Energy-efficient joint transmit beamforming and subarray selection with non-linear power amplifier efficiency

Abstract

Another important fact arising from the use of large numbers of antennas is the limited numbers of RF chains, i.e., the latter may be smaller than the former. This means that the beamforming gain and the number of parallel streams becomes limited. However, huge numbers of antenna elements can be installed in the transmitter in particular at higher center frequencies, like mm-waves [11]. The same has also been proposed for more conventional microwave frequencies below 10 GHz [11]. One option to benefit from the large number of antenna elements with a smaller number of transceiver processing chains to achieve array gain is to divide the antennas into subarrays each of which is connected to an RF chain. In general, the number of RF chains may be smaller than that of subarrays. This kind of system model is called hybrid beamforming [12] which becomes very relevant in mm-wave systems. In addition to enable hybrid beamforming, the model results in smaller power variations between antennas, which means that the non-linear effects of the power amplifiers become less significant. Such antenna grouping could be used even in the case with conventional antenna selection problem, where we could group the antennas and select the sub-groups just to simplify the antenna selection problem.In this paper, we consider the energy efficiency with joint beamforming and subarray selection (JBSAS) and non-linear efficiency of PA in multiuser multiple-input single-output (MISO) system. This is different and more practical system compared to the conventional joint beamforming and antenna selection problem considered in [9] where each antenna is individually connected with an RF chain (using a switch). In addition, here we consider non-linear PA efficiency whereas the linear case has been assumed in the prior works. To tackle the resulting challenging mixed-Boolean non-convex optimization problem, we rely on continuous relaxation and successive convex approximation framework where a convex problem is solved in each iteration. Numerical results demonstrate the achieved energy efficiency gains of the subarray selection and shows that non-linear PA efficiency has a significant impact on the optimization. We also observe that on contrast to using linear PA efficiency model, the nonlinear PA efficiency model yields the fact that it is better to stay silent rather than transmit with very low transmit power.Notations: X T is transpose of X; |x| represents the absolute value of x and x 2 is 2-norm of x; Im(X) means the imaginary part of X. PROBLEM FORMULATION System ModelWe consider a single-cell MISO downlink channel, where a base station with N antenna elements transmits data to K single-antenna ABSTRACTWe study the problem of energy efficiency maximization (EEmax) with joint beamforming and subarray selection, by taking into account the non-linear power amplifier (PA) efficiency in a multi-user multiple-input single-output system. The subarray selection problem is formulated using the concept of perspective formulation with additional penalty t...

Energy Efficiency Fairness for Multi-Pair Wireless-Powered Relaying Systems

“…We focus on the nonconvex convexity induced by (19), (22), (25d), and (46b). Again, by using the change of variables in Section III-B1 and introducing additional variables, we transform (46) into the following equivalent problem minimizẽ q,w,r,τ ,η v,s,u,t,zη…”

“…However, signal processing power is often rate-dependent [19] and PAs' efficiency depends on output power level [20]. It has been demonstrated that such aspects may have significant impacts on the network level EE performances [21], [22].…”

“…minimizẽ p,w,r,τ,ηη (46a) subject to f EE,TW k (τ,p,r) ≥η −1 , ∀k ∈ K (46b)(19),(22), (25b), (25c), (25d).…”

Energy-efficient transmission strategies for CoMP downlink—overview, extension, and numerical comparison

“…bu }) is some feasible point of (24). As a result, we arrive at the approximate convex program at iteration n as maximize v,η,z,t,{g bu } η subject to {(4), (5), (24c), (24d), (25), (26)}.…”

“…However, in practice, PA efficiency is highly dependent on the output power region and the employed PA type. To account this, the non-linear power consumption models of PAs have been introduced [21][22][23][24] in which the PA efficiency of RF chain m at BS b is expressed as…”