdl,...resource_grid=rg)

whererg is an instance ofResourceGrid.

Notes

The following tables from[TR38901] provide typical values for the delayspread.

Model	Delay spread [ns]
Very short delay spread	\(10\)
Short short delay spread	\(10\)
Nominal delay spread	\(100\)
Long delay spread	\(300\)
Very long delay spread	\(1000\)

Delay spread [ns]		Frequency [GHz]
		2	6	15	28	39	60	70
Indoor office	Short delay profile	20	16	16	16	16	16	16
	Normal delay profile	39	30	24	20	18	16	16
	Long delay profile	59	53	47	43	41	38	37
UMi Street-canyon	Short delay profile	65	45	37	32	30	27	26
	Normal delay profile	129	93	76	66	61	55	53
	Long delay profile	634	316	307	301	297	293	291
UMa	Short delay profile	93	93	85	80	78	75	74
	Normal delay profile	363	363	302	266	249	228	221
	Long delay profile	1148	1148	955	841	786	720	698
RMa / RMa O2I	Short delay profile	32	32	N/A	N/A	N/A	N/A	N/A
	Normal delay profile	37	37	N/A	N/A	N/A	N/A	N/A
	Long delay profile	153	153	N/A	N/A	N/A	N/A	N/A
UMi / UMa O2I	Normal delay profile	242
	Long delay profile	616

Parameters:

• model ("A" |"B" |"C" |"D" |"E" |"A30" |"B100" |"C300") – TDL model to use

• delay_spread (float) – RMS delay spread [s].For the “A30”, “B100”, and “C300” models, the delay spread must be setto 30ns, 100ns, and 300ns, respectively.

• carrier_frequency (float) – Carrier frequency [Hz]

• num_sinusoids (int, (default 20)) – Number of sinusoids for the sum-of-sinusoids model. Defaults to 20.

• los_angle_of_arrival (float, (default pi/4)) – Angle-of-arrival for LoS path [radian]. Only used with LoS models

• min_speed (float, (default 0.0)) – Minimum speed [m/s]

• max_speed (None (default) | float) – Maximum speed [m/s]. If set toNone,thenmax_speed takes the same value asmin_speed.

• num_rx_ant (int, (default 1)) – Number of receive antennas

• num_tx_ant (int, (default 1)) – Number of transmit antennas

• spatial_corr_mat (None (default) | [num_rx_ant*num_tx_ant,num_rx_ant*num_tx_ant],tf.complex) – Spatial correlation matrix.If not set toNone, thenrx_corr_mat andtx_corr_mat are ignored andthis matrix is used for spatial correlation.If set toNone andrx_corr_mat andtx_corr_mat are also set toNone,then no correlation is applied.

• rx_corr_mat (None (default) | [num_rx_ant,num_rx_ant],tf.complex) – Spatial correlation matrix for the receiver.If set toNone andspatial_corr_mat is also set toNone, then no receivecorrelation is applied.

• tx_corr_mat (None (default) | [num_tx_ant,num_tx_ant],tf.complex) – Spatial correlation matrix for the transmitter.If set toNone andspatial_corr_mat is also set toNone, then no transmitcorrelation is applied.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• batch_size (int) – Batch size

• num_time_steps (int) – Number of time steps

• sampling_frequency (float) – Sampling frequency [Hz]

Output:

• a ([batch size, num_rx = 1, num_rx_ant = 1, num_tx = 1, num_tx_ant = 1, num_paths, num_time_steps],tf.complex) – Path coefficients

• tau ([batch size, num_rx = 1, num_tx = 1, num_paths],tf.float) – Path delays [s]

propertydelay_spread

RMS delay spread [s]

propertydelays

Path delays [s]

propertyk_factor

K-factor in linear scale. Only available with LoS models.

propertylos

True if this is a LoS model.False otherwise.

propertymean_power_los

LoS component power in linear scale.Only available with LoS models.

propertymean_powers

Path powers in linear scale

propertynum_clusters

Number of paths (\(M\))

classsionna.phy.channel.tr38901.CDL(model,delay_spread,carrier_frequency,ut_array,bs_array,direction,ut_orientation=None,bs_orientation=None,min_speed=0.0,max_speed=None,precision=None)[source]

Clustered delay line (CDL) channel model from the 3GPP[TR38901] specification

The power delay profiles (PDPs) are normalized to have a total energy of one.

If a minimum speed and a maximum speed are specified such that themaximum speed is greater than the minimum speed, then UTs speeds arerandomly and uniformly sampled from the specified interval for each linkand each batch example.

The CDL model only works for systems with a single transmitter and a singlereceiver. The transmitter and receiver can be equipped with multipleantennas.

Example

The following code snippet shows how to setup a CDL channel model assumingan OFDM waveform:

>>># Panel array configuration for the transmitter and receiver>>>bs_array=PanelArray(num_rows_per_panel=4,...num_cols_per_panel=4,...polarization='dual',...polarization_type='cross',...antenna_pattern='38.901',...carrier_frequency=3.5e9)>>>ut_array=PanelArray(num_rows_per_panel=1,...num_cols_per_panel=1,...polarization='single',...polarization_type='V',...antenna_pattern='omni',...carrier_frequency=3.5e9)>>># CDL channel model>>>cdl=CDL(model="A",>>>delay_spread=300e-9,...carrier_frequency=3.5e9,...ut_array=ut_array,...bs_array=bs_array,...direction='uplink')>>>channel=OFDMChannel(channel_model=cdl,...resource_grid=rg)

whererg is an instance ofResourceGrid.

Notes

The following tables from[TR38901] provide typical values for the delayspread.

Model	Delay spread [ns]
Very short delay spread	\(10\)
Short short delay spread	\(10\)
Nominal delay spread	\(100\)
Long delay spread	\(300\)
Very long delay spread	\(1000\)

Delay spread [ns]		Frequency [GHz]
		2	6	15	28	39	60	70
Indoor office	Short delay profile	20	16	16	16	16	16	16
	Normal delay profile	39	30	24	20	18	16	16
	Long delay profile	59	53	47	43	41	38	37
UMi Street-canyon	Short delay profile	65	45	37	32	30	27	26
	Normal delay profile	129	93	76	66	61	55	53
	Long delay profile	634	316	307	301	297	293	291
UMa	Short delay profile	93	93	85	80	78	75	74
	Normal delay profile	363	363	302	266	249	228	221
	Long delay profile	1148	1148	955	841	786	720	698
RMa / RMa O2I	Short delay profile	32	32	N/A	N/A	N/A	N/A	N/A
	Normal delay profile	37	37	N/A	N/A	N/A	N/A	N/A
	Long delay profile	153	153	N/A	N/A	N/A	N/A	N/A
UMi / UMa O2I	Normal delay profile	242
	Long delay profile	616

Parameters:

• model ("A" |"B" |"C" |"D" |"E") – CDL model to use

• delay_spread (float) – RMS delay spread [s]

• carrier_frequency (float) – Carrier frequency [Hz]

• ut_array (PanelArray) – Panel array used by the UTs. All UTs share the same antenna arrayconfiguration.

• bs_array (PanelArray) – Panel array used by the Bs. All BSs share the same antenna arrayconfiguration.

• direction ("uplink" |"downlink") – Link direction

• ut_orientation (None (default) | [3],tf.float) – Orientation of the UT. If set toNone, [\(\pi\), 0, 0] is used.

• bs_orientation (None (default) | [3],tf.float) – Orientation of the BS. If set toNone, [0, 0, 0] is used.

• min_speed (float,(default 0.0)) – Minimum speed [m/s]

• max_speed (None (default) |float) – Maximum speed [m/s]. If set toNone,thenmax_speed takes the same value asmin_speed.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• batch_size (int) – Batch size

• num_time_steps (int) – Number of time steps

• sampling_frequency (float) – Sampling frequency [Hz]

Output:

• a ([batch size, num_rx = 1, num_rx_ant, num_tx = 1, num_tx_ant, num_paths, num_time_steps], tf.complex) – Path coefficients

• tau ([batch size, num_rx = 1, num_tx = 1, num_paths], tf.float) – Path delays [s]

propertydelay_spread

RMS delay spread [s]

propertydelays

Path delays [s]

propertyk_factor

K-factor in linear scale. Only available with LoS models.

propertylos

True is this is a LoS model.False otherwise.

propertynum_clusters

Number of paths (\(M\))

propertypowers

Path powers in linear scale

classsionna.phy.channel.tr38901.UMi(carrier_frequency,o2i_model,ut_array,bs_array,direction,enable_pathloss=True,enable_shadow_fading=True,always_generate_lsp=False,precision=None)[source]

Urban microcell (UMi) channel model from 3GPP[TR38901] specification

Setting up a UMi model requires configuring the network topology, i.e., theUTs and BSs locations, UTs velocities, etc. This is achieved using theset_topology() method. Setting a differenttopology for each batch example is possible. The batch size used when setting up the network topologyis used for the link simulations.

The following code snippet shows how to setup a UMi channel model operatingin the frequency domain:

>>># UT and BS panel arrays>>>bs_array=PanelArray(num_rows_per_panel=4,...num_cols_per_panel=4,...polarization='dual',...polarization_type='cross',...antenna_pattern='38.901',...carrier_frequency=3.5e9)>>>ut_array=PanelArray(num_rows_per_panel=1,...num_cols_per_panel=1,...polarization='single',...polarization_type='V',...antenna_pattern='omni',...carrier_frequency=3.5e9)>>># Instantiating UMi channel model>>>channel_model=UMi(carrier_frequency=3.5e9,...o2i_model='low',...ut_array=ut_array,...bs_array=bs_array,...direction='uplink')>>># Setting up network topology>>># ut_loc: UTs locations>>># bs_loc: BSs locations>>># ut_orientations: UTs array orientations>>># bs_orientations: BSs array orientations>>># in_state: Indoor/outdoor states of UTs>>>channel_model.set_topology(ut_loc,...bs_loc,...ut_orientations,...bs_orientations,...ut_velocities,...in_state)>>># Instanting the frequency domain channel>>>channel=OFDMChannel(channel_model=channel_model,...resource_grid=rg)

whererg is an instance ofResourceGrid.

Parameters:

• carrier_frequency (float) – Carrier frequency in Hertz

• o2i_model ("low" |"high") – Outdoor-to-indoor loss model for UTs located indoor.Set this parameter to “low” to use the low-loss model, or to “high”to use the high-loss model.See section 7.4.3 of[TR38901] for details.

• rx_array (PanelArray) – Panel array used by the receivers. All receivers share the sameantenna array configuration.

• tx_array (PanelArray) – Panel array used by the transmitters. All transmitters share thesame antenna array configuration.

• direction ("uplink" |"downlink") – Link direction

• enable_pathloss (bool, (defaultTrue)) – IfTrue, apply pathloss. Otherwise don’t.

• enable_shadow_fading (bool, (defaultTrue)) – IfTrue, apply shadow fading. Otherwise don’t.

• always_generate_lsp (bool, (defaultFalse)) – IfTrue, new large scale parameters (LSPs) are generated for everynew generation of channel impulse responses. Otherwise, always reusethe same LSPs, except if the topology is changed.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• num_time_steps (int) – Number of time steps

• sampling_frequency (float) – Sampling frequency [Hz]

Output:

• a ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths, num_time_steps],tf.complex) – Path coefficients

• tau ([batch size, num_rx, num_tx, num_paths],tf.float) – Path delays [s]

propertycdtype

Type for complex floating point numbers

Type:

tf.complex

propertyprecision

Precision used for all compuations

Type:

str, “single” | “double”

propertyrdtype

Type for real floating point numbers

Type:

tf.float

propertyreturn_rays

Indicates whether the call method returns the generated rays

Type:

bool

set_topology(ut_loc=None,bs_loc=None,ut_orientations=None,bs_orientations=None,ut_velocities=None,in_state=None,los=None,bs_virtual_loc=None)

Set the network topology

It is possible to set up a different network topology for each batchexample. The batch size used when setting up the network topologyis used for the link simulations.

When calling this function, not specifying a parameter leads to thereuse of the previously given value. Not specifying a value that was notset at a former call rises an error.

Input:

• ut_loc (None (default) | [batch size,num_ut, 3],tf.float) – Locations of the UTs

• bs_loc (None (default) | [batch size,num_bs, 3],tf.float) – Locations of BSs

• ut_orientations (None (default) | [batch size,num_ut, 3],tf.float) – Orientations of the UTs arrays [radian]

• bs_orientations (None (default) | [batch size,num_bs, 3],tf.float) – Orientations of the BSs arrays [radian]

• ut_velocities (None (default) | [batch size,num_ut, 3],tf.float) – Velocity vectors of UTs

• in_state (None (default) | [batch size,num_ut],tf.bool) – Indoor/outdoor state of UTs.True means indoor andFalsemeans outdoor.

• los (None (default) |tf.bool) – If notNone, all UTs located outdoor areforced to be in LoS iflos is set toTrue, or in NLoSif it is set toFalse. If set toNone, the LoS/NLoS statesof UTs is set following 3GPP specification[TR38901].

• bs_virtual_loc (None (default) | [batch size, number of BSs, number of UTs, 3],tf.float) – Virtual locations of BSs for each UT [m].Used to compute BS-UT relative distance and angles.IfNone whilebs_loc is specified, then it is set tobs_loc upon reshaping.

show_topology(bs_index=0,batch_index=0)

Shows the network topology of the batch example with indexbatch_index.

Thebs_index parameter specifies with respect to which BS theLoS/NLoS state of UTs is indicated.

Input:

• bs_index (int, (default 0)) – BS index with respect to which the LoS/NLoS state of UTs isindicated

• batch_index (int, (default 0)) – Batch example for which the topology is shown

classsionna.phy.channel.tr38901.UMa(carrier_frequency,o2i_model,ut_array,bs_array,direction,enable_pathloss=True,enable_shadow_fading=True,always_generate_lsp=False,precision=None)[source]

Urban macrocell (UMa) channel model from 3GPP[TR38901] specification.

Setting up a UMa model requires configuring the network topology, i.e., theUTs and BSs locations, UTs velocities, etc. This is achieved using theset_topology() method. Setting a differenttopology for each batch example is possible. The batch size used when setting up the network topologyis used for the link simulations.

The following code snippet shows how to setup an UMa channel model assumingan OFDM waveform:

>>># UT and BS panel arrays>>>bs_array=PanelArray(num_rows_per_panel=4,...num_cols_per_panel=4,...polarization='dual',...polarization_type='cross',...antenna_pattern='38.901',...carrier_frequency=3.5e9)>>>ut_array=PanelArray(num_rows_per_panel=1,...num_cols_per_panel=1,...polarization='single',...polarization_type='V',...antenna_pattern='omni',...carrier_frequency=3.5e9)>>># Instantiating UMa channel model>>>channel_model=UMa(carrier_frequency=3.5e9,...o2i_model='low',...ut_array=ut_array,...bs_array=bs_array,...direction='uplink')>>># Setting up network topology>>># ut_loc: UTs locations>>># bs_loc: BSs locations>>># ut_orientations: UTs array orientations>>># bs_orientations: BSs array orientations>>># in_state: Indoor/outdoor states of UTs>>>channel_model.set_topology(ut_loc,...bs_loc,...ut_orientations,...bs_orientations,...ut_velocities,...in_state)>>># Instanting the OFDM channel>>>channel=OFDMChannel(channel_model=channel_model,...resource_grid=rg)

whererg is an instance ofResourceGrid.

Parameters:

• carrier_frequency (float) – Carrier frequency in Hertz

• o2i_model ("low" |"high") – Outdoor-to-indoor loss model for UTs located indoor.Set this parameter to “low” to use the low-loss model, or to “high”to use the high-loss model.See section 7.4.3 of[TR38901] for details.

• rx_array (PanelArray) – Panel array used by the receivers. All receivers share the sameantenna array configuration.

• tx_array (PanelArray) – Panel array used by the transmitters. All transmitters share thesame antenna array configuration.

• direction ("uplink" |"downlink") – Link direction

• enable_pathloss (bool, (defaultTrue)) – IfTrue, apply pathloss. Otherwise don’t.

• enable_shadow_fading (bool, (defaultTrue)) – IfTrue, apply shadow fading. Otherwise don’t.

• always_generate_lsp (bool, (defaultFalse)) – IfTrue, new large scale parameters (LSPs) are generated for everynew generation of channel impulse responses. Otherwise, always reusethe same LSPs, except if the topology is changed.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• num_time_steps (int) – Number of time steps

• sampling_frequency (float) – Sampling frequency [Hz]

Output:

• a ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths, num_time_steps],tf.complex) – Path coefficients

• tau ([batch size, num_rx, num_tx, num_paths],tf.float) – Path delays [s]

propertycdtype

Type for complex floating point numbers

Type:

tf.complex

propertyprecision

Precision used for all compuations

Type:

str, “single” | “double”

propertyrdtype

Type for real floating point numbers

Type:

tf.float

propertyreturn_rays

Indicates whether the call method returns the generated rays

Type:

bool

set_topology(ut_loc=None,bs_loc=None,ut_orientations=None,bs_orientations=None,ut_velocities=None,in_state=None,los=None,bs_virtual_loc=None)

Set the network topology

It is possible to set up a different network topology for each batchexample. The batch size used when setting up the network topologyis used for the link simulations.

When calling this function, not specifying a parameter leads to thereuse of the previously given value. Not specifying a value that was notset at a former call rises an error.

Input:

• ut_loc (None (default) | [batch size,num_ut, 3],tf.float) – Locations of the UTs

• bs_loc (None (default) | [batch size,num_bs, 3],tf.float) – Locations of BSs

• ut_orientations (None (default) | [batch size,num_ut, 3],tf.float) – Orientations of the UTs arrays [radian]

• bs_orientations (None (default) | [batch size,num_bs, 3],tf.float) – Orientations of the BSs arrays [radian]

• ut_velocities (None (default) | [batch size,num_ut, 3],tf.float) – Velocity vectors of UTs

• in_state (None (default) | [batch size,num_ut],tf.bool) – Indoor/outdoor state of UTs.True means indoor andFalsemeans outdoor.

• los (None (default) |tf.bool) – If notNone, all UTs located outdoor areforced to be in LoS iflos is set toTrue, or in NLoSif it is set toFalse. If set toNone, the LoS/NLoS statesof UTs is set following 3GPP specification[TR38901].

• bs_virtual_loc (None (default) | [batch size, number of BSs, number of UTs, 3],tf.float) – Virtual locations of BSs for each UT [m].Used to compute BS-UT relative distance and angles.IfNone whilebs_loc is specified, then it is set tobs_loc upon reshaping.

show_topology(bs_index=0,batch_index=0)

Shows the network topology of the batch example with indexbatch_index.

Thebs_index parameter specifies with respect to which BS theLoS/NLoS state of UTs is indicated.

Input:

• bs_index (int, (default 0)) – BS index with respect to which the LoS/NLoS state of UTs isindicated

• batch_index (int, (default 0)) – Batch example for which the topology is shown

classsionna.phy.channel.tr38901.RMa(carrier_frequency,ut_array,bs_array,direction,enable_pathloss=True,enable_shadow_fading=True,average_street_width=20.0,average_building_height=5.0,always_generate_lsp=False,precision=None)[source]

Rural macrocell (RMa) channel model from 3GPP[TR38901] specification

Setting up a RMa model requires configuring the network topology, i.e., theUTs and BSs locations, UTs velocities, etc. This is achieved using theset_topology() method. Setting a differenttopology for each batch example is possible. The batch size used when setting up the network topologyis used for the link simulations.

The following code snippet shows how to setup an RMa channel model assumingan OFDM waveform:

>>># UT and BS panel arrays>>>bs_array=PanelArray(num_rows_per_panel=4,...num_cols_per_panel=4,...polarization='dual',...polarization_type='cross',...antenna_pattern='38.901',...carrier_frequency=3.5e9)>>>ut_array=PanelArray(num_rows_per_panel=1,...num_cols_per_panel=1,...polarization='single',...polarization_type='V',...antenna_pattern='omni',...carrier_frequency=3.5e9)>>># Instantiating RMa channel model>>>channel_model=RMa(carrier_frequency=3.5e9,...ut_array=ut_array,...bs_array=bs_array,...direction='uplink')>>># Setting up network topology>>># ut_loc: UTs locations>>># bs_loc: BSs locations>>># ut_orientations: UTs array orientations>>># bs_orientations: BSs array orientations>>># in_state: Indoor/outdoor states of UTs>>>channel_model.set_topology(ut_loc,...bs_loc,...ut_orientations,...bs_orientations,...ut_velocities,...in_state)>>># Instanting the OFDM channel>>>channel=OFDMChannel(channel_model=channel_model,...resource_grid=rg)

whererg is an instance ofResourceGrid.

Parameters:

• carrier_frequency (float) – Carrier frequency [Hz]

• rx_array (PanelArray) – Panel array used by the receivers. All receivers share the sameantenna array configuration.

• tx_array (PanelArray) – Panel array used by the transmitters. All transmitters share thesame antenna array configuration.

• direction ("uplink" |"downlink") – Link direction

• enable_pathloss (bool, (defaultTrue)) – IfTrue, apply pathloss. Otherwise don’t.

• enable_shadow_fading (bool, (defaultTrue)) – IfTrue, apply shadow fading. Otherwise don’t.

• average_street_width (float, (default 20.0)) – Average street width [m]

• average_building_height (float, (default 5.0)) – Average building height [m]

• always_generate_lsp (bool, (defaultFalse)) – IfTrue, new large scale parameters (LSPs) are generated for everynew generation of channel impulse responses. Otherwise, always reusethe same LSPs, except if the topology is changed.

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Input:

• num_time_steps (int) – Number of time steps

• sampling_frequency (float) – Sampling frequency [Hz]

Output:

• a ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths, num_time_steps],tf.complex) – Path coefficients

• tau ([batch size, num_rx, num_tx, num_paths],tf.float) – Path delays [s]

propertycdtype

Type for complex floating point numbers

Type:

tf.complex

propertyprecision

Precision used for all compuations

Type:

str, “single” | “double”

propertyrdtype

Type for real floating point numbers

Type:

tf.float

propertyreturn_rays

Indicates whether the call method returns the generated rays

Type:

bool

set_topology(ut_loc=None,bs_loc=None,ut_orientations=None,bs_orientations=None,ut_velocities=None,in_state=None,los=None,bs_virtual_loc=None)

Set the network topology

It is possible to set up a different network topology for each batchexample. The batch size used when setting up the network topologyis used for the link simulations.

When calling this function, not specifying a parameter leads to thereuse of the previously given value. Not specifying a value that was notset at a former call rises an error.

Input:

• ut_loc (None (default) | [batch size,num_ut, 3],tf.float) – Locations of the UTs

• bs_loc (None (default) | [batch size,num_bs, 3],tf.float) – Locations of BSs

• ut_orientations (None (default) | [batch size,num_ut, 3],tf.float) – Orientations of the UTs arrays [radian]

• bs_orientations (None (default) | [batch size,num_bs, 3],tf.float) – Orientations of the BSs arrays [radian]

• ut_velocities (None (default) | [batch size,num_ut, 3],tf.float) – Velocity vectors of UTs

• in_state (None (default) | [batch size,num_ut],tf.bool) – Indoor/outdoor state of UTs.True means indoor andFalsemeans outdoor.

• los (None (default) |tf.bool) – If notNone, all UTs located outdoor areforced to be in LoS iflos is set toTrue, or in NLoSif it is set toFalse. If set toNone, the LoS/NLoS statesof UTs is set following 3GPP specification[TR38901].

• bs_virtual_loc (None (default) | [batch size, number of BSs, number of UTs, 3],tf.float) – Virtual locations of BSs for each UT [m].Used to compute BS-UT relative distance and angles.IfNone whilebs_loc is specified, then it is set tobs_loc upon reshaping.

show_topology(bs_index=0,batch_index=0)

Shows the network topology of the batch example with indexbatch_index.

Thebs_index parameter specifies with respect to which BS theLoS/NLoS state of UTs is indicated.

Input:

• bs_index (int, (default 0)) – BS index with respect to which the LoS/NLoS state of UTs isindicated

• batch_index (int, (default 0)) – Batch example for which the topology is shown

External datasets

classsionna.phy.channel.CIRDataset(cir_generator,batch_size,num_rx,num_rx_ant,num_tx,num_tx_ant,num_paths,num_time_steps,precision=None,**kwargs)[source]

Creates a channel model from a dataset that can be used with classes such asTimeChannel andOFDMChannel.The dataset is defined by agenerator.

The batch size is configured when instantiating the dataset or through thebatch_size property.The number of time steps (num_time_steps) and sampling frequency (sampling_frequency) can only be set when instantiating the dataset.The specified values must be in accordance with the data.

Example

The following code snippet shows how to use this class as a channel model.

>>>my_generator=MyGenerator(...)>>>channel_model=sionna.phy.channel.CIRDataset(my_generator,...batch_size,...num_rx,...num_rx_ant,...num_tx,...num_tx_ant,...num_paths,...num_time_steps+l_tot-1)>>>channel=sionna.phy.channel.TimeChannel(channel_model,bandwidth,num_time_steps)

whereMyGenerator is a generator

>>>classMyGenerator:......def__call__(self):.........yielda,tau

that returns complex-valued path coefficientsa with shape[num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths, num_time_steps]and real-valued path delaystau (in second)[num_rx, num_tx, num_paths].

Parameters:

• cir_generator – Generator that returns channel impulse responses(a,tau) wherea is the tensor of channel coefficients of shape[num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths, num_time_steps]and dtypetf.complex, andtau the tensor of path delaysof shape[num_rx, num_tx, num_paths] and dtypedtype.real_dtype.

• batch_size (int) – Batch size

• num_rx (int) – Number of receivers (\(N_R\))

• num_rx_ant (int) – Number of antennas per receiver (\(N_{RA}\))

• num_tx (int) – Number of transmitters (\(N_T\))

• num_tx_ant (int) – Number of antennas per transmitter (\(N_{TA}\))

• num_paths (int) – Number of paths (\(M\))

• num_time_steps (int) – Number of time steps

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Output:

• a ([batch size, num_rx, num_rx_ant, num_tx, num_tx_ant, num_paths, num_time_steps],tf.complex) – Path coefficients

• tau ([batch size, num_rx, num_tx, num_paths],tf.float) – Path delays [s]

propertybatch_size

Get/set batch size

Type:

int

propertycdtype

Type for complex floating point numbers

Type:

tf.complex

propertyprecision

Precision used for all compuations

Type:

str, “single” | “double”

propertyrdtype

Type for real floating point numbers

Type:

tf.float

Utility functions

sionna.phy.channel.subcarrier_frequencies(num_subcarriers,subcarrier_spacing,precision=None)[source]

Compute the baseband frequencies ofnum_subcarrier subcarriers spaced bysubcarrier_spacing, i.e.,

>>># If num_subcarrier is even:>>>frequencies=[-num_subcarrier/2,...,0,...,num_subcarrier/2-1]*subcarrier_spacing>>>>>># If num_subcarrier is odd:>>>frequencies=[-(num_subcarrier-1)/2,...,0,...,(num_subcarrier-1)/2]*subcarrier_spacing

Input:

• num_subcarriers (int) – Number of subcarriers

• subcarrier_spacing (float) – Subcarrier spacing [Hz]

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Output:

frequencies ([num_subcarrier],tf.float) – Baseband frequencies of subcarriers

sionna.phy.channel.time_lag_discrete_time_channel(bandwidth,maximum_delay_spread=3e-06)[source]

Compute the smallest and largest time-lag for the descrete complex basebandchannel, i.e.,\(L_{\text{min}}\) and\(L_{\text{max}}\).

The smallest time-lag (\(L_{\text{min}}\)) returned is always -6, as this valuewas found small enough for all models included in Sionna.

The largest time-lag (\(L_{\text{max}}\)) is computed from thebandwidthandmaximum_delay_spread as follows:

\[L_{\text{max}} = \lceil W \tau_{\text{max}} \rceil + 6\]

where\(L_{\text{max}}\) is the largest time-lag,\(W\) thebandwidth,and\(\tau_{\text{max}}\) themaximum_delay_spread.

The default value for themaximum_delay_spread is 3us, which was foundto be large enough to include most significant paths with all channel modelsincluded in Sionna assuming a nominal delay spread of 100ns.

Note

The values of\(L_{\text{min}}\) and\(L_{\text{max}}\) computedby this function are only recommended values.\(L_{\text{min}}\) and\(L_{\text{max}}\) should be set according tothe considered channel model. For OFDM systems, one also needs to be carefulthat the effective length of the complex baseband channel is not larger thanthe cyclic prefix length.

Input:

• bandwidth (float) – Bandwith (\(W\)) [Hz]

• maximum_delay_spread (float, (default 3e-6)) – Maximum delay spread [s]

Output:

• l_min (int) – Smallest time-lag (\(L_{\text{min}}\)) for the descrete complex basebandchannel. Set to -6, , as this value was found small enough for all modelsincluded in Sionna.

• l_max (int) – Largest time-lag (\(L_{\text{max}}\)) for the descrete complex basebandchannel

sionna.phy.channel.deg_2_rad(x)[source]

Convert degree to radian

Input:

x (Tensor,tf.float) – Angles in degree

Output:

y (Tensor,tf.float) – Anglesx converted to radian

sionna.phy.channel.rad_2_deg(x)[source]

Convert radian to degree

Input:

x (Tensor,tf.float) – Angles in radian

Output:

y (Tensor,tf.float) – Anglesx converted to degree

sionna.phy.channel.wrap_angle_0_360(angle)[source]

Wrapangle to (0,360)

Input:

angle (Tensor,tf.float) – Input to wrap

Output:

y (Tensor,tf.float) –angle wrapped to (0,360)

sionna.phy.channel.drop_uts_in_sector(batch_size,num_ut,min_bs_ut_dist,isd,bs_height=0.0,ut_height=0.0,precision=None)[source]

Sample UT locations uniformly at random within a sector

The sector from which UTs are sampled is shown in the following figure.The BS is assumed to be located at the origin (0,0) of the coordinatesystem.

Input:

• batch_size (int) – Batch size

• num_ut (int) – Number of UTs to sample per batch example

• min_bs_ut_dist (tf.float) – Minimum BS-UT distance [m]

• isd (tf.float) – Inter-site distance, i.e., the distance between two adjacent BSs [m]

• bs_height (tf.float, (default 0)) – BS height, i.e., distance between the BS and the X-Y plane [m]

• ut_height (tf.float) – UT height, i.e., distance between the UT and the X-Y plane [m]

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Output:

ut_loc ([batch_size, num_ut, 2],tf.float) – UT locations in the X-Y plane

sionna.phy.channel.relocate_uts(ut_loc,sector_id,cell_loc)[source]

Relocate the UTs by rotating them into the sector with indexsector_idand transposing them to the cell centered oncell_loc

sector_id gives the index of the sector to which the UTs arerotated to. The picture below shows how the three sectors of a cell areindexed.

Ifsector_id is a scalar, then all UTs are relocated to the samesector indexed bysector_id.Ifsector_id is a tensor, it should be broadcastable with[batch_size,num_ut], and give the sector in which each UT orbatch example is relocated to.

When calling the function,ut_loc gives the locations of the UTs torelocate, which are all assumed to be in sector with index 0, and in thecell centered on the origin (0,0).

Input:

• ut_loc ([batch_size, num_ut, 2],tf.float) – UTs locations in the X-Y plan

• sector_id (Tensor broadcastable with [batch_size, num_ut],int) – Indexes of the sector to which to relocate the UTs

• cell_loc (Tensor broadcastable with [batch_size, num_ut],tf.float) – Center of the cell to which to transpose the UTs

Output:

ut_loc ([batch_size, num_ut, 2],tf.float) – Relocated UTs locations in the X-Y plan

sionna.phy.channel.set_3gpp_scenario_parameters(scenario,min_bs_ut_dist=None,isd=None,bs_height=None,min_ut_height=None,max_ut_height=None,indoor_probability=None,min_ut_velocity=None,max_ut_velocity=None,precision=None)[source]

Set valid parameters for a specified 3GPP system levelscenario(RMa, UMi, or UMa)

If a parameter is given, then it is returned. If it is set toNone,then a parameter valid according to the chosen scenario is returned(see[TR38901]).

Input:

• scenario (“uma” | “umi” | “rma” | “uma-calibration” | “umi-calibration”) – System level model scenario

• min_bs_ut_dist (None (default) |tf.float) – Minimum BS-UT distance [m]

• isd (None (default) |tf.float) – Inter-site distance [m]

• bs_height (None (default) |tf.float) – BS elevation [m]

• min_ut_height (None (default) |tf.float) – Minimum UT elevation [m]

• max_ut_height (None (default) |tf.float) – Maximum UT elevation [m]

• indoor_probability (None (default) |tf.float) – Probability of a UT to be indoor

• min_ut_velocity (None (default) |tf.float) – Minimum UT velocity [m/s]

• max_ut_velocity (None (default) |tf.float) – Maximim UT velocity [m/s]

• precision (str,None (default) | ‘single’ | ‘double’) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Output:

• min_bs_ut_dist (tf.float) – Minimum BS-UT distance [m]

• isd (tf.float) – Inter-site distance [m]

• bs_height (tf.float) – BS elevation [m]

• min_ut_height (tf.float) – Minimum UT elevation [m]

• max_ut_height (tf.float) – Maximum UT elevation [m]

• indoor_probability (tf.float) – Probability of a UT to be indoor

• min_ut_velocity (tf.float) – Minimum UT velocity [m/s]

• max_ut_velocity (tf.float) – Maximim UT velocity [m/s]

sionna.phy.channel.gen_single_sector_topology(batch_size,num_ut,scenario,min_bs_ut_dist=None,isd=None,bs_height=None,min_ut_height=None,max_ut_height=None,indoor_probability=None,min_ut_velocity=None,max_ut_velocity=None,precision=None)[source]

Generate a batch of topologies consisting of a single BS located at theorigin andnum_ut UTs randomly and uniformly dropped in a cell sector

The following picture shows the sector from which UTs are sampled.

UT velocity and orientation are drawn uniformly at random, whereas the BS pointstowards the center of the sector it serves.

The drop configuration can be controlled through the optional parameters.Parameters set toNone are set to valid values according to the chosenscenario (see[TR38901]).

The returned batch of topologies can be used as-is with theset_topology() method of the system level models, i.e.UMi,UMa,andRMa.

Example

>>># Create antenna arrays>>>bs_array=PanelArray(num_rows_per_panel=4,...num_cols_per_panel=4,...polarization='dual',...polarization_type='VH',...antenna_pattern='38.901',...carrier_frequency=3.5e9)>>>>>>ut_array=PanelArray(num_rows_per_panel=1,...num_cols_per_panel=1,...polarization='single',...polarization_type='V',...antenna_pattern='omni',...carrier_frequency=3.5e9)>>># Create channel model>>>channel_model=UMi(carrier_frequency=3.5e9,...o2i_model='low',...ut_array=ut_array,...bs_array=bs_array,...direction='uplink')>>># Generate the topology>>>topology=gen_single_sector_topology(batch_size=100,...num_ut=4,...scenario='umi')>>># Set the topology>>>ut_loc,bs_loc,ut_orientations,bs_orientations,ut_velocities,in_state=topology>>>channel_model.set_topology(ut_loc,...bs_loc,...ut_orientations,...bs_orientations,...ut_velocities,...in_state)>>>channel_model.show_topology()

Input:

• batch_size (int) – Batch size

• num_ut (int) – Number of UTs to sample per batch example

• scenario (“uma” | “umi” | “rma” | “uma-calibration” | “umi-calibration”) – System level model scenario

• min_bs_ut_dist (None (default) |tf.float) – Minimum BS-UT distance [m]

• isd (None (default) |tf.float) – Inter-site distance [m]

• bs_height (None (default) |tf.float) – BS elevation [m]

• min_ut_height (None (default) |tf.float) – Minimum UT elevation [m]

• max_ut_height (None (default) |tf.float) – Maximum UT elevation [m]

• indoor_probability (None (default) |tf.float) – Probability of a UT to be indoor

• min_ut_velocity (None (default) |tf.float) – Minimum UT velocity [m/s]

• max_ut_velocity (None (default) |tf.float) – Maximim UT velocity [m/s]

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Output:

• ut_loc ([batch_size, num_ut, 3],tf.float) – UTs locations

• bs_loc ([batch_size, 1, 3],tf.float) – BS location. Set to (0,0,0) for all batch examples.

• ut_orientations ([batch_size, num_ut, 3],tf.float) – UTs orientations [radian]

• bs_orientations ([batch_size, 1, 3],tf.float) – BS orientations [radian]. Oriented towards the center of the sector.

• ut_velocities ([batch_size, num_ut, 3],tf.float) – UTs velocities [m/s]

• in_state ([batch_size, num_ut],tf.float) – Indoor/outdoor state of UTs.True means indoor,False meansoutdoor.

sionna.phy.channel.gen_single_sector_topology_interferers(batch_size,num_ut,num_interferer,scenario,min_bs_ut_dist=None,isd=None,bs_height=None,min_ut_height=None,max_ut_height=None,indoor_probability=None,min_ut_velocity=None,max_ut_velocity=None,precision=None)[source]

Generate a batch of topologies consisting of a single BS located at theorigin,num_ut UTs randomly and uniformly dropped in a cell sector, andnum_interferer interfering UTs randomly dropped in the adjacent cells

The following picture shows how UTs are sampled

UT velocity and orientation are drawn uniformly at random, whereas the BS pointstowards the center of the sector it serves.

The drop configuration can be controlled through the optional parameters.Parameters set toNone are set to valid values according to the chosenscenario (see[TR38901]).

The returned batch of topologies can be used as-is with theset_topology() method of the system level models, i.e.UMi,UMa,andRMa.

In the returnedut_loc,ut_orientations,ut_velocities, andin_state tensors, the firstnum_ut items along the axis with index1 correspond to the served UTs, whereas the remainingnum_interfereritems correspond to the interfering UTs.

Example

>>># Create antenna arrays>>>bs_array=PanelArray(num_rows_per_panel=4,...num_cols_per_panel=4,...polarization='dual',...polarization_type='VH',...antenna_pattern='38.901',...carrier_frequency=3.5e9)>>>>>>ut_array=PanelArray(num_rows_per_panel=1,...num_cols_per_panel=1,...polarization='single',...polarization_type='V',...antenna_pattern='omni',...carrier_frequency=3.5e9)>>># Create channel model>>>channel_model=UMi(carrier_frequency=3.5e9,...o2i_model='low',...ut_array=ut_array,...bs_array=bs_array,...direction='uplink')>>># Generate the topology>>>topology=gen_single_sector_topology_interferers(batch_size=100,...num_ut=4,...num_interferer=4,...scenario='umi')>>># Set the topology>>>ut_loc,bs_loc,ut_orientations,bs_orientations,ut_velocities,in_state=topology>>>channel_model.set_topology(ut_loc,...bs_loc,...ut_orientations,...bs_orientations,...ut_velocities,...in_state)>>>channel_model.show_topology()

Input:

• batch_size (int) – Batch size

• num_ut (int) – Number of UTs to sample per batch example

• num_interferer (int) – Number of interfeering UTs per batch example

• scenario (“uma” | “umi” | “rma” | “uma-calibration” | “umi-calibration”) – System level model scenario

• min_bs_ut_dist (None (default) |tf.float) – Minimum BS-UT distance [m]

• isd (None (default) |tf.float) – Inter-site distance [m]

• bs_height (None (default) |tf.float) – BS elevation [m]

• min_ut_height (None (default) |tf.float) – Minimum UT elevation [m]

• max_ut_height (None (default) |tf.float) – Maximum UT elevation [m]

• indoor_probability (None (default) |tf.float) – Probability of a UT to be indoor

• min_ut_velocity (None (default) |tf.float) – Minimum UT velocity [m/s]

• max_ut_velocity (None (default) |tf.float) – Maximim UT velocity [m/s]

• precision (None (default) | “single” | “double”) – Precision used for internal calculations and outputs.If set toNone,precision is used.

Output:

• ut_loc ([batch_size, num_ut, 3],tf.float) – UTs locations. The firstnum_ut items along the axis with index1 correspond to the served UTs, whereas the remainingnum_interferer items correspond to the interfeering UTs.

• bs_loc ([batch_size, 1, 3],tf.float) – BS location. Set to (0,0,0) for all batch examples.

• ut_orientations ([batch_size, num_ut, 3],tf.float) – UTs orientations [radian]. The firstnum_ut items along theaxis with index 1 correspond to the served UTs, whereas theremainingnum_interferer items correspond to the interfeeringUTs.

• bs_orientations ([batch_size, 1, 3],tf.float) – BS orientation [radian]. Oriented towards the center of the sector.

• ut_velocities ([batch_size, num_ut, 3],tf.float) – UTs velocities [m/s]. The firstnum_ut items along the axiswith index 1 correspond to the served UTs, whereas the remainingnum_interferer items correspond to the interfeering UTs.

• in_state ([batch_size, num_ut],tf.float) – Indoor/outdoor state of UTs.True means indoor,False meansoutdoor. The firstnum_ut items along the axis withindex 1 correspond to the served UTs, whereas the remainingnum_interferer items correspond to the interfering UTs.