Zero-Forcing Precoding for the MIMO Broadcast Channel under 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.

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.

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.

Zero-forcing (ZF) precoding scheme can achieve the asymptotic sum capacity as dirty-paper coding (DPC) in multiple-input multiple-output broadcast (MIMO-BC) channel when the number of users, K, approaches infinity. However, the gap between ZF and DPC is not negligible in a practical range of K, that is, K ≤ 100. The capacity loss is partly due to the excessive transmission power penalty incurred by ZF when the channel matrix of the selected user subset is poorly conditioned. To avoid this power penalty, we propose to use a variation of ZF, channel inversion regularization (CIR), as a precoding scheme in MIMO-BC channels. But, unlike the interference-free ZF, the problem of maximizing sum-rate capacity using CIR precoding becomes nonconvex, which cannot be solved by water-filling strategy. Thus, we propose an efficient algorithm based on gradient projection (GP) as the optimal power allocation strategy for selected users, and show that the proposed CIR precoding scheme can achieve asymptotically the optimum sum-rate of the DPC strategy. Moreover, simulation results show that the CIR precoding scheme with the proposed optimal power allocation scheme achieves better sum-rate performance than ZF for a wide range of K.

For multiple-input multiple-output (MIMO) transceiver designs, sum power constraint is an elegant and ideal model. When various practical limitations are taken into account e.g., peak power constraints, per-antenna power constraints, etc., covariance shaping constraints will act as an effective and reasonable model. In this paper, we develop a framework for transceiver designs for multi-hop communications under covariance shaping constraints. Particularly, we focus on multi-hop amplify-and-forward (AF) MIMO relaying communications which are recognized as a key enabling technology for device-to-device (D2D) communications for next generation wireless systems such as 5G. The proposed framework includes a broad range of various linear and nonlinear transceiver designs as its special cases. It reveals an interesting fact that the relaying operation in each hop can be understood as a matrix version weighting operation. Furthermore, the nonlinear operations of Tomolision-Harashima Precoding (THP) and Decision Feedback Equalizer (DFE) also belong to the category of this kind of matrix version weighting operation. Furthermore, for both the cases with only pure shaping constraints or joint power constraints, the closed-form optimal solutions have been derived. At the end of this paper, the performance of the various designs is assessed by simulations.

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 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.

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.

This paper presents an empirical study of the achievable data rates of network multiple-input multiple-output (MIMO) techniques including zero-forcing (ZF), zero-forcing dirty paper coding (ZF-DPC) and dirty paper coding (DPC) using actual 4-by-4 indoor wireless channel measurements at 3.5 GHz. Their performances are contrasted with those of conventional techniques, in which either the base stations are not coordinated (NC), or their interference is avoided using frequency division (FD) multiplexing. The measurements were taken in aisle-to-office and large unobstructed hall scenarios. The study of these results reveals that, at high signal-to-noise ratios (SNRs), DPC and ZF-DPC can yield more than a three-fold increase in attainable data rates when compared to NC and FD. The gains obtained using ZF are smaller, but still significant. At low SNRs the system is noise-(rather than interference-) limited, and only DPC exhibits gains. The evaluations in this paper also show that collaborative systems such as DPC can benefit from interference-prone environments to yield increased transmission capacity. With regard to the propagation channel, the classical log-normal plus Rayleigh/Ricean fading model, with parameters fitted to the scenario type, was found to be good at predicting the statistics of the achievable data rates of all the strategies considered.

This paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base-station. In contrast to the conventional sum-power constraint on the transmit antennas, this paper adopts a more realistic per-antenna power constraint, because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier. Assuming perfect channel knowledge at the transmitter, this paper investigates two different transmission schemes under the per-antenna power constraint: a minimum-power beamforming design for downlink channels with a single antenna at each remote user and a capacity-achieving transmitter design for downlink channels with multiple antennas at each remote user. It is shown that in both cases, the per-antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise. This generalizes previous uplink-downlink duality results and transforms the per-antenna transmitter optimization problem into an equivalent minimax optimization problem. Further, it is shown that various notions of uplink-downlink duality may be unified under a Lagrangian duality framework. This new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per-antenna transmitter optimization problem

Recently, studies on suboptimal precoding techniques for multiple-input multiple-output broadcast channels (MIMO-BC), which achieve performance near to that of the dirty paper coding (DPC), have drawn attention to vector perturbation (VP) precoding. In practice, each antenna or more generally each antenna group has its own limit on the transmitted power, which makes per-antenna-group power constraints more meaningful than the sum power constraint. In this paper, we introduce an optimization technique for VP precoding employing the minimum mean-square error (MMSE) criterion with per-antenna-group power constraints. This technique is inspired by the p-sphere encoding in a sense that it involves finding the node with the lowest mean-square error (MSE) over a lattice. We demonstrate that the MSE metric, as well as the p-norm one, can be enclosed in a proper Frobenius-norm ball. This Frobenius-norm ball shrinks until it captures the perturbing vector minimizing the MSE. Numerical results show that the proposed algorithm outperforms conventional VP precoding and the p-sphere encoding, but at higher complexity. Consequently, we investigate a couple of simplified techniques employing the MMSE criterion, which perform almost as well as the proposed precoding technique, but are less complex.

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.

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.

In transmit beamforming (BF) systems, one of key issues is how to design an appropriate BF vector to optimize the performance of the whole system. This paper addresses the transmit BF design problem for cyclic prefixed (CP) transmissions over Multiple Input Single Output (MISO) frequency-selective channels under per-antenna power constraints (PPC).In previous studies, several methods have been used to solve this problem, however, all lead to suboptimal solutions. In an attempt to get the optimal solution, we propose an efficient algorithm based on barrier method, which performs closely to the optimal total power constraint (TPC) solution and significantly outperforms the existing PPC solutions. Moreover, the simulation results also show that the proposed algorithm is robust on the different antenna power allocation and antenna number.

Multiuser multiple-input multiple-output (MU-MIMO) systems can achieve higher data rates compared to single user (SU-MIMO) by exploiting multi-user diversity. The capacity bound for MU-MIMO systems is given by the MIMO broadcast channel (BC) capacity. Dirty paper coding (DPC) is a well known non-linear algorithm to achieve this bound. Zero forcing DPC (ZF-DPC) is a sub-optimal way to achieve DPC by triagularizing the channel. In our previous work, we had proposed an enhancement of ZF-DPC by introducing additional receiver which was shown to improve the achievable rates over linear schemes such as block diagonalization. In practise Block Diagonalization is implemented by the receiver feeding back quantized information about the channel and the transmitter figuring out the precoders subsequently. To establish a comparison of ZF-DPC to Block Diagonalization for such practical feedback, we first derive the framework for operating ZF-DPC with quantized feedback. Next we compare the performance of ZF-DPC over Block Diagonalization with quantized feedback and demonstrate that the former still performs better.