MIMO Capacity with Per-Antenna Power Constraint

We study the design of linear precoders for secure transmission in the two-user multiple-input single-output (MISO) broadcast channel with confidential messages (BC-CM). The transmitter has multiple antennas, and each user has a single receive antenna. Two independent messages are simultaneously transmitted, one intended for each user, and each message should be kept confidential from the other user. Assuming real-valued transmitted signals, we design the linear precoders subject to total and per-antenna average power constraints, and also subject to amplitude constraints. In both cases, we tackle the design problem via weighted secrecy sum rate maximization. The resulting problem, however, involves a fractional objective, making it nonconvex and difficult to solve. Nevertheless, we show that this difficult problem can be transformed into a more tractable problem, for which a solution can be obtained by an iterative search algorithm. In addition, we characterize a condition under which the obtained solution is guaranteed to be optimal. Furthermore, we show that the problem formulation and solution approach can be easily extended to handle the robust version of the design problem with uncertain channel information. We provide numerical examples to demonstrate the performance of the proposed precoder in terms of the achievable secrecy rate regions subject to the aforementioned constraints. We also demonstrate the performance of the robust precoder under different channel uncertainty levels.

We investigate optimum zero-forcing beamforming in multiple antenna broadcast channels with per-antenna power constraints. We show that standard zero-forcing techniques, such as the Moore-Penrose pseudo-inverse, considered mainly in the context of sum-power constrained systems are suboptimal when there are per-antenna power constraints. We formulate convex optimization problems to find the optimum zero-forcing beamforming vectors. Our results indicate that optimizing the antenna outputs based on the per-antenna constraints may improve the rate considerably when the number of transmit antennas is larger the number of receive antennas. Having more transmit antennas gives rise to additional signal space dimensions that may be exploited effectively to reduce transmit power at particular antennas with limited power budget.

This paper considers the design of hybrid precoders and combiners for mmWave MIMO systems with per-antenna power constraints and the additional limitations introduced by the phase-shifting network in the analog processing stage. Previous hybrid designs were obtained using a total power constraint, but in practical implementations per-antenna constraints are more realistic, specially at mmWave, given the large number of power amplifiers used in the transmit array. Assuming perfect channel knowledge, we obtain first an approximation to the alldigital solution for the precoder and the combiner given the per-antenna constraints. Then, we develop a new method for the design of the hybrid precoder and combiner which attempts to match such all- digital approximation. Simulation results show the effectiveness of the proposed approach, which performs close to the all-digital solution.

We propose a semi-closed-form solution to the problem of computing the capacity and optimal signaling for a Gaussian MIMO channel under a joint sum power constraint (SPC) and per-antenna power constraint (PAPC). Existing efficient solutions to this fundamental problem are only applicable to some special cases: multiple-input single-output (MISO) systems, or full column rank MIMO channels with sufficiently high transmit power, or full-rank optimal signaling. For the general case, we present an efficient numerical method to solve the considered problem which does not make any assumptions on the rank of the channel matrix or the maximum transmit power. To achieve this, the considered problem is transformed into an equivalent minimax problem. We then exploit the special structure of the minimax problem to derive a closed-form solution based on a concave-convex procedure (CCP)-like algorithm. Extensive simulation results show that our proposed algorithm outperforms the existing solutions in terms of complexity and generality.

This paper considers transmit covariance optimization for a multi-input multi-output (MIMO) Gaussian wiretap channel. Specifically, we aim to maximize the MIMO secrecy capacity by judiciously designing the transmit covariance under the sum power and per-antenna power constraints. The MIMO secrecy capacity maximization (SCM) problem is nonconvex, and so far there is no tractable solution available. We propose an alternating optimization (AO) approach to handle the SCM problem. In particular, our development consists of two steps: First, we show that the SCM problem can be reexpressed to a form that can be conveniently processed by AO. Second, we develop a custom-designed fast algorithm for each AO iteration. Interestingly, with this fast implementation, the overall AO algorithm can be viewed as performing iterative reweighting and water-filling. Finally, the convergence of the proposed algorithm to a stationary solution of SCM is shown, and numerical results are provided to demonstrate its efficacy.

This paper considers a two user Gaussian multiple-input single-output (MISO) broadcast channel with a per-antenna peak power constraint (or simply peak power constraint). It is more realistic to consider the peak power constraint on each transmit antenna because each antenna is equipped with its own power amplifier in many practical implementations. Assuming the perfect channel state information (CSI) at the transmitter, we propose an achievable scheme using a dirty-tape coding (DTC). The uniform input in a fixed range of the DTC scheme helps to control the peak power of the transmit signal easily. We also present an optimization algorithm that finds the capacity achieving beamforming vectors and power allocations under a per-antenna average power constraint used in our achievable scheme. Simulation results show that as the transmit power increases, the achievable rate region under the peak power constraint is getting close to the capacity region under the reduced per-antenna average power constraint by 1/3. Compared to a non-DTC scheme based on minimum mean square error (MMSE) beamforming, the proposed scheme performs better.

We consider the downlink transmission of a wireless communication system where M antennas transmit independent information to a subset of K users, each equipped with a single antenna. The Shannon capacity of this MIMO broadcast channel (MIMO-BC) can be achieved using a non-linear preceding technique known as dirty paper coding (DPC) which is difficult to implement in practice. Motivated to study simpler transmission techniques, we focus on a linear precoding technique based on the zero-forcing (ZF) algorithm. In contrast to the typical sum power constraint (SPC), we consider a per-antenna power constraint (PAPC) motivated both by current antenna array designs where each antenna is powered by a separate amplifier and by future wireless networks where spatially separated antennas transmit cooperatively to users. We show that the problem of power allocation for maximizing the weighted sum rate under ZF with PAPC is a constrained convex optimization problem that can be solved using conventional numerical optimization techniques. For the special case of two users, we find an analytic solution based on waterfilling techniques. For the case where the number of users increases without bound, we show that ZF with PAPC is asymptotically optimal in the sense that the ratio of the expected sum-rate capacities between ZF with PAPC and DPC with SPC approaches one. We also show how the results can be generalized for multiple frequency bands and for a hybrid power constraint. Finally, we provide numerical results that show ZF with PAPC achieves a significant fraction of the optimum DPC sum-rate capacity in practical cases where K is bounded

Many MIMO capacity analyses and precoding algorithms are obtained based on the assumption of total power constraint while assuming power can be allocated freely across antennas. In practical MIMO systems, however, per-antenna power constraints are often more predominant design consideration than the total power constraints. In this paper, we study the transmission schemes for MIMO systems with per-antenna power constraints. We derive the necessary and sufficient conditions for the optimal transmission scheme. We also develop an iterative algorithm and prove its convergence to the optimal solution.

This paper proposes two low-complexity iterative algorithms to compute the capacity of a single-user multiple-input multiple-output channel with per-antenna power constraint. The first method results from manipulating the optimality conditions of the considered problem and applying fixed-point iteration. In the second approach, we transform the considered problem into a minimax optimization program using the well-known MAC- BC duality, and then solve it by a novel alternating optimization method. In both proposed iterative methods, each iteration involves an optimization problem which can be efficiently solved by the water-filling algorithm. The proposed iterative methods are provably convergent. Complexity analysis and extensive numerical experiments are carried out to demonstrate the superior performance of the proposed algorithms over an existing approach known as the mode-dropping algorithm.

We determine the capacity-optimal transmission strategy for a multiple-input-multiple-output (MIMO) Gaussian channel under multiple power constraints, namely joint sum power constraint (SPC), per group power constraints (PGPC), and per antenna power constraints (PAPC). First, we focus on cases where we can analytically determine the optimal transmit strategy under joint SPC-PGPC-PAPC. We obtain results for the following cases: 1) $n_{t} \times 1$ multiple-input-single-output (MISO); 2) MIMO channel with full column rank and full rank optimal covariance matrix; and 3) $2 \times n_{r}$ MIMO channel. These results generalize some recent results for the special cases of PAPC only and joint SPC-PAPC. Then, we propose a projected factored gradient descent (PFGD) algorithm for the general MIMO Gaussian channel under joint SPC-PGPC-PAPC including the possibility of additional rank constraints. This algorithm matches the solution of standard convex optimization tools with lower complexity. The algorithm also overcomes the limitations of existing algorithms, in terms of accuracy and applicability to low rank channels.

In this paper, three novel efficient power control algorithms are proposed for V-BLAST system with both total power constraint (TPC) and per-antenna power constraints (PAPC). Through analysis of the Karush-Kuhn-Tucker (KKT) conditions of the optimization problem, we find out that the antennas with the optimal power control can be divided into two sets. The optimal allocated power (OAP) of each antenna in the first set is its per-antenna power constraint, and the OAPs of the antennas in the second set can be obtained easily through a new optimization problem with TPC only. Based on the above analysis, three novel efficient power allocation algorithms are developed, which have much lower computational complexities compared with the existing dual update method. Simulation results are presented to demonstrate the efficiency of the proposed power control schemes.

We propose an iterative mode-dropping algorithm that optimizes input signals to achieve the sum capacity of the MIMO-MAC with per-antenna power constraint. The algorithm successively optimizes each user's input covariance matrix by applying mode-dropping to the equivalent single-user MIMO rate maximization problem. Both analysis and simulation show fast convergence. We then use the algorithm to briefly highlight the difference in MIMO-MAC capacities under sum and per-antenna power constraints.

MISO NOMA downlink beamforming optimization with per-antenna power constraints

We consider the MIMO broadcast channel (MIMO-BC) where an array equipped with M antennas transmits distinct information to K users, each equipped with N antennas. We propose a linear precoding technique, called multiuser eigenmode transmission (MET), based on the block diagonalization precoding technique. MET addresses the shortcomings of previous ZF-based beamformers by transmitting to each user on one or more eigenmodes chosen using a greedy algorithm. We consider both the typical sum-power constraint (SPC), and a per-antenna power constraint (PAPC) motivated by array architectures where antennas are powered by separate amplifiers and are either co-located or spatially separated. Numerical results show that the proposed MET technique outperforms previous linear techniques with both SPC and PAPC. Asymptotically as the number of user K increases without bound, we show that block diagonalization with receive antenna selection under PAPC and SPC are asymptotically optimal.

This paper considers the linear transceiver optimization problem for multi-carrier multiple-input multiple-output (MIMO) channels with per-antenna power constraints. Because in practical implementations each antenna is limited individually by its equipped power amplifier, this paper adopts the more realistic per-antenna power constraints, in contrast to the conventional sum-power constraint on the transmitter antennas. Assuming perfect channel knowledge both at the transmitter and the receiver, the optimization problem can be transformed into a semi-definite program (SDP), which can be solved by convex optimization tools. Furthermore, several objective functions of the MIMO system, including average bit error rate, can also be optimized by the introduction of the majorization theory.