Generalized linear precoder and decoder design for MIMO channelsusing the weighted MMSE criterion

We address the problem of designing jointly optimum linear precoder and decoder for a MIMO channel possibly with delay-spread, using a weighted minimum mean-squared error (MMSE) criterion subject to a transmit power constraint. We show that the optimum linear precoder and decoder diagonalize the MIMO channel into eigen subchannels, for any set of error weights. Furthermore, we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights. We show how to obtain: (1) the maximum information rate design; (2) QoS-based design (we show how to achieve any set of relative SNRs across the subchannels); and (3) the (unweighted) MMSE and equal-error design for fixed rate systems     

Multiuser MIMO Transceiver Design for Uplink and Downlink with Imperfect CSI

This paper considers a joint linear transmitter and receiver design for multi-user multiple-input multiple-output (MU-MIMO) systems using total mean square error (TMSE) criterion, subject to a total transmit power constraint assuming imperfect channel state information. Both the uplink and downlink MU-MIMO systems, which is employed with improper constellations such as binary phase shift-keying and $M$ -ary amplitude shift-keying are considered. A minimum TMSE design is formulated as a nonconvex optimization problem under a total transmit power constraint and the closed-form optimum linear precoder and decoder for both the downlink and uplink MU-MIMO systems with improper modulation are determined by solving this nonconvex optimization problem. A novel contribution in this paper is to derive a closed-form optimum linear precoder and decoder for both the downlink and uplink MU-MIMO systems with improper modulation by solving the nonconvex optimization problem under total power constraint. The simulation results show that the performance of the proposed design is improved over the previous design.     

Optimal precoder design for non‐regenerative multiple‐input multiple‐output cognitive relay systems with perfect and imperfect channel state information

This paper studies optimal precoder design for non‐regenerative multiple‐input multiple‐output (MIMO) cognitive relay systems, where the secondary user (SU) and relay station (RS) share the same spectrum with the primary user (PU). We aim to maximize the system capacity subject to the transmit power constraints at the SU transmitter (SU‐Tx) and RS, and the interference power constraint at the PU. We jointly optimize precoders for the SU‐Tx and RS with perfect and imperfect channel state information (CSI) between the SU‐Tx/RS and PU, where our design approach is based on the alternate optimization method. With perfect CSI, we derive the optimal structures of the RS and SU‐Tx precoding matrices and develop the gradient projection algorithm to find numerical solution of the RS precoder. Under imperfect CSI, we derive equivalent conditions for the interference power constraints and convert the robust SU‐Tx precoder optimization into the form of semi‐definite programming. For the robust RS precoder optimization, we relax the interference power constraint related with the RS precoder to be convex by using an upper bound and apply the gradient projection algorithm to deal with it. Simulation results demonstrate the effectiveness of the proposed schemes. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal Precoder Design for Non-Regenerative MIMO Cognitive Two-Way Relay Systems with Underlay Spectrum Sharing

We study the optimal precoder design for a MIMO cognitive two-way relay system with underlay spectrum sharing. The system consists of two secondary users (SUs) and one relay station (RS). We jointly optimize the precoders for SUs and RS with perfect and imperfect channel state information (CSI) between SUs/RS and the primary user, where our design approach is based on the alternate optimization method. For the perfect CSI case, we derive the optimal structure of the RS precoding matrix, which generalizes the result for single-antenna SUs and helps to reduce the search complexity. We develop gradient projection (GP) algorithm to calculate the optimal RS precoder numerically. When the RS precoder is given, we propose a fast algorithm based on generalized water-filling theorem to compute the optimal SU precoders. For the imperfect CSI case, we derive equivalent conditions for the interference power constraints and convert the robust SU precoder optimization into the form of semi-definite programming. As for the robust RS precoder optimization, we relax the interference power constraint related with the RS precoder to be convex and then the GP algorithm can be applied. Finally, simulation results demonstrate the effectiveness of the proposed schemes.     

Joint Transceiver Design for Cooperative Multi-cell Systems with Multiple Users

In this paper, the joint transceiver design issue is investigated for multi-cell systems with multiple mobile terminals (MTs). An optimization problem is formulated based on the criterion of mean squared error minimization for the joint design of the cooperative precoder of all multi-input multi-output (MIMO) cells and the cooperative decoder of all MIMO MTs. With a fixed decoder, the optimum precoder is first derived in a closed-form expression, where no exchange of data streams among all of the MIMO cells is required due to the limited capability of the backhaul. Subsequently, an optimum decoder is then obtained in an analytical expression with the fixed precoder. Based on these two expressions, an iterative algorithm with guaranteed convergence is finally developed to carry out the joint optimization of the cooperative precoders and decoders. Simulation results demonstrating the effectiveness of the proposed algorithm are also provided.     

SVD-Assisted Joint Precoder and Decoder Design for the Uplink of MU-MIMO Systems With Improper Modulation

This paper considers noniterative joint precoder and decoder design for uplink multi-user multiple-input, multiple-output systems, for both cases of perfect channel state information (CSI) and imperfect CSI at the transmitter and receiver. Instead of counting on complex iterative based algorithms, an efficient and noniterative SVD-based joint precoder and decoder pair design is employed. It also focusing on the scenario when an improper constellation such as binary phase shift-keying or $M$ -ary amplitude shift-keying ( $M$ -ASK) is employed. The proposed are novel joint linear precoders and decoders design aims to minimize the total mean squared error of the symbol estimation. Simulations are conducted to provide a comparative evaluation of the proposed design over the previous designs on the bit-error-rate performance.     

Design of Robust Transceiver for Precoded Uplink MU-MIMO Transmission in Limited Feedback System

This paper proposes a robust transceiver design against the effect of channel state information (CSI) estimation error to optimize precoded uplink (UL) multi-user multiple-input multiple-output (MU-MIMO) transmission in limited feedback system under the consideration of the least-square technique on CSI estimation. To improve this limited feedback precoding, the constrained minimum variance (MV) approach with quadratic form to realize the computationally-efficient optimization problem, advantageously invoking the characteristics of the CSI estimation error, is proposed to suppress the effect of CSI estimation error, multiple user interference and noise. According to the Lagrange multiplier method on this MV approach, the deterministic function to resist uncertain CSI can be obtained to optimize design of the precoder and adaptive matrices jointly. With these optimum adaptive and precoder matrices, an optimum robust weighting matrix can be obtained to facilitate the user-wise detection in precoded UL MU-MIMO system. Performance analysis shows that the proposed robust weighting matrix is an unbiased design and it also can regularize the diagonal loading factor technique, and the detection performance of the proposed robust transceiver design can be predicted simplistically by applying our derived signal-to-interference-plus-noise ratio formulation. Computer simulations are conducted to confirm the efficacy of the proposed design in both perfect and imperfect CSI estimation.     

Joint optimization of relay-precoders and decoders with partial channel side information in cooperative networks

We jointly optimize the relay-precoders and decoders with full or partial channel side information (CSI) in a cooperative network. Specifically, three different CSI assumptions are considered: 1) full CSI at the destination terminal and the relay terminals; 2) full CSI at the destination terminal and partial CSI at the relay terminals; 3) partial CSI at the destination terminal and the relay terminals. We show that, under the assumption of full CSI at the destination terminal and the relay terminals, the optimum relay-precoder is the cooperative transmission beamforming and the optimum decoder is a maximum ratio combiner. Under the two partial CSI assumptions, the optimum relay-precoders and decoders work in a fashion of channel selection. It is demonstrated that the proposed optimum relay-precoders and decoders improve the performance considerably     

Generalized co-phasing for multiple transmit and receive antennas

We propose and study a class of transmit beamforming techniques for systems with multiple transmit and multiple receive antennas with a per-antenna transmit power constraint. The per-antenna transmit power constraint is more realistic than the widely used total (across all transmit antennas) power constraint, since in practice each transmit antenna is driven by a separate power amplifier with a maximum power rating. Under the per-antenna power constraint, from an implementation perspective, it becomes desirable to vary only the phases (as opposed to both power and phase variation) of the signals departing from the transmit antennas. We name this class of techniques generalized co-phasing and formulate an optimization problem to calculate the transmit antenna phases. Furthermore, we propose five heuristic algorithms to solve the optimization problem. All the proposed algorithms except one are optimal for the case of two transmit antennas and an arbitrary number of receive antennas. For an arbitrary number of transmit and receive antennas, simulations indicate that the proposed algorithms perform very close to the optimal solution calculated through an exhaustive search of all possible transmit phases.     

两跳中继通信系统中基于QoS的联合预编码设计

针对多入多出（MIMO）中继系统中接收端服务质量（QoS）的要求,即目的节点各子信道所要求达到的信噪比值（SNR）,在文中我们研究了一种中继节点和目的节点的联合预编码算法.该算法基于权值最小均方误差（WMMSE）准则,通过接收端的QoS要求选取适当的权值,从而设计出最优的预编码矩阵和检测矩阵.     

Joint Source and Relay Precoder Design in Amplify-and-Forward MIMO Relay Systems with Direct Link

This paper investigates the precoder design problem in a two-hop amplify-and-forward multiple-input-multiple-output relay system. Many previous works on this problem are based on the minimum mean-square error criterion and the presence of a direct link between the source and the destination is ignored. In this paper, we propose a new method for joint source and relay precoder design based on maximizing the mutual information between the source and the destination, taking both the relay link and the direct link into account. In contrast to previous works, which consider the transmit power constraints of the source and the relay independently, we assume a total power constraint on the sum transmit power of the source and the relay instead to study also the optimal power distribution over the two nodes. A constrained optimization problem with respect to the unknown source precoder matrix and relay precoder matrix is then formulated, which is nonconvex and very difficult to solve directly. We propose a structural constraint on the precoders by analyzing the structure of the problem and referring to related works. With the proposed precoders’ structure and by applying the Hadamard’s inequality, the original problem is simplified from a matrix-valued problem to a scalar-valued one. However, the new scalar-valued problem is still nonconvex and we manage to convert it into two subproblems and solve it in an iterative fashion. By using the Karash–Kuhn–Tucker (KKT) conditions, we give out the closed-form solutions to the subprobelms. Simulation results demonstrate that the proposed design method converges rapidly and significantly outperforms the existing methods.     

单天线功率约束下的能效预编码优化设计

针对多小区多用户下行链路系统,研究了能效传输预编码设计问题。不同于传统设计中的和功率约束,由于实际系统中各天线的功率由其各自配备的功率放大器的线性度所限制,考虑更加实际的单天线功率约束。目标优化问题建模为最大化能效/谱效,同时满足各用户速率约束以及单天线功率约束。为了求解该优化问题,利用凸近似逼近的方法,将原始问题转化为凸优化问题,并提出了一种有效迭代优化算法求解该优化问题。MATLABAL数值仿真结果验证了所提算法的有效性。      

Robust Tomlinson-Harashima Precoders for Multiuser MISO Downlink with Imperfect CSI

In this paper, we consider robust non-linear precoding for the downlink of a multiuser multiple-input single-output (MISO) communication system in the presence of imperfect channel state information (CSI). The base station (BS) is equipped with multiple transmit antennas and each user terminal is equipped with a single receive antenna. We propose two robust Tomlinson-Harashima precoder (THP) designs. The first design is based on the minimization of the total BS transmit power under constraints on the mean square error (MSE) at the individual user receivers. We show that this problem can be solved by an iterative procedure, where each iteration involves the solution of a pair of convex optimization problems that can be solved efficiently. A robust linear precoder with MSE constraints can be obtained as a special case of this robust THP. The second design is based on the minimization of a stochastic function of the sum MSE under a constraint on the total BS transmit power. We formulate this design problem as an optimization problem that can be solved by the method of alternating optimization, the application of which results in a second-order cone program that can be numerically solved efficiently. Simulation results illustrate the improvement in performance of the proposed precoders compared to other robust linear and non-linear precoders in the literature.     

Ergodic capacity and outage probability optimization for secondary user in cognitive radio networks under interference outage constraint

This paper considers a cognitive radio network where a secondary user (SU) coexists with a primary user (PU). The interference outage constraint is applied to protect the primary transmission. The power allocation problem to jointly maximize the ergodic capacity and minimize the outage probability of the SU, subject to the average transmit power constraint and the interference outage constraint, is studied. Suppose that the perfect knowledge of the instantaneous channel state information (CSI) of the interference link between the SU transmitter and the PU receiver is available at the SU, the optimal power allocation strategy is then proposed. Additionally, to manage more practical situations, we further assume only the interference link channel distribution is known and derive the corresponding optimal power allocation strategy. Extensive simulation results are given to verify the effectiveness of the proposed strategies. It is shown that the proposed strategies achieve high ergodic capacity and low outage probability simultaneously, whereas optimizing the ergodic capacity (or outage probability) only leads to much higher outage probability (or lower ergodic capacity). It is also shown that the SU performance is not degraded due to partial knowledge of the interference link CSI if tight transmit power constraint is applied.     

MIMO下行链路联合波束成形稳健性设计

针对MIMO下行链路中的发射/接收波束成行器,提出了一种对非精确CSI稳健的联合设计方案。方案采用的设计准则是在总发射功率受限的条件下最小化系统和MSE。根据此非凸和非线性优化问题的最优解条件,通过交替地计算每个用户的最优解来近似地获得原问题最优解。仿真结果表明,与非稳健性方法相比,该方案能有效地减少非精确CSI引起的性能损失。     

Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory

The problem of joint beamforming and power allocation for cognitive multi-input multi-output systems is studied via game theory. The objective is to maximize the sum utility of secondary users (SUs) subject to the primary user (PU) interference constraint, the transmission power constraint of SUs, and the signal-to-interference-plus-noise ratio (SINR) constraint of each SU. In our earlier work, the problem was formulated as a non-cooperative game under the assumption of perfect channel state information (CSI). Nash equilibrium (NE) is considered as the solution of this game. A distributed algorithm is proposed which can converge to the NE. Due to the limited cooperation between the secondary base station (SBS) and the PU, imperfect CSI between the SBS and the PU is further considered in this work. The problem is formulated as a robust game. As it is difficult to solve the optimization problem in this case, existence of the NE cannot be analyzed. Therefore, convergence property of the sum utility of SUs will be illustrated numerically. Simulation results show that under perfect CSI the proposed algorithm can converge to a locally optimal pair of transmission power vector and beamforming vector, while under imperfect CSI the sum utility of SUs converges with the increase of the transmission power constraint of SUs.     

Analog Precoder and Equalizer Designs and their Geometry for Multichannel Communication

This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective additive Gaussian noise (AGN) channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. We assume a continuous channel model with precoder transmissions for m subchannels that lie in an n-dimensional linear subspace of L²(R). m and n are design parameters. We first design the subspace according to the channel characteristics, and then design the precoders as functions in this subspace. After the design of the optimal precoder and equalizer, we explore the geometry of these designs. We show that all of these precoder and equalizer designs are, in fact, decompositions of a virtual twochannel problem into a system of canonical coordinates, wherein variables in the canonical message channel are correlated only pairwise with corresponding variables in the canonical measurement channel. This finding clarifies the geometry of precoder and equalizer designs and illustrates that they decompose the two-channel communication problem into what might be called the Shannon channel     

Joint linear precoder and power allocation design for uplink MIMO systems with limited feedback

In this article, the authors consider joint design of a linear precoder and power allocation for uplink multiuser multiple input multiple output (MIMO) communication systems with limited feedback to improve the bit error rate (BER) performance for all users. Precoder selection from the codebook set is directly based on the exact BER performance, instead of other suboptimal criteria, to achieve the optimal precoder matrix, but closed-form expressions may not exist in the view of power allocation based directly on the BER criterion. From this perspective, the authors propose the joint transmitter optimization algorithm for the consideration ofprecoder design, with total power constraint for asymptotic MBER (AMBER) criterion. In this AMBER criterion, a closed-form solution has been derived for power allocation with an optimal precoder. The simulation results show that the proposed joint design algorithm can achieve a much better performance than precoding with uniform power allocation and only consideration of power allocation.     

Power Control of V-BLAST System with Per-Antenna Power Constraints

This letter considers power control for the V- BLAST system with successive interference cancellation (SIC) receiver. In addition to a conventional sum-power constraint across the transmit antennas, this letter adopts a per-antenna power constraint, which is more realistic in practice. Average uncoded BER of all detection stages is minimized under the given constraints. Simulation results are presented to illustrate the effect of the additional per-antenna power constraint.     

Linear precoding via conic optimization for fixed MIMO receivers

In this paper, the problem of designing linear precoders for fixed multiple-input-multiple-output (MIMO) receivers is considered. Two different design criteria are considered. In the first, the transmitted power is minimized subject to signal-to-interference-plus-noise-ratio (SINR) constraints. In the second, the worst case SINR is maximized subject to a power constraint. It is shown that both problems can be solved using standard conic optimization packages. In addition, conditions are developed for the optimal precoder for both of these problems, and two simple fixed-point iterations are proposed to find the solutions that satisfy these conditions. The relation to the well-known uplink-downlink duality in the context of joint transmit beamforming and power control is also explored. The proposed precoder design is general, and as a special case, it solves the transmit rank-one beamforming problem. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders.