Uplink

sionna.sys.open_loop_uplink_power_control(pathloss,num_allocated_subcarriers,alpha=1.0,p0_dbm=-90.0,ut_max_power_dbm=26.0,precision=None)[source]

Implements an open-loop uplink power control procedure inspired by 3GPP TS38.213, Section 7.1.1[3GPP38213].

For each user, the uplink transmission power\(P^{\mathrm{UL}}\)is computed as:

\[P^{\mathrm{UL}} = \min \{ P_0 + \alpha PL + 10 \log_{10}(\mathrm{\#PRB}), \ P^{\mathrm{max}}\} \quad [\mathrm{dBm}]\]

where\(P^{\mathrm{max}}\) is the maximum power,\(P_0\) [dBm] isthe target received power per Physical Resource Block (PRB),\(PL\) isthe pathloss and\(\alpha\in [0,1]\) is the pathloss compensation factor.

Note that if\(\alpha=1\), the pathloss is fully compensated and thepower per PRB received by the base station equals\(P_0\) [dBm], assuming\(P^{\mathrm{max}}\) is not reached. Lower values of\(\alpha\) can helpreducing interference caused to neighboring cells.

With respect to 3GPP TS 38.213, additional factors such asclosed-loop control and transport format adjustments are here ignored

Input:

• pathloss ([…, num_ut],tf.float) – Pathloss for each user relative to the serving base station, in linear scale

• num_allocated_subcarriers ([…, num_ut]) – Number of allocated subcarriers for each user

• alpha ([…, num_ut],tf.float |float (default: 1.0)) – Pathloss compensation factor. If afloat, the same value isapplied to all users.

• p0_dbm ([…, num_ut],tf.float |float (default: -90.0)) – Target received power per PRB. If afloat, the same value isapplied to all users.

• ut_max_power_dbm ([…, num_ut],tf.float |float (default: 26.0)) – Maximum transmit power [dBm] for each user. If afloat, the samevalue is applied to all users.

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

Output:

tx_power_per_ut ([…, num_ut],tf.float) – Uplink transmit power [W] for each user, across subcarriers, streamsand time steps

Example

importmatplotlib.pyplotaspltfromsionna.sysimportopen_loop_uplink_power_controlfromsionna.phyimportconfigfromsionna.phy.utilsimportdb_to_lin,watt_to_dbm# N. usersnum_ut=100# Max tx power per UTut_max_power_dbm=26# [dBm]# Pathloss [dB]pathloss_db=config.tf_rng.uniform([num_ut],minval=80,maxval=120)# N. allocated subcarriers per UTnum_allocated_subcarriers=tf.fill([num_ut],40)# Parameters (pathloss compensation factor, reference rx power)alpha_p0=[(1,-90),(.8,-75)]foralpha,p0,inalpha_p0:# Power allocationtx_power_per_ut=open_loop_uplink_power_control(db_to_lin(pathloss_db),num_allocated_subcarriers=num_allocated_subcarriers,alpha=alpha,p0_dbm=p0,ut_max_power_dbm=ut_max_power_dbm)# Plot CDF of tx powerplt.ecdf(watt_to_dbm(tx_power_per_ut),label=fr'$\alpha$={alpha}, $P_0$={p0} dBm')# Plot max UT powerplt.plot([ut_max_power_dbm]*2,[0,1],'k--',label='max UT power')plt.legend()plt.grid()plt.xlabel('Tx power [dBm]')plt.ylabel('Cumulative density function')plt.title('Uplink tx power distribution')plt.show()

Downlink

sionna.sys.downlink_fair_power_control(pathloss,interference_plus_noise,num_allocated_re,bs_max_power_dbm=56.0,guaranteed_power_ratio=0.5,fairness=0.0,return_lagrangian=False,precision=None,**kwargs)[source]

Allocates the downlink transmit power fairly across all users served by asingle base station (BS)

The maximum BS transmit power\(\overline{P}\) is distributed across usersby solving the following optimization problem:

\[\begin{split}\begin{align} \mathbf{p}^* = \operatorname{argmax}_{\mathbf{p}} & \, \sum_{u=1}^{U} g^{(f)} \big( r_u \log( 1 + p_u q_u) \big) \\ \mathrm{s.t.} & \, \sum_{u=1}^U r_u p_u = \overline{P} \\ & r_u p_u \ge \rho \frac{\overline{P}}{U} , \quad \forall \, u=1,\dots,U\end{align}\end{split}\]

where\(q_u\) represents the estimated channel quality, defined as theratio between the channel gain (being the inverse of pathloss) and theinterference plus noise ratio,\(r_u>0\) denotes the number of allocated resources, and\(p_u\) is the per-resource allocated power, for every user\(u\).

The parameter\(\rho\in[0;1]\) denotes the guaranteed power ratio; ifset to 1, the power is distributed uniformly across all users.

The fairness function\(g^{(f)}\) is defined as in[MoWalrand]:

\[\begin{split}\begin{align} g^{(f)}(x) = \left\{ \begin{array}{l} \log(x), \quad f=1 \\ \frac{x^{1-f}}{1-f}, \quad \forall\, f>0, \ f\ne 1. \end{array} \right.\end{align}\end{split}\]

When the fairness parameter\(f=0\), the sum of utilities\(\log( 1+ p_u q_u)\) is maximized, leading to a waterfilling-like solution(see, e.g.,[Tse]).As\(f\) increases, the allocation becomes increasinglyegalitarian. The case\(f=1\) maximizes proportional fairness;as\(f\to \infty\), the solution approaches a max-minallocation.

For optimal power allocations\(p^*_u>\frac{\overline{P}}{U r_u}\), theKarush-Kuhn-Tucker (KKT) conditions can be expressed as:

\[\big[ r_u \log (1+p^*_u q_u) \big]^f (1+p^*_u q_u) = q_u \mu^{-1}, \quad \forall \, u\]

where\(\mu\) is the Lagrangian multiplier associated with theconstraint on the total transmit power.

This function returns the optimal power allocation\(r_u p_u^*\) and thecorresponding utility\(r_u \log( 1 + p^*_u q_u)\), for each user\(u=1,\dots,U\).Ifreturn_lagrangian isTrue,\(\mu^{-1}\) is returned, too.

Input:

• pathloss ([…, num_ut],tf.float) – Pathloss for each user in linear scale

• interference_plus_noise ([…, num_ut],tf.float |float) – Interference plus noise [Watt] for each user. Iffloat, the samevalue is assigned to all users.

• num_allocated_re ([…, num_ut],tf.int32 |int) – Number of allocated resources to each user. Ifint, the samevalue is assigned to all users.

• bs_max_power_dbm ([…],tf.float |float (default: 56.)) – Maximum transmit power for the base station [dBm]. Iffloat, thesame value is assigned to all batches.

• guaranteed_power_ratio (float (default: 0.2)) – The power allocated to a user is guaranteed to exceed a portionguaranteed_power_ratio ofbs_max_power_dbm divided by the numberof scheduled users. Must be within [0;1].

• fairness (float (default: 0.)) – Fairness parameter. If 0, the sum of utilities ismaximized; when 1, proportional fairness is achieved. Asfairnessincreases, the optimal allocation approaches a max-min one.

• return_lagrangian (bool (default:False)) – IfTrue, the inverse of the optimal Lagrangian multipliermu_inv_star is returned

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

• kwargs (dict) – Additional inputs forbisection_method() used to compute the optimalpower allocation, such aseps_x,eps_y,max_n_iter,step_expand

Output:

• tx_power ([…, num_ut],tf.float) – Optimal downlink power allocation\(p_u^*\) [Watt] for each user\(u\)

• utility ([…, num_ut],tf.float) – Optimal utility for each user, computed as\(r_u \log( 1 + p^*_uq_u)\) for user\(u\)

• mu_inv_star ([…],tf.float) – Inverse of the optimal Lagrangian multiplier\(\mu\) associated with thetotal power constraint. Only returned ifreturn_lagrangian isTrue.

Example

importtensorflowastfimportnumpyasnpimportmatplotlib.pyplotaspltfromsionna.phyimportconfigfromsionna.phy.utilsimportdb_to_lin,dbm_to_wattfromsionna.sysimportdownlink_fair_power_controlconfig.seed=45# Evaluate the impact of 'fairness' and 'guaranteed_power_ratio'# parameters on the DL power allocation and utility# Guaranteed power ratiosguaranteed_power_ratio_vec=[0,.35,.7]# Fairness parametersfairness_vec=[0,1,2,5]# N. usersnum_ut=30# BS tx powerbs_max_power_dbm=56max_power_bs=dbm_to_watt(bs_max_power_dbm)# Interference plus noiseinterference_plus_noise=5e-10# [W]# Generate random pathlosspathloss_db=config.tf_rng.uniform([num_ut],minval=70,maxval=110)# [dB]pathloss=db_to_lin(pathloss_db)# Channel qualitycq=1/(pathloss*interference_plus_noise)fig,axs=plt.subplots(3,len(guaranteed_power_ratio_vec),figsize=(3.5*len(guaranteed_power_ratio_vec),8),sharey='row')fig.subplots_adjust(top=0.8)foraxinaxs.flatten():ax.yaxis.set_tick_params(labelbottom=True)ax.grid()ax.set_xlabel(r'User terminal $u$',fontsize=12)# Show channel quality in decreasing orderind_sort=np.argsort(cq)[::-1]axs[0,1].plot(10*np.log10(cq)[ind_sort],'.-')axs[0,1].set_ylabel(r'$q_u$ [dB]',fontsize=12)axs[0,1].set_title('Channel quality')forii,guar_ratioinenumerate(guaranteed_power_ratio_vec):# Guaranteed power for each userguaranteed_power=guar_ratio*max_power_bs/num_utforfairnessinfairness_vec:# DL fair power allocationtx_power,utility=downlink_fair_power_control(pathloss,interference_plus_noise=interference_plus_noise,num_allocated_re=1,bs_max_power_dbm=bs_max_power_dbm,guaranteed_power_ratio=guar_ratio,fairness=fairness)# Show utilityaxs[2,ii].plot(utility.numpy()[ind_sort],'.-',label=f'fairness ={fairness}')# Show transmit poweraxs[1,ii].plot(tx_power.numpy()[ind_sort],'.-',label=f'fairness ={fairness}')axs[1,ii].plot([0,num_ut-1],[guaranteed_power]*2,'--k',label='guaranteed power')axs[1,ii].set_ylabel(r'Power $r_u p^*_u$ [W]',fontsize=12)axs[1,ii].legend(fontsize=9)axs[2,ii].set_ylabel(r'Utility $r_u \log(1+p^*_u q_u)$',fontsize=12)axs[1,ii].set_title(f'Guaranteed power ratio ={guar_ratio}')fig.suptitle('Downlink fair power control',y=.98,fontsize=18)fig.tight_layout()fig.delaxes(axs[0,0])fig.delaxes(axs[0,2])plt.show()

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