技术领域technical field
本发明涉及无线通信技术领域，具体涉及一种时域角度域双稀疏多径信道模型，还涉及一种基于压缩感知的双稀疏多径信道估计方法。The present invention relates to the technical field of wireless communication, in particular to a double-sparse multipath channel model in the time-domain angle domain, and also relates to a method for estimating a double-sparse multipath channel based on compressed sensing.
背景技术Background technique
随着1G、2G、3G、4G的发展，传输频率越来越高。而频率越高，频段越宽，传输速率也就越快。5G预计可支持的频率范围将从400MHZ到100GHZ，以30GHZ为例，其波长为10mm。即5G主要在毫米波段通信，毫米波通信技术的最大特点是波长极短和带宽极大。同时，因为毫米波波长短、主要以直射路径为主，所以传播稳定性高。且毫米波千倍于LTE的超带宽，为5G系统的超高速率和超连接数量提供了保证，若加上空分、时分、正交极化或其他复用技术，5G中万物互联所需的多址问题，也是可以轻易解决的。另外，毫米波通信技术也是相当成熟的。毫米波技术在通信领域的应用主要是毫米波波导通信、毫米波无线地面通信和毫米波卫星通信，且以无线地面通信和卫星通信为主。With the development of 1G, 2G, 3G, and 4G, the transmission frequency is getting higher and higher. The higher the frequency, the wider the frequency band, and the faster the transmission rate. 5G is expected to support a frequency range from 400MHZ to 100GHZ, taking 30GHZ as an example, its wavelength is 10mm. That is to say, 5G mainly communicates in the millimeter wave band. The biggest feature of millimeter wave communication technology is extremely short wavelength and huge bandwidth. At the same time, because the wavelength of the millimeter wave is short and the direct path is the main route, the propagation stability is high. Moreover, the ultra-bandwidth of millimeter wave is thousands of times that of LTE, which provides a guarantee for the ultra-high speed and ultra-connection number of 5G systems. If space division, time division, orthogonal polarization or other multiplexing technologies are added, the Internet of Everything required in 5G The problem of multiple addresses can also be easily solved. In addition, millimeter wave communication technology is quite mature. The application of millimeter wave technology in the field of communication is mainly millimeter wave waveguide communication, millimeter wave wireless ground communication and millimeter wave satellite communication, and wireless ground communication and satellite communication are the main ones.
显然，毫米波通信频率高、波长短，遇到阻挡就被反射或被阻断，以直射方式传播，波束窄，具有良好的方向性。与传统的无线信道相比，毫米波传输不仅在时域具有更强的稀疏性，在角度域也会表现出较强的稀疏性。时域稀疏是指信号在多个时间空间分布路径上传播，是传统无线信道的显著特征；角度域稀疏是指信号在多个角度域空间分布的路径上传播，是下一代无线信道的重要特点。两者均涉及大量的传播参数，且大量研究表明毫米波技术能够满足5G的传输需求，因此建立统计信道模型和设计信道的估计方法就显得尤为重要。Obviously, millimeter wave communication has a high frequency and a short wavelength, and it will be reflected or blocked when it encounters obstacles. It propagates in a direct way, with narrow beams and good directivity. Compared with traditional wireless channels, mmWave transmission not only has stronger sparsity in the time domain, but also exhibits stronger sparsity in the angle domain. Sparse in the time domain means that the signal propagates on multiple paths distributed in time and space, which is a prominent feature of traditional wireless channels; sparseness in the angle domain means that the signal propagates on paths distributed in multiple angle domains, which is an important feature of the next-generation wireless channel . Both involve a large number of propagation parameters, and a large number of studies have shown that millimeter wave technology can meet the transmission requirements of 5G, so it is particularly important to establish a statistical channel model and design a channel estimation method.
另一方面，根据天线特性，天线长度与波长成正比，天线长度大约在波长的1/10---1/4之间。即频率越高，波长越短，天线也就跟着变短了。也就是说，毫米波通信中，天线也就变成了毫米级。因此，LTE时代的MIMO(Multiple-Input Multiple-Output)在5G时代变成了加强版的Massive MIMO(大规模多输入多输出)。因此，5G时代，一般都为天线阵列。On the other hand, according to the characteristics of the antenna, the length of the antenna is proportional to the wavelength, and the length of the antenna is about 1/10---1/4 of the wavelength. That is, the higher the frequency, the shorter the wavelength, and the shorter the antenna. That is to say, in millimeter wave communication, the antenna becomes millimeter level. Therefore, MIMO (Multiple-Input Multiple-Output) in the LTE era has become an enhanced version of Massive MIMO (Massive Multiple-Input Multiple-Output) in the 5G era. Therefore, in the 5G era, it is generally an antenna array.
在Massive MIMO系统中，若利用只考虑时域稀疏的传统信道模型进行信道估计，导频开销巨大且信道估计的复杂度将大大增加，此外由于天线数量大，传输过程中引入的噪音也多，从而会降低信道的估计性能。In a Massive MIMO system, if the traditional channel model that only considers time-domain sparseness is used for channel estimation, the pilot overhead will be huge and the complexity of channel estimation will be greatly increased. In addition, due to the large number of antennas, there will be a lot of noise introduced in the transmission process. Thus, the estimation performance of the channel will be degraded.
发明内容Contents of the invention
本发明的目的在于克服现有技术中的不足，提供一种双稀疏多径信道模型，解决了传统稀疏多径信道的估计性能较低的技术问题。The purpose of the present invention is to overcome the deficiencies in the prior art, provide a dual-sparse multi-path channel model, and solve the technical problem of low estimation performance of traditional sparse multi-path channels.
为解决上述技术问题，本发明提供了一种双稀疏多径信道模型，其特征是，此双稀疏是指时域稀疏和角域稀疏，时域角域双稀疏的多径信道模型为：In order to solve the above-mentioned technical problem, the present invention provides a kind of double sparse multipath channel model, it is characterized in that, this double sparse refers to time domain sparse and angle domain sparse, the multipath channel model of time domain angle domain double sparse is:
Ha＝[Ha(0),Ha(1),Ha(2),...,Ha(L-1)] (17)Ha =[Ha (0), Ha (1), Ha (2),..., Ha (L-1)] (17)
其中，L为信道长度，Ha是时延为L的时域角域的双稀疏信道模型，Ha(τ)即为τ时刻角域的信道矩阵，m为时域的稀疏度，τj为第j条路径的时延，Among them, L is the channel length, Ha is the double-sparse channel model in the time domain angle domain with a delay of L, Ha (τ) is the channel matrix in the angle domain at time τ, m is the sparsity in the time domain, τj is the delay of the jth path,
而其中and among them
其中，σi表示第i条路径的衰减，nt表示发射天线数量，nr表示接收天线数量，di表示第一副发射天线到第一副接收天线的第i条路径的长度，λc为载波波长，n代表信道路径数量，Ur,Ut为空间正交基，er(·)、et(·)为单位空间特征图，将式15代入式18得：in, σi represents the attenuation of the i-th path, nt represents the number of transmitting antennas, nr represents the number of receiving antennas, di represents the length of the i-th path from the first transmitting antenna to the first receiving antenna, and λc is the carrier wavelength, n represents the number of channel paths, Ur , Ut are spatial orthogonal bases, er (·), et (·) are feature maps of unit space, and substituting Equation 15 into Equation 18:
本发明还提供了一种基于双稀疏多径信道模型的信道估计方法，其特征是，包括以下步骤：The present invention also provides a kind of channel estimation method based on double sparse multipath channel model, it is characterized in that, comprises the following steps:
步骤S1，假设MIMO信道的角域表示矩阵，并引入时间波动；Step S1, assuming the angular domain representation matrix of the MIMO channel, and introducing time fluctuations;
步骤S2，基于压缩感知的时域稀疏的估计:由公式得到时域信道表示，并用压缩感知理论高概率恢复时域信道Step S2, estimation of time-domain sparsity based on compressed sensing: by the formula Get the time-domain channel representation, and use compressed sensing theory to recover the time-domain channel with high probability
步骤S3，基于压缩感知的角度域稀疏的估计:将向量化，再利用压缩感知理论高概率恢复出角域表示的MIMO信道Step S3, estimation of angle domain sparseness based on compressed sensing: the Vectorization, and then use the compressed sensing theory to restore the MIMO channel represented by the angle domain with high probability
步骤S4，测量双稀疏多径信道模型估计的精确度。Step S4, measuring the estimation accuracy of the dual-sparse multipath channel model.
优选的，步骤2中，基于压缩感知的时域稀疏的估计的具体过程为：将假设的角域表示转化成信道的时域表示，并将时域表示向量化；针对单个信道利用压缩感知理论高概率恢复时域信道，其它信道同理，加入循环即可。Preferably, in step 2, the specific process of compressive sensing-based time-domain sparse estimation is as follows: transform the hypothetical angle-domain representation into a channel time-domain representation, and vectorize the time-domain representation; use compressive sensing theory for a single channel High-probability restoration of the time-domain channel, the same for other channels, just add a loop.
优选的，利用压缩感知理论高概率恢复时域信道的具体步骤：Preferably, the specific steps of recovering the time-domain channel with high probability using compressed sensing theory:
1)时域到频域的转换1) Conversion from time domain to frequency domain
对于第k副发送天线到第g副接收天线信道hgk，时域有ygk＝hgk(t)*xk(τ-t)+w，0≤t≤L，ygk为第g副接收天线接收到的信号，*表示卷积，xk为第k个发送天线的发送数据，w为传输过程中的噪音，L为信道长度；For the channel hgk from the kth transmitting antenna to the gth receiving antenna, the time domain has ygk =hgk (t)*xk (τ-t)+w, 0≤t≤L, and ygk is the gth secondary The signal received by the receiving antenna, * means convolution, xk is the transmitted data of the kth transmitting antenna, w is the noise during transmission, and L is the channel length;
将其转换到频域即：Ygk＝XkHgk+W (21)Convert it to the frequency domain: Ygk ＝Xk Hgk +W (21)
2)在MIMO-OFDM系统中放导频2) Put the pilot in the MIMO-OFDM system
在子载波个数为N的OFDM系统中，假设OFDM符号的循环前缀长度不小于信道长度L；OFDM中第i个发送数据为x(i),i＝1,2,3,...N-1；为避免干扰，发送天线之间的导频位置正交，在OFDM符号的N个子载波中，有p个用于放置导频，Ψ＝(es1,es2,......esp)为p×N的导频选择矩阵，si,i＝1,2,3,...p，表示第i个导频的位置，esi是长度为N的列向量，它的第si个元素为1，其它元素全为0，则式(21)中，In an OFDM system with N subcarriers, it is assumed that the cyclic prefix length of the OFDM symbol is not less than the channel length L; the i-th transmission data in OFDM is x(i), i=1,2,3,...N -1; In order to avoid interference, the pilot positions between the transmitting antennas are orthogonal, and among the N subcarriers of the OFDM symbol, p are used to place pilots, Ψ=(es1 , es2 ,..... .esp ) is a p×N pilot selection matrix, si , i=1,2,3,...p, represents the position of the i-th pilot, esi is a column vector of length N, it The i-th element of si is 1, and the other elements are all 0, then in formula (21),
Ygk＝[Ygk(0),Ygk(1)......Ygk(N-1)]，Xk＝[xk(0),xk(1)......xk(N-1)]Ygk ＝[Ygk (0), Ygk (1)...Ygk (N-1)], Xk ＝[xk (0), xk (1)..... .xk (N-1)]
Hgk＝FN×Lhgk为信道频域响应采样值，其中FN×L为部分DFT变换矩阵，由N维DFT变换矩阵的前L列构成。W是一个方差为σ2的N维加性复高斯白噪声向量，将导频选择矩阵Ψ作用于(21)式两端，可得：Hgk =FN×L hgk is the channel frequency domain response sampling value, where FN×L is a part of the DFT transformation matrix, consisting of the first L columns of the N-dimensional DFT transformation matrix. W is an N-dimensional additive complex Gaussian white noise vector with a variance ofσ2 , and the pilot selection matrix Ψ is applied to both sides of (21), and it can be obtained:
Ygk_p＝Xg_pFphgk+Wp (22)Ygk_p ＝Xg_p Fp hgk +Wp (22)
其中，Ygk_p＝ΨYgk,Wp＝ΨW均为p维列向量，分别为接收到的导频信号及其对应的信道噪声。Xk_p＝ΨXΨT为p×p的对角阵，对角线上的元素为发送端的p个导频。Fp＝ΨFN×L为p×L的矩阵。Wherein, Ygk_p =ΨYgk , Wp =ΨW are both p-dimensional column vectors, which are respectively the received pilot signal and its corresponding channel noise. Xk_p =ΨXΨT is a p×p diagonal matrix, and the elements on the diagonal are p pilots of the transmitting end. Fp =ΨFN×L is a p×L matrix.
令T＝Xt_pFp，则式(22)可写为：Let T=Xt_p Fp , then formula (22) can be written as:
Ygk_p＝Thgk+Wp (23)Ygk_p =Thgk +Wp (23)
其中，T是p×L矩阵，hgk表示第k副发送天线到第g副接收天线的信道时域冲击响应，在无线通信中呈现稀疏性，由于Yik_p,Xi_p,Fp在发送端和接收端是已知的，因此可以利用稀疏度已知的重构算法根据Ygk_p高概率恢复hik。Among them, T is a p×L matrix, and hgk represents the channel time domain impulse response from the kth transmitting antenna to the gth receiving antenna, which is sparse in wireless communication. Since Yik_p ,Xi_p , and Fp are at the transmitting end and the receiving end are known, so the reconstruction algorithm with known sparsity can be used to restore hik according to Ygk_p with high probability.
优选的，将假设的角域表示向量化，针对单个信道利用压缩感知理论高概率恢复角域信道，其它信道同理，加入循环即可。Preferably, the assumed angular domain representation is vectorized, and the compressed sensing theory is used to restore the angular domain channel with high probability for a single channel. The same is true for other channels, just add a loop.
优选的，利用归一化的均方误差来计算信道估计的精确度。Preferably, the accuracy of the channel estimation is calculated using the normalized mean square error.
与现有技术相比，本发明所达到的有益效果是：本发明利用毫米波通信中时域和角域均稀疏的特性，对毫米波MIMO系统随时间波动的下行信道传播特性进行研究，建立了双稀疏多径信道模型。并且，根据时域和角度域的稀疏性，设计了基于压缩感知的双稀疏多径信道的估计方法，结果显示，与传统稀疏多径信道的估计性能相比，双稀疏多径信道的估计性能往往更好，即使在稀疏度未知的情况下，双稀疏多径信道的估计性能也表现较好，能够高概率的恢复出原始信道。Compared with the prior art, the beneficial effects achieved by the present invention are: the present invention utilizes the characteristics of both time domain and angular domain sparseness in the millimeter wave communication to study the downlink channel propagation characteristics of the millimeter wave MIMO system fluctuating with time, and establish A dual-sparse multipath channel model is proposed. Moreover, according to the sparsity of time domain and angle domain, an estimation method of dual sparse multipath channel based on compressed sensing is designed. The results show that, compared with the estimation performance of traditional sparse multipath channel, the estimation performance of dual sparse multipath channel is Often better, even in the case of unknown sparsity, the estimation performance of the dual-sparse multipath channel is also better, and the original channel can be restored with a high probability.
附图说明Description of drawings
图1为一副发射天线和nr副接收天线的SIMO视距传输信道示意图；Fig. 1 is a schematic diagram of the SIMO line-of-sight transmission channel of a pair of transmitting antennas and nr receiving antennas;
图2为nt副发射天线和一副接收天线的MISO视距传输信道示意图；Fig. 2 is a schematic diagram of the MISO line-of-sight transmission channel of nt secondary transmitting antennas and a secondary receiving antenna;
图3为包括直射路径和反射路径的MIMO物理信道图；FIG. 3 is a MIMO physical channel diagram including a direct path and a reflected path;
图4为4副接收天线(Lr＝2)和4副发射天线(Lt＝2)的角域划分示意图；Fig. 4 is a schematic diagram of angular domain division of 4 receiving antennas (Lr =2) and 4 transmitting antennas (Lt =2);
图5为双稀疏信道模型示意图；Fig. 5 is a schematic diagram of a dual sparse channel model;
图6为时域离散稀疏信道模型图；Fig. 6 is a time-domain discrete sparse channel model diagram;
图7为双稀疏多径信道模型的估计方法流程图；Fig. 7 is the estimation method flowchart of double sparse multipath channel model;
图8为OFDM导频形状图；Figure 8 is an OFDM pilot shape diagram;
图9为双稀疏信道与现有技术中只考虑时域稀疏的信道估计性能对比图。FIG. 9 is a comparison diagram of channel estimation performance between a dual sparse channel and a channel estimation that only considers time domain sparsity in the prior art.
具体实施方式Detailed ways
下面结合附图对本发明作进一步描述。以下实施例仅用于更加清楚地说明本发明的技术方案，而不能以此来限制本发明的保护范围。The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solution of the present invention more clearly, but not to limit the protection scope of the present invention.
下一代无线通信中，毫米波传输时具有时域和角度域均稀疏的特性，因此本发明建立了时域和角度域双稀疏多径信道模型。其建模的具体过程如下。In the next generation of wireless communication, millimeter wave transmission has the characteristic of being sparse in both the time domain and the angle domain, so the present invention establishes a dual-sparse multipath channel model in the time domain and the angle domain. The specific process of its modeling is as follows.
1)视距SIMO信道1) Line-of-sight SIMO channel
首先考虑一副发射天线和nr副接收天线的SIMO(single input multipleoutput)视距传输信道,此SIMO传输信道如图1所示，nr副接收天线分别排列在归一化长度为Lr的均匀线性阵列中，△r＝Lr/nr为归一化的接收天线间隔。First consider the SIMO (single input multiple output) line-of-sight transmission channel of a transmitting antenna and nr receiving antennas. The SIMO transmission channel is shown in Figure 1. The nr receiving antennas are respectively arranged in a normalized length Lr In a uniform linear array, △r = Lr /nr is the normalized receiving antenna spacing.
则发射天线与第i副接收天线之间信道的连续时间冲击响应hi(τ)为:Then the continuous-time impulse response hi (τ) of the channel between the transmitting antenna and the i-th receiving antenna is:
hi(τ)＝aδ(τ-di/c) i＝1,2,...,nrhi (τ)=aδ(τ-di /c) i=1,2,...,nr
其中di为发射天线与第i副接收天线之间的距离，c为光速，a为路径衰减，假设路径衰减对所有天线对都相同。设di/c<<1/W，其中W为传输带宽，则发射天线和nr副接收天线的视距传输信道的基带增益为：where di is the distance between the transmitting antenna and the i-th receiving antenna, c is the speed of light, and a is the path attenuation, assuming that the path attenuation is the same for all antenna pairs. Let di /c<<1/W, where W is the transmission bandwidth, then the baseband gain of the line-of-sight transmission channel between the transmitting antenna and nr receiving antennas is:
其中，fc为载波频率，λc为载波波长，且由于发射机与接收机之间的距离远大于接收天线阵列的尺寸，所以从第一副发射天线到各接收天线的路径为并行的，故：Wherein,fc is the carrier frequency,λc is the carrier wavelength, and since the distance between the transmitter and the receiver is much larger than the size of the receiving antenna array, the paths from the first secondary transmitting antenna to each receiving antenna are parallel, Therefore:
di≈d+(i-1)△rλccosΦr i＝1,2,...,nrdi ≈d+(i-1)△r λc cosΦr i=1,2,...,nr
其中，d为发射天线到第一副接收天线的距离，△r为归一化的接收天线间隔，Φr为发射天线视距路径与接收天线阵列的夹角，即到达角(angle of arrival,AOA)。Among them, d is the distance from the transmitting antenna to the first receiving antenna, △r is the normalized receiving antenna spacing, and Φr is the angle between the line-of-sight path of the transmitting antenna and the receiving antenna array, that is, the angle of arrival (angle of arrival, AOA).
令Ωr:＝cosΦr，表示接收天线阵列的方向余弦，则发射天线和nr副接收天线的视距传输信道增益矢量为：Let Ωr :=cosΦr represent the direction cosine of the receiving antenna array, then the line-of-sight transmission channel gain vector of the transmitting antenna and nr receiving antennas is:
为符号表示方便，定义For the convenience of notation, define
为方向余弦Ωr上的单位空间特征图。is the unit space feature map on the direction cosine Ωr .
将(2)式代入(1)式得SIMO视距传输信道增益矢量为：Substituting equation (2) into equation (1), the gain vector of the SIMO line-of-sight transmission channel is:
2)视距MISO信道2) Line of sight MISO channel
图2为nt副发射天线和一副接收天线的MISO(multiple input single output)视距传输信道，nt副接收天线分别排列在归一化长度为Lt的均匀线性阵列中，△t＝Lt/nt为归一化的接收天线间隔。Φt为发射天线阵列视距路径与接收天线之间的夹角，即离开角(angle of departure,AOD)。令Ωt:＝cosΦt，表示发送天线阵列的方向余弦。同理SIMO视距传输信道，则MISO视距传输信道增益矢量为：Fig. 2 is the MISO (multiple input single output) line-of-sight transmission channel of nt secondary transmitting antennas and a pair of receiving antennas, nt secondary receiving antennas are respectively arranged in a uniform linear array with normalized length Lt , △t = Lt /nt is the normalized receiving antenna spacing.Φt is the angle between the line-of-sight path of the transmitting antenna array and the receiving antenna, that is, the angle of departure (AOD). Let Ωt :=cosΦt represent the direction cosine of the transmitting antenna array. Similarly to the SIMO line-of-sight transmission channel, the MISO line-of-sight transmission channel gain vector is:
定义：definition:
为发射方向Ωt上的单位空间特征图。is the feature map of unit space in the emission direction Ωt .
则(5)式代入(4)式得：Then (5) is substituted into (4) to get:
其中，d为第一副发射天线到接收天线的距离。Wherein, d is the distance from the first secondary transmitting antenna to the receiving antenna.
3)存在一条视距路径的MIMO信道3) There is a MIMO channel with a line-of-sight path
考虑具有nt副天线的发射机和具有nr副天线的接收机相对应的时域和角度域稀疏的多天线MIMO(multiple input multiple output)信道；假设nt副发射天线与nr副接收天线分别排列在归一化长度为Lt与Lr的均匀线性阵列中。△r＝Lr/nr为归一化的接收天线间隔，△t＝Lt/nt为归一化的发射天线间隔。则第t副发射天线与第r副接收天线之间的信道增益为：Consider a multi-antenna MIMO (multiple input multiple output) channel with sparse time and angle domains corresponding to a transmitter with nt antennas and a receiver with nr antennas; assuming nt transmit antennas and nr receivers The antennas are respectively arranged in uniform linear arrays with normalized lengths Lt and Lr . △r = Lr /nr is the normalized receiving antenna spacing, and △t = Lt /nt is the normalized transmitting antenna spacing. Then the channel gain between the tth transmitting antenna and the rth receiving antenna is:
hrt＝aexp(-j2πdrt/λc) (7)hrt ＝aexp(-j2πdrt /λc ) (7)
式中，a为路径的衰减(假设所有天线的衰减都相同),drt为第t副发射天线与第r副接收天线之间的距离，一般假天线阵列尺寸远小于发送天线与接收天线阵列之间的距离，则有：In the formula, a is the attenuation of the path (assuming that the attenuation of all antennas is the same), and drt is the distance between the t-th transmitting antenna and the r-th receiving antenna. Generally, the size of the false antenna array is much smaller than that of the transmitting antenna and the receiving antenna array The distance between them is:
drt≈d+(r-1)△rλccosΦr-(t-1)△tλc cosΦtdrt ≈d+(r-1)△r λc cosΦr -(t-1)△t λc cosΦt
d为第一副发射天线与第一副接收天线之间的距离。Φr为发射天线视距路径与接收天线阵列的夹角，即到达角(angle of arrival,AOA)。Ωr:＝cosΦr，表示接收天线阵列的方向余弦。Φt为发射天线阵列视距路径与接收天线之间的夹角，即离开角(angle ofdeparture,AOD)。令Ωt:＝cosΦt，表示发送天线阵列的方向余弦。则代入(7)式等于：d is the distance between the first secondary transmitting antenna and the first secondary receiving antenna. Φr is the angle between the line-of-sight path of the transmitting antenna and the receiving antenna array, that is, the angle of arrival (AOA). Ωr := cosΦr , indicating the direction cosine of the receiving antenna array. Φt is the angle between the line-of-sight path of the transmitting antenna array and the receiving antenna, that is, the angle of departure (AOD). Let Ωt :=cosΦt represent the direction cosine of the transmitting antenna array. Substituting into (7) is equal to:
hrt＝aexp(-j2πd/λc)·exp(j2π(t-1)△tΩt)·exp(-j2π(r-1)△rΩr) (8)hrt ＝aexp(-j2πd/λc )·exp(j2π(t-1)△t Ωt )·exp(-j2π(r-1)△r Ωr ) (8)
故，在某个时刻，存在一条视距路径的MIMO信道矩阵为：Therefore, at a certain moment, there is a MIMO channel matrix for a line-of-sight path:
er(·)、et(·)分别由式(2)式(5)定义，(·)H表示共轭转置。er (·), et (·) are defined by formula (2) and formula (5), respectively, and (·)H represents the conjugate transpose.
4)包括一条直射路径和一条反射路径的MIMO信道4) MIMO channel including a direct path and a reflected path
如图3所示，在MIMO传输信道中存在A，B两点，B是遇到障碍物的反射点，A则是根据反射路径的反射点在直射路径上选取的一点(虚拟点，是我们假设的，实际中不存在)。我们可把A，B两点看作中继，则包括一条直射路径(记为路径1)和一条反射路径(记为路径2)的MIMO信道可以分成两个信道。As shown in Figure 3, there are two points A and B in the MIMO transmission channel, B is the reflection point encountering an obstacle, and A is a point selected on the direct path according to the reflection point of the reflection path (the virtual point is our hypothetical, does not exist in reality). We can regard A and B as relays, and then a MIMO channel including a direct path (marked as path 1) and a reflected path (marked as path 2) can be divided into two channels.
信道1：nt副发射天线和两副在地理位置上间隔的接收天线A、B的视距传输信道，由于两幅接收射天线A、B在地理位置上间隔较大，故发射天线阵列到A,B的离开角是不同的。Channel 1: The line-of-sight transmission channel of nt secondary transmitting antennas and two receiving antennas A and B geographically separated. Since the two receiving antennas A and B are geographically separated, the transmitting antenna array The departure angles of A and B are different.
信道2：正好与信道1相反，是两副在地理位置上间隔的发射天线A、B与nr副接收天线的视距传输信道，由于两幅发射天线在地理位置上间隔较大，故到接收天线阵列的到达角是不同的。Channel 2: Just the opposite of channel 1, it is the line-of-sight transmission channel of two transmitting antennas A, B and nr receiving antennas separated geographically. The angle of arrival of the receiving antenna array is different.
信道1的信道增益矢量即为视距MISO信道增益矢量(6)的叠加，为The channel gain vector of channel 1 is the superposition of line-of-sight MISO channel gain vector (6), which is
式中,at1，at2分别为发射天线到A点和B点的衰减(假设所有天线的衰减都相同)。dt1，dt2分别为第一副发射天线到A点和B点的距离。Φt1，Φt2分别为图3中路径1和路径2的离开角。令Ωt1:＝cosΦt1，Ωt2:＝cosΦt2表示发送天线阵列的方向余弦。et(·)由式(5)定义。In the formula, at1 and at2 are the attenuation of the transmitting antenna to point A and point B respectively (assuming that the attenuation of all antennas is the same). dt1 and dt2 are the distances from the first transmitting antenna to point A and point B respectively. Φt1 , Φt2 are the departure angles of path 1 and path 2 in Fig. 3, respectively. Let Ωt1 :=cosΦt1 , Ωt2 :=cosΦt2 denote the direction cosine of the transmitting antenna array. et (·) is defined by formula (5).
信道2的信道增益矢量即为视距SIMO信道增益矢量(3)的叠加，为The channel gain vector of channel 2 is the superposition of line-of-sight SIMO channel gain vector (3), which is
式中,ar1，ar2分别为A点和B点到接收天线阵列的衰减(假设所有天线的衰减都相同)。dr1，dr2分别为A点和B点到第一副接收天线的距离。Φr1，Φr2分别为图3中路径1和路径2的到达角。令Ωr1:＝cosΦr1，Ωr2:＝cosΦr2表示接收天线阵列的方向余弦。er(·)由式(2)定义。In the formula, ar1 and ar2 are the attenuation from point A and point B to the receiving antenna array respectively (assuming that the attenuation of all antennas is the same). dr1 , dr2 are the distances from point A and point B to the first receiving antenna, respectively. Φr1 and Φr2 are the arrival angles of path 1 and path 2 in Fig. 3, respectively. Let Ωr1 :=cosΦr1 , Ωr2 :=cosΦr2 denote the direction cosine of the receiving antenna array. er (·) is defined by formula (2).
包括一条直射路径和一条反射路径的MIMO信道增益即为信道1和信道2的组合，为：The MIMO channel gain including a direct path and a reflected path is the combination of channel 1 and channel 2 as:
令σi＝ariati表示第i条路径的衰减(假设所有天线的衰减都相同)，di＝dri+dti表示第一副发射天线到第一副接收天线的第i条路径的长度。将其带入式(12)得：Let σi =ari ati represent the attenuation of the i-th path (assuming that the attenuation of all antennas is the same), and di =dri +dti represent the i-th path from the first transmit antenna to the first receive antenna length. Bring it into formula (12) to get:
为书写方便，令且将MIMO信道扩展到n条路径，则窄带MIMO多径信道为：For the convenience of writing, let And the MIMO channel is extended to n paths, then the narrowband MIMO multipath channel is:
5)窄带MIMO多径信道角度域建模5) Angle domain modeling of narrowband MIMO multipath channel
在窄带MIMO信道中，发射天线阵列长度Lt与接收天线阵列长度Lr控制着角度域的可分辨程度：发射方向余弦之差小于1/Lt并且接收方向余弦之差小于1/Lr的路径是天线阵列无法分辨的路径。这表明在角度域中，发射机应该以固定的角度间隔1/Lt进行“采样”，同时接收机应该以固定的角度间隔1/Lr进行“采样”。In a narrowband MIMO channel, the transmit antenna array length Lt and the receive antenna array length Lr control the resolution in the angular domain: the difference between the transmit direction cosines is less than 1/Lt and the receive direction cosine difference is less than 1/Lr A path is one that cannot be resolved by the antenna array. This means that in the angular domain, the transmitter should "sample" at a fixed angular interval 1/Lt , while the receiver should "sample" at a fixed angular interval 1/Lr .
故可定义接收信号和发射信号的空间正交基(酉矩阵)为：Therefore, the spatial orthogonal basis (unitary matrix) of the received signal and the transmitted signal can be defined as:
其分别提供了接收信号和发送信号的角度域表示。It provides an angle-domain representation of the received signal and the transmitted signal, respectively.
当归一化的接收天线间隔△r和归一化的发射天线间隔△t均为时，角域窗口与角域基矢量为一一对应关系，这种情况是最简单的。在后续讨论中，假设天线是临界间隔的，即如图4所示，其中4副发射天线与4副接收天线分别排列在归一化长度为Lt＝2与Lr＝2的均匀线性阵列中。△r＝Lr/nr＝1/2,△t＝Lt/nt＝1/2为临界间隔，故角域被划分为4个接收区域(图4右侧)和4个发射区域(图4左侧)。When the normalized receiving antenna spacing △r and the normalized transmitting antenna spacing △t are both When , there is a one-to-one correspondence between the angle domain window and the angle domain base vector, which is the simplest case. In the ensuing discussion, it is assumed that the antennas are critically spaced, i.e. As shown in FIG. 4 , 4 transmit antennas and 4 receive antennas are respectively arranged in uniform linear arrays with normalized lengths Lt =2 and Lr =2. △r ＝Lr /nr ＝1/2, △t ＝Lt /nt ＝1/2 is the critical interval, so the angular domain is divided into 4 receiving areas (right side of Figure 4) and 4 transmitting areas (Figure 4 left).
因此在角域，第k个发送区域到第g个接收区域的信道增益粗略地等于发射方向余弦位于k/Lt周围的宽度为1/Lt的角域窗口内，接收方向余弦位于g/Lr周围的宽度为1/Lr的角域窗口内的所有路径增益之和。Therefore, in the angular domain, the channel gain from the kth transmitting region to the gth receiving region is roughly equal to the transmit direction cosine in an angular domain window of width 1/Lt around k/L t and the receive direction cosine in g/Lt The sum of all path gains within an angular domain window of width 1/Lr aroundLr .
故窄带MIMO多径信道即公式(14)在角域表示为：Therefore, the narrowband MIMO multipath channel, that is, formula (14), is expressed in the angle domain as:
即：which is:
ha中的第1行第1列的元素表示从第一个发射区域到第一个接收区域的角域区域增益，h中的第1行第1列元素表示第1副发射天线到第1副接收天线的信道增益。由于毫米波通信频率高、波长短，遇到阻挡就被反射或被阻断，主要以直射方式传播，因此，窄带MIMO信道在角域具有很强的稀疏性，即在很多角域区域中，信道增益为0。The element in row 1 and column 1 in ha represents the angular domain area gain from the first transmitting area to the first receiving area, and the element in row 1 and column 1 in h represents the first transmitting antenna to the first The channel gain of the secondary receive antenna. Due to the high frequency and short wavelength of millimeter-wave communication, it is reflected or blocked when encountering obstacles, and mainly propagates in a direct way. Therefore, narrowband MIMO channels have strong sparsity in the angular domain, that is, in many angular domain areas, Channel gain is 0.
6)时域角域双稀疏多径信道的模型6) Model of double sparse multipath channel in time domain and angle domain
如图5所示的双稀疏多径信道的模型。横轴表示时间轴，图示中有三个时间抽头处存在路径集合，即时域稀疏，而每个非零抽头点处(存在路径集合的时刻)，其角域又是稀疏的，即图示中，每个时域的非零抽头点处，均在三个角域方向上有路径集合。且角域增益通常比时延增益变化慢。因此，在所研究的时间尺度内，可以合理的假定，在不同时刻，角度域的非零路径集合的方向不变。The model of the dual sparse multipath channel as shown in Fig. 5 . The horizontal axis represents the time axis. In the illustration, there are three time taps where there are path sets, and the time domain is sparse, and at each non-zero tap point (the moment when there is a path set), the angular domain is sparse, that is, in the illustration, At each non-zero tap point in the time domain, there are path sets in the three angular domain directions. And the angle domain gain usually changes more slowly than the delay gain. Therefore, within the studied time scale, it is reasonable to assume that the direction of the set of non-zero paths in the angle domain does not change at different time instants.
具体的，时域角域双稀疏的多径信道模型为:Specifically, the double-sparse multipath channel model in the time domain and angle domain is:
Ha＝[Ha(0),Ha(1),Ha(2),...,Ha(L-1)] (17)Ha =[Ha (0), Ha (1), Ha (2),..., Ha (L-1)] (17)
其中，L为信道长度，Ha是时延为L的时域角域的双稀疏信道模型，Ha(τ)即为τ时刻角域的信道矩阵，m为信道在时域非零抽头点(存在路径集合的时刻)的个数，即时域的稀疏度，ha为窄带MIMO多径信道的角域表示(见式(15))，τj为第j条路径的时延。Among them, L is the channel length, Ha is the double-sparse channel model in the time domain angle domain with a delay of L, Ha (τ) is the channel matrix in the angle domain at time τ, and m is the non-zero tap point of the channel in the time domain The number of (moment when there is a path set), the sparsity in the instant domain, ha is the angle domain representation of the narrowband MIMO multipath channel (see formula (15)), τj is the delay of the jth path.
首先该信道在时域上是稀疏的，即有些时刻有路径集合，有些时刻没有路径集合。如图6为叠加瑞利信道模型生成的时域离散稀疏信道模型(此时信道长度L＝60，信道在时域非零抽头点个数m＝5，即只有5个时刻存在路径集合)。First, the channel is sparse in the time domain, that is, there are path sets at some moments and no path sets at some moments. As shown in Figure 6, the time-domain discrete sparse channel model generated by the superimposed Rayleigh channel model (at this time, the channel length L=60, and the number of non-zero tap points of the channel in the time domain m=5, that is, there are only 5 path sets in time).
其次，在存在路径集合的时刻(比如某个时刻总共汇聚了10条路径)，由于毫米波的一些特性(毫米波通信频率高、波长短，遇到阻挡就被反射或被阻断，以直射方式传播，波束窄，具有良好的方向性)，这10条路径可能来自一个或较少的角域区域，故其在角度域也是稀疏的。Secondly, when there is a collection of paths (for example, a total of 10 paths are gathered at a certain moment), due to some characteristics of millimeter waves (millimeter wave communication frequency is high and wavelength is short, it will be reflected or blocked when it encounters obstacles, and direct transmission propagation, narrow beam, and good directivity), these 10 paths may come from one or less angular domain areas, so they are also sparse in the angular domain.
具体的，将式(15)代入(18)得：Specifically, substitute formula (15) into (18) to get:
设计模型的信道估计方法与建立模型同等重要。目前，用于学习多径无线信道的最流行最广泛的一种方法是用接收机已知的信令波形(称为训练波形)来探测信道并处理相应的信道输出以估计信道参数。这种基于训练的信道估计方法的性能一般以假设的原始信道和根据接收信号和发送信号估计信道的均方误差(Mean squared error，MSE)来评判。因此，基于训练的信道估计方案有两个显著的特征：感知和重建。感知是指探测信道的训练波形的设计，而重建是在接收器处得到相应信道输出以恢复信道响应的问题。Designing the channel estimation method of the model is as important as building the model. Currently, the most popular and widespread method for learning multipath wireless channels is to use the known signaling waveforms (called training waveforms) of the receiver to detect the channel and process the corresponding channel output to estimate the channel parameters. The performance of this training-based channel estimation method is generally judged by the assumed original channel and the mean squared error (Mean squared error, MSE) of the estimated channel according to the received signal and the transmitted signal. Therefore, training-based channel estimation schemes have two salient features: perception and reconstruction. Sensing refers to the design of training waveforms to probe the channel, while reconstruction is the problem of obtaining the corresponding channel output at the receiver to recover the channel response.
然而，传统的信道估计方法会导致稀疏多径信道中能量和带宽的关键通信资源过度利用。因此，传统有许多基于训练的方法来估计单天线和多天线稀疏多径信道，而这些类似的研究缺乏对所提出的方法的性能的定量理论分析。相比之下，通过利用压缩感知(Compressed sensing，CS)理论的关键思想和基于训练的信道估计方法更有效。However, traditional channel estimation methods lead to overutilization of energy and bandwidth, critical communication resources in sparse multipath channels. Therefore, there are traditionally many training-based methods to estimate single-antenna and multi-antenna sparse multipath channels, and these similar studies lack quantitative theoretical analysis on the performance of the proposed methods. In contrast, it is more effective by utilizing the key ideas of Compressed Sensing (CS) theory and training-based channel estimation methods.
另外，利用时域和角度域的双稀疏性，便可只在某些角度域方向(这些角度域有路径集合)上放导频，而又因为毫米波的角度域具有很强的稀疏性，故利用时域角度域双稀疏多径信道的模型，导频开销可大大减小，信道估计的复杂度大大降低。另外，由于只在有路径集的角度域方向上放导频，故较少的噪声混入，使信道的估计性能也会大幅提升。用双稀疏多径信道模型进行估计，不仅去除了时域上的噪声，同时也过滤掉了角度域的噪声。In addition, by using the double sparsity of the time domain and angle domain, pilots can only be placed in certain angle domain directions (these angle domains have path sets), and because the millimeter wave angle domain has strong sparsity, Therefore, using the dual-sparse multipath channel model in the time domain and angle domain, the pilot overhead can be greatly reduced, and the complexity of channel estimation can be greatly reduced. In addition, since the pilot is only placed in the direction of the angle domain with the path set, less noise is mixed in, and the channel estimation performance is also greatly improved. Estimating with a dual sparse multipath channel model not only removes the noise in the time domain, but also filters out the noise in the angle domain.
本发明中一种基于双稀疏多径信道模型的信道估计方法，如图7所示，包括以下步骤：A kind of channel estimation method based on double sparse multipath channel model among the present invention, as shown in Figure 7, comprises the following steps:
步骤S1，初始化MIMO信道的角域表示矩阵，并引入时间波动。Step S1, initialize the angular domain representation matrix of the MIMO channel, and introduce time fluctuations.
具体地，首先假设有16副发射天线和8副接收天线，信道长度为60，时域稀疏度为5(即只有5个时刻有路径集合)，角域稀疏度为3。利用matlab产生16x8x60的全零矩阵Ha(含义同公式17中的Ha)，再用matlab产生3x5个正态分布的随机数，矩阵Ha的第一第二个维度表示角域，第三个维度表示时域，随机的选出5个时刻，每个时刻放3个数据，且每个时刻的3个数据的存放位置是相同的。因为角度通常比时域增益慢的多的时间尺度变化，因此，在所研究的时间尺度内，可以合理的假定路径不会从一个角域区域变化到另一个角域区域。Specifically, it is first assumed that there are 16 transmitting antennas and 8 receiving antennas, the channel length is 60, the sparsity in the time domain is 5 (that is, there are only 5 paths in time), and the sparsity in the angular domain is 3. Use matlab to generate a 16x8x60 all-zero matrix Ha (the meaning is the same as Ha in formula 17), and then use matlab to generate 3x5 normally distributed random numbers. The first and second dimensions of the matrix Ha represent the angle domain, and the third Dimensions represent the time domain, 5 moments are randomly selected, and 3 data are stored at each moment, and the storage locations of the 3 data at each moment are the same. Because angles typically vary on a much slower timescale than temporal gain, it is therefore reasonable to assume that paths do not change from one angular region to another over the timescales studied.
步骤S2，基于压缩感知的时域稀疏的估计:公式(16)且Ur,Ut都为酉矩阵，而酉矩阵的共轭转置和它的逆矩阵相等，所以得到时域信道表示，并用压缩感知理论高概率恢复时域信道Step S2, estimation of time domain sparsity based on compressed sensing: formula (16) And Ur , Ut are both unitary matrices, and the conjugate transpose of unitary matrix is equal to its inverse matrix, so Get the time-domain channel representation, and use compressed sensing theory to recover the time-domain channel with high probability
ha指的是某一时刻的角域表示，即Ha(τj)，见公式(18)，因此，可将假设的角域表示转化成信道的时域表示，并将h向量化；需要指出的是这里的h仅为某一时刻的，其它时刻同理，加入循环即可。最后得到128x60的矩阵(16x8＝128，表示128个信道，60指的是信道长度)，并针对某一个信道利用压缩感知理论高概率恢复时域信道其它信道同理，加入循环即可。ha refers to the angular domain representation at a certain moment, that is, Ha (τj ), see formula (18), therefore, the assumed angular domain representation can be transformed into the time domain representation of the channel, and h is vectorized; It should be pointed out that h here is only for a certain moment, and the same is true for other moments, just add a loop. Finally, a 128x60 matrix (16x8=128, representing 128 channels, 60 refers to the channel length) is obtained, and the compressed sensing theory is used to restore the time domain channel with high probability for a certain channel The same is true for other channels, just add a loop.
下面为利用压缩感知理论高概率恢复时域信道的具体步骤(此属于现有技术已知的)：The following are specific steps for recovering the time-domain channel with high probability using compressed sensing theory (this is known in the prior art):
利用压缩感知理论高概率恢复时域信道时，用到了OFDM技术。OFDM技术将无线传输信道分成若干个相互正交的子信道，使得每个子信道的频谱都呈现近似平坦的特性，从而可以有效的克服频率选择性衰落。另外OFDM技术采用循环前缀(Cyclic prefix，CP)作为保护间隔(Guard Interval)，使保护间隔大于信道的最大时延扩展，可以避免由多径效应引起的符号间干扰。OFDM technology is used when compressive sensing theory is used to restore the time-domain channel with high probability. OFDM technology divides the wireless transmission channel into several mutually orthogonal sub-channels, so that the frequency spectrum of each sub-channel presents an approximately flat characteristic, which can effectively overcome frequency selective fading. In addition, the OFDM technology uses a cyclic prefix (CP) as a guard interval (Guard Interval), so that the guard interval is greater than the maximum delay extension of the channel, which can avoid inter-symbol interference caused by multipath effects.
1)时域到频域的转换1) Conversion from time domain to frequency domain
对于任意一个信道hgk(表示第k副发送天线到第g副接收天线)，时域有ygk＝hgk(t)*xk(τ-t)+w，0≤t≤LFor any channel hgk (representing the kth transmitting antenna to the gth receiving antenna), the time domain has ygk = hgk (t)*xk (τ-t)+w, 0≤t≤L
ygk为第g副接收天线接收到的信号(由天线k发送)，*表示卷积，xk为第k副发送天线的发送数据。w为传输过程中的噪音，一般为高斯白噪声。L为信道长度。ygk is the signal received by the gth receiving antenna (sent by antenna k), * means convolution, and xk is the transmitted data of the kth transmitting antenna. w is the noise in the transmission process, generally Gaussian white noise. L is the channel length.
将其转换到频域即：Ygk＝XkHgk+W(21)Convert it to the frequency domain: Ygk = Xk Hgk + W(21)
2)在MIMO-OFDM系统中放导频2) Put the pilot in the MIMO-OFDM system
在子载波个数为N的OFDM系统中，假设OFDM符号的循环前缀(CP)长度不小于信道长度(L)。OFDM中第i个发送数据为x(i),(i＝1,2,3,...N-1)。为避免干扰，发送天线之间的导频位置正交，如图8所示(图8中示意的就是导频位置正交的信息)。在OFDM符号的N个子载波中，有p个用于放置导频，Ψ＝(es1,es2,......esp)为p×N的导频选择矩阵，si(i＝1,2,3,...p)表示第i个导频的位置，esi是长度为N的列向量，它的第si个元素为1，其它元素全为0。则式(21)中，In an OFDM system with N subcarriers, it is assumed that the length of the cyclic prefix (CP) of the OFDM symbol is not less than the channel length (L). The i-th transmission data in OFDM is x(i), (i=1, 2, 3,...N-1). In order to avoid interference, the pilot positions between the transmitting antennas are orthogonal, as shown in FIG. 8 (the information in FIG. 8 is the orthogonality of the pilot positions). Among the N subcarriers of the OFDM symbol, p are used to place pilots, Ψ=(es1 , es2 ,...esp ) is a p×N pilot selection matrix, si (i =1,2,3,...p) indicates the position of the i-th pilot, esi is a column vector with length N, its si -th element is 1, and other elements are all 0. In formula (21),
Ygk＝[Ygk(0),Ygk(1)......Ygk(N-1)]，Xk＝[xk(0),xk(1)......xk(N-1)]Ygk ＝[Ygk (0), Ygk (1)...Ygk (N-1)], Xk ＝[xk (0), xk (1)..... .xk (N-1)]
Hgk＝FN×Lhgk为信道频域响应采样值，其中FN×L为部分DFT变换矩阵，由N维DFT变换矩阵的前L列构成。W是一个方差为σ2的N维加性复高斯白噪声向量。将导频选择矩阵Ψ作用于(20)式两端，可得：Hgk =FN×L hgk is the channel frequency domain response sampling value, where FN×L is a part of the DFT transformation matrix, consisting of the first L columns of the N-dimensional DFT transformation matrix. W is an N-dimensional additive complex Gaussian white noise vector with varianceσ2 . Applying the pilot selection matrix Ψ to both ends of Equation (20), we can get:
Ygk_p＝Xg_pFphgk+Wp (22)Ygk_p ＝Xg_p Fp hgk +Wp (22)
其中，Ygk_p＝ΨYgk,Wp＝ΨW均为p维列向量，分别为接收到的导频信号及其对应的信道噪声。Xk_p＝ΨXΨT为p×p的对角阵，对角线上的元素为发送端的p个导频。Fp＝ΨFN×L为p×L的矩阵。Wherein, Ygk_p =ΨYgk , Wp =ΨW are both p-dimensional column vectors, which are respectively the received pilot signal and its corresponding channel noise. Xk_p =ΨXΨT is a p×p diagonal matrix, and the elements on the diagonal are p pilots of the transmitting end. Fp =ΨFN×L is a p×L matrix.
令T＝Xt_pFp，则式(22)可写为：Let T=Xt_p Fp , then formula (22) can be written as:
Ygk_p＝Thgk+Wp (23)Ygk_p =Thgk +Wp (23)
其中，T是p×L矩阵，hgk表示第k副发送天线到第g副接收天线的信道时域冲击响应，在无线通信中呈现稀疏性。由于Yik_p,Xi_p,Fp在发送端和接收端是已知的，因此可以利用稀疏度已知的重构算法根据Ygk_p高概率恢复hgk。稀疏度已知的重构算法属于现有技术，具体计算过程如下：Among them, T is a p×L matrix, and hgk represents the time domain impulse response of the channel from the kth transmitting antenna to the gth receiving antenna, which presents sparsity in wireless communication. Since Yik_p ,Xi_p , and Fp are known at the sending end and receiving end, a reconstruction algorithm with known sparsity can be used to restore hgk according to Ygk_p with high probability. The reconstruction algorithm with known sparsity belongs to the existing technology, and the specific calculation process is as follows:
根据式(23),输入：Ygk_p：接收导频信号；T:恢复矩阵；m：信道时域的稀疏度；According to formula (23), input: Ygk_p : received pilot signal; T: recovery matrix; m: sparsity of channel time domain;
初始化：残差r0＝Ygk_p，索引集Λ0＝O，迭代次数i＝1,Γ0＝O,这里O表示空集；Initialization: residual r0 =Ygk_p , index set Λ0 =O, number of iterations i=1, Γ0 =O, where O represents an empty set;
第i次迭代过程如下：The i-th iteration process is as follows:
(1)残差ri-1与恢复矩阵T中的每列进行匹配，找出相关程度最高的列，由于两个向量内积越大，相关程度越高，故利用内积得残差与恢复矩阵相关性最高的列的索引为：τj为矩阵T的第j列；(1) The residual ri-1 is matched with each column in the recovery matrix T to find the column with the highest correlation. Since the inner product of the two vectors is larger, the correlation is higher, so the residual and The index of the most correlated column of the recovery matrix is: τj is the jth column of matrix T;
(2)更新Λi＝{Λi-1∪λi},Γi＝Γi-1∪τλi；(2) Update Λi ＝{Λi-1 ∪λi }, Γi ＝Γi-1 ∪τλi ;
(3)利用LS算法获得新的信道估计值：其中表示Γi的伪逆；(3) Use the LS algorithm to obtain a new channel estimate: in Represents the pseudo-inverse of Γi ;
(4)计算新的残差值：(4) Calculate the new residual value:
(5)i＝i+1,令矩阵T的第λi列为0向量,λi由步骤(1)得出。(5) i=i+1, let the λi column of the matrix T be a 0 vector, and λi is obtained from step (1).
(6)从步骤(1)开始循环。(6) Cycle from step (1).
终止循环条件：当i>＝m时，终止迭代。Termination loop condition: when i>=m, the iteration is terminated.
输出：信道估计值并将其转换成nr×nt的矩阵形式，即估计得到的时域信道Output: channel estimate And convert it into nr × nt matrix form, that is, the estimated time-domain channel
此实施例中仅以一个信道为例，其它信道同理，在仿真中加入循环即可。In this embodiment, only one channel is taken as an example, and the same is true for other channels, just add a loop in the simulation.
在MIMO—OFDM系统中导频即可以放在频域，也可以直接放在角域。为说明方便本发明将导频放在频域。将导频放在角域，对于实际中的大规模MIMO系统，能减少开销。比如测出某些角域区域中含有路径集合，只需在这些含有路径集合的角域区域中放置导频即可。根据毫米波传输的特性，只有很少的角域区域含有路径集合。因此导频的数量相对就比较少，估计的流程和上述的流程相似，都是在时域和角域双重去噪，提高信道估计的性能。In the MIMO-OFDM system, the pilot can be placed in the frequency domain or directly in the angle domain. For the convenience of description, the present invention puts the pilot frequency in the frequency domain. Putting the pilot frequency in the angular domain can reduce the overhead for the actual massive MIMO system. For example, if it is detected that some angular domain areas contain path sets, it is only necessary to place pilots in these angular domain areas containing path sets. According to the characteristics of mmWave transmission, only a few angular domain areas contain path sets. Therefore, the number of pilots is relatively small, and the estimation process is similar to the above-mentioned process, which is double denoising in the time domain and angle domain to improve the performance of channel estimation.
步骤S3，基于压缩感知的角度域稀疏的估计:根据式(20)向量化，再利用压缩感知理论高概率恢复出角域表示的MIMO信道Step S3, estimation of angle domain sparseness based on compressed sensing: according to formula (20) Vectorization, and then use the compressed sensing theory to restore the MIMO channel represented by the angle domain with high probability
其中表示估计值。in Indicates estimated value.
1)将向量化，以符合使用重构算法的条件。1) Will Vectorized to qualify for use with reconstruction algorithms.
根据其中为两者的克罗克内积，将向量化：according to in is the Crock inner product of the two, the Vectorization:
其中(·)*表示复共轭 where (·)* represents the complex conjugate
记：remember:
由于本专利中讨论的天线是临界间隔的，即角域窗口与角域基矢量为一一对应关系，也就是说，角域量化的网格数等于接收天线数nt乘以发射天线数nr。Since the antennas discussed in this patent are critically spaced, i.e. There is a one-to-one correspondence between the angle domain window and the angle domain base vector, that is to say, the grid number of angle domain quantization is equal to the number nt of receiving antennas multiplied by the number nr of transmitting antennas.
2)用压缩感知的重构算法高概率恢复出角域稀疏信道2) Use the reconstruction algorithm of compressed sensing to restore the sparse channel in the angle domain with high probability
由于角域具有稀疏性，故角域信道估计问题也可规划为稀疏信号的重建问题。即：g＝Af，由于g,A是已知的，且f是稀疏的，故可用压缩感知的重构算法高概率恢复出f。最后，将向量f转化为nr×nt的矩阵形式，即得到估计的角域表示的MIMO信道Due to the sparseness of the angle domain, the channel estimation problem in the angle domain can also be formulated as a sparse signal reconstruction problem. That is: g=Af, since g and A are known, and f is sparse, f can be recovered with a high probability using the reconstruction algorithm of compressed sensing. Finally, the vector f is transformed into an nr ×nt matrix form, that is, the MIMO channel represented by the estimated angular domain is obtained
上述使用的压缩感知重构算法同上述稀疏度已知的重构算法。其它时域非零抽头点处的角域估计同理。The compressed sensing reconstruction algorithm used above is the same as the above reconstruction algorithm with known sparsity. The angle domain estimation at other time domain non-zero tap points is the same.
步骤S4，利用NMSE测量双稀疏多径信道模型估计性能。Step S4, using NMSE to measure the estimation performance of the dual-sparse multipath channel model.
如图9展示了本发明双稀疏信道与现有技术中只考虑时域稀疏的信道估计性能对比图。图中，横坐标为信噪比(signal-noise ratio，SNR，其计量单位是dB)，通过改变噪声(根据实际情况，一般假设为高斯白噪声)的功率来改变信噪比，信号的功率一般是固定的；纵坐标表示最初假设信道与最后估计出的信道的归一化的均方误差(Normalized mean-square error，NMSE，计算方法是其中H表示假设的信道，表示估计得出的信道)，并将其换成以dB为单位，10*log10(NMSE)。MIMO信道为假设有16副发射天线和16副接收天线，天线为临界间隔，信道长度为60。假设时域稀疏度为5，角度域稀疏度为3。带有*的折线表示的是本发明双稀疏多径信道的估计性能，即同时考虑了时域稀疏和角域的稀疏性。带有的折线表示传统时域稀疏多径信道的估计性能，即此种情况仅考虑了时域的稀疏性。由于毫米波在时域和角度域的双稀疏性，即在时域，仅有某几个时刻是有信息的，但在传输的过程中，其他时刻也会收到‘信息’，而这些信息即所谓的噪声。用本发明介绍的基于压缩感知的信道估计算法，利用其稀疏性，很好的抑制了噪声。同理在某一时刻，仅有几个角度区域是有信息的，同样，其他的角度区域在接收端也会收到‘信息’，而这些信息也是传输过程中的噪声。利用基于压缩感知的信道估计算法，利用其稀疏性，也能很好的抑制来自其他方向的噪声。也就是说，在进行信道估计时，考虑信道传输时时域和角度域的双稀疏性，进行两次去噪，必然比传统的仅考虑时域稀疏的信道估计方法抑制噪声的能力强。即使在稀疏度未知的情况下，双稀疏多径信道的估计性能也表现较好，能够高概率的恢复出原始信号，具有更强的抑制噪声的能力。FIG. 9 shows a performance comparison between the dual-sparse channel of the present invention and the channel estimation performance of the prior art that only considers time-domain sparseness. In the figure, the abscissa is the signal-noise ratio (signal-noise ratio, SNR, the unit of measurement is dB), the signal-to-noise ratio is changed by changing the power of the noise (according to the actual situation, it is generally assumed to be Gaussian white noise), and the power of the signal It is generally fixed; the ordinate represents the normalized mean square error (Normalized mean-square error, NMSE, of the initially assumed channel and the final estimated channel, the calculation method is where H represents the hypothesized channel, represents the estimated channel), and replace it in dB, 10*log10(NMSE). The MIMO channel assumes that there are 16 transmitting antennas and 16 receiving antennas, the antennas are critically spaced, and the channel length is 60. Assume that the time domain sparsity is 5 and the angle domain sparsity is 3. The broken line with * represents the estimation performance of the dual-sparse multipath channel of the present invention, that is, the sparsity in the time domain and the sparsity in the angle domain are considered at the same time. with The broken line of represents the estimated performance of the traditional sparse multipath channel in the time domain, that is, only the sparsity in the time domain is considered in this case. Due to the double sparsity of the millimeter wave in the time domain and the angle domain, that is, in the time domain, only certain moments have information, but in the process of transmission, other moments will also receive 'information', and these information That is the so-called noise. The channel estimation algorithm based on compressed sensing introduced by the present invention utilizes its sparsity to suppress noise well. Similarly, at a certain moment, only a few angle areas have information. Similarly, other angle areas will also receive 'information' at the receiving end, and this information is also noise in the transmission process. Using the channel estimation algorithm based on compressed sensing and its sparsity, it can also suppress the noise from other directions very well. That is to say, when performing channel estimation, considering the double sparsity in the time domain and angle domain during channel transmission, and performing two denoising, it is bound to have a stronger ability to suppress noise than the traditional channel estimation method that only considers time domain sparsity. Even when the sparsity is unknown, the estimation performance of the dual-sparse multipath channel is better, and the original signal can be recovered with a high probability, and it has a stronger ability to suppress noise.
以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明技术原理的前提下，还可以做出若干改进和变型，这些改进和变型也应视为本发明的保护范围。The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the technical principles of the present invention, some improvements and modifications can also be made. These improvements and modifications It should also be regarded as the protection scope of the present invention.
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810761934.5ACN109005133B (en) | 2018-07-12 | 2018-07-12 | Double sparse multipath channel model and channel estimation method based on this model |
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810761934.5ACN109005133B (en) | 2018-07-12 | 2018-07-12 | Double sparse multipath channel model and channel estimation method based on this model |
| Publication Number | Publication Date |
|---|---|
| CN109005133Atrue CN109005133A (en) | 2018-12-14 |
| CN109005133B CN109005133B (en) | 2021-04-16 |
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810761934.5AActiveCN109005133B (en) | 2018-07-12 | 2018-07-12 | Double sparse multipath channel model and channel estimation method based on this model |
| Country | Link |
|---|---|
| CN (1) | CN109005133B (en) |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110099016A (en)* | 2019-05-14 | 2019-08-06 | 东南大学 | A kind of sparse front channel estimation methods of millimeter wave based on deep learning network |
| CN111385006A (en)* | 2018-12-27 | 2020-07-07 | 财团法人工业技术研究院 | mmWave channel estimation method |
| CN111049767B (en)* | 2019-12-16 | 2021-01-15 | 西安交通大学 | Data detection method for sparse orthogonal frequency division multiplexing amplification forwarding (OFDM-AF) system |
| CN112422458A (en)* | 2019-08-23 | 2021-02-26 | 中兴通讯股份有限公司 | Channel estimation method, apparatus and computer storage medium |
| CN112448750A (en)* | 2019-08-27 | 2021-03-05 | 三星电子株式会社 | System and method for providing channel recovery for angle domain sparse channels |
| CN114553643A (en)* | 2022-04-24 | 2022-05-27 | 杭州电子科技大学 | A Channel Estimation Method for Millimeter-Wave Smart Metasurfaces Based on Cooperative Sensing on Two Time Scales |
| CN115243255A (en)* | 2022-05-31 | 2022-10-25 | 北京邮电大学 | Authentication method, device, electronic device and storage medium based on compressed sensing |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040179627A1 (en)* | 2002-10-25 | 2004-09-16 | Ketchum John W. | Pilots for MIMO communication systems |
| CN104052691A (en)* | 2014-07-02 | 2014-09-17 | 东南大学 | Channel Estimation Method for MIMO-OFDM System Based on Compressed Sensing |
| CN105656819A (en)* | 2016-03-21 | 2016-06-08 | 电子科技大学 | Self-adaptive channel estimation method based on compressed sensing and large-scale MIMO |
| CN106506415A (en)* | 2016-11-25 | 2017-03-15 | 重庆邮电大学 | A method for channel estimation in a multi-user MIMO‑OFDM system |
| CN106656874A (en)* | 2017-01-10 | 2017-05-10 | 河海大学 | Mobile OFDM system channel estimation method based on compressed sensing |
| CN108259397A (en)* | 2018-01-12 | 2018-07-06 | 东北大学 | Extensive mimo system channel estimation based on adaptive regularization subspace tracking compressed sensing algorithm |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040179627A1 (en)* | 2002-10-25 | 2004-09-16 | Ketchum John W. | Pilots for MIMO communication systems |
| CN104052691A (en)* | 2014-07-02 | 2014-09-17 | 东南大学 | Channel Estimation Method for MIMO-OFDM System Based on Compressed Sensing |
| CN105656819A (en)* | 2016-03-21 | 2016-06-08 | 电子科技大学 | Self-adaptive channel estimation method based on compressed sensing and large-scale MIMO |
| CN106506415A (en)* | 2016-11-25 | 2017-03-15 | 重庆邮电大学 | A method for channel estimation in a multi-user MIMO‑OFDM system |
| CN106656874A (en)* | 2017-01-10 | 2017-05-10 | 河海大学 | Mobile OFDM system channel estimation method based on compressed sensing |
| CN108259397A (en)* | 2018-01-12 | 2018-07-06 | 东北大学 | Extensive mimo system channel estimation based on adaptive regularization subspace tracking compressed sensing algorithm |
| Title |
|---|
| DANIEL C. ARAUJO等: "《Compressive Sensing Based Channel Estimation for Massive MIMO Systems with Planar Arrays》", 《2015 IEEE 6TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP)》* |
| 杨亮等: "《基于压缩感知的MIMO-OFDM系统的信道估计》", 《通信技术》* |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111385006A (en)* | 2018-12-27 | 2020-07-07 | 财团法人工业技术研究院 | mmWave channel estimation method |
| CN110099016A (en)* | 2019-05-14 | 2019-08-06 | 东南大学 | A kind of sparse front channel estimation methods of millimeter wave based on deep learning network |
| CN110099016B (en)* | 2019-05-14 | 2022-05-31 | 东南大学 | A channel estimation method for millimeter-wave sparse fronts based on deep learning networks |
| CN112422458A (en)* | 2019-08-23 | 2021-02-26 | 中兴通讯股份有限公司 | Channel estimation method, apparatus and computer storage medium |
| CN112448750A (en)* | 2019-08-27 | 2021-03-05 | 三星电子株式会社 | System and method for providing channel recovery for angle domain sparse channels |
| US12119917B2 (en) | 2019-08-27 | 2024-10-15 | Samsung Electronics Co., Ltd | System and method for providing channel recovery for angle domain sparse channels |
| CN111049767B (en)* | 2019-12-16 | 2021-01-15 | 西安交通大学 | Data detection method for sparse orthogonal frequency division multiplexing amplification forwarding (OFDM-AF) system |
| CN114553643A (en)* | 2022-04-24 | 2022-05-27 | 杭州电子科技大学 | A Channel Estimation Method for Millimeter-Wave Smart Metasurfaces Based on Cooperative Sensing on Two Time Scales |
| CN114553643B (en)* | 2022-04-24 | 2022-08-02 | 杭州电子科技大学 | A Channel Estimation Method for Millimeter-Wave Smart Metasurfaces with Cooperative Sensing on Two Time Scales |
| CN115243255A (en)* | 2022-05-31 | 2022-10-25 | 北京邮电大学 | Authentication method, device, electronic device and storage medium based on compressed sensing |
| Publication number | Publication date |
|---|---|
| CN109005133B (en) | 2021-04-16 |
| Publication | Publication Date | Title |
|---|---|---|
| CN109005133B (en) | Double sparse multipath channel model and channel estimation method based on this model | |
| CN108964726B (en) | Low-complexity large-scale MIMO uplink transmission channel estimation method | |
| CN104052691B (en) | MIMO-OFDM system channel estimation method based on compressed sensing | |
| CN103560985B (en) | Space-time correlated channel massive MIMO transmission method | |
| CN104698430B (en) | It is a kind of for carrying the high-precision angle estimating method based on virtual antenna array | |
| CN106559367A (en) | MIMO ofdm system millimeter wave channel estimation methods based on low-rank tensor resolution | |
| CN102160346B (en) | Methods for precoding signals for transmission in wireless mimo system | |
| CN107276646B (en) | Massive MIMO-OFDM Uplink Iterative Detection Method | |
| CN106506415B (en) | A method for channel estimation in multi-user MIMO-OFDM systems | |
| CN108881076A (en) | A kind of compressed sensing based MIMO-FBMC/OQAM system channel estimation method | |
| CN106341169B (en) | An Uplink Antenna Selection Method for Multi-user Massive MIMO System | |
| CN107171985B (en) | Channel estimation method and system | |
| CN110212951B (en) | A Massive MIMO Channel Estimation Method Based on Butler Matrix | |
| CN108964725A (en) | The sparse estimation method of channel parameter in the extensive MIMO network of time-varying | |
| CN118316486A (en) | Channel knowledge map construction method, device, equipment, medium and program product | |
| CN104168047A (en) | Single-ended time domain beam searching method based on compressed sensing | |
| CN103475603B (en) | Communication system blind channel estimation method based on S order parameter non-orthogonal transformation | |
| CN114221838B (en) | Channel estimation method and system using channel conjugate data in large-scale MIMO system | |
| CN104168046A (en) | Single-ended frequency domain beam searching method based on compressed sensing | |
| Aquino et al. | A Review of Direction of Arrival Estimation Techniques in Massive MIMO 5G Wireless Communication Systems | |
| CN104218984B (en) | Using the both-end frequency domain beam search method of compressed sensing | |
| CN104639473B (en) | A kind of mimo channel method of estimation based on fully-complementary sequence and compressed sensing | |
| CN106911367A (en) | The extensive mimo channel method of estimation of multiple cell and device based on iterative interference cancellation | |
| CN103873127A (en) | Method for rapidly generating block matrix in self-adaptive beam forming process | |
| CN116248210A (en) | Method, system and medium for predicting large-scale multiple-input multiple-output system channel |
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |