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.     

Exponential Diversity Achieving Spatio–Temporal Power Allocation Scheme for Fading Channels

In this paper, we analyze optimal (in space and time) adaptive power transmission policies for fading channels when the channel-state information (CSI) at the transmitter (CSIT) and the receiver (CSIR) is available. The transmitter has a long-term (time) average power constraint. There can be multiple antennas at the transmitter and at the receiver. The channel experiences Rayleigh fading. We consider beamforming and space-time coded systems with perfect/imperfect CSIT and CSIR. The performance measure is the bit error rate (BER). We show that in both coded and uncoded systems, our power allocation policy provides exponential diversity order if perfect CSIT is available. We also show that, if the quality of CSIT degrades then the exponential diversity is retained in the low SNR region but we get only polynomial diversity in the high SNR region. Another interesting conclusion is that in case of imperfect CSIT and CSIR, knowledge of CSIT at the receiver is very important. Finally, for the optimal power control policy of the uncoded system we find the error-exponents which provide the rate versus diversity-order tradeoff for this policy. This tradeoff is of an entirely different nature than the well-known Zheng-Tse tradeoff.     

Outage probability of multiple-input single-output (MISO) systems with delayed feedback

We investigate the effect of feedback delay on the outage probability of multiple-input single-output (MISO) fading channels. Channel state information at the transmitter (CSIT) is a delayed version of the channel state information available at the receiver (CSIR). We consider two cases of CSIR: (a) perfect CSIR and (b) CSI estimated at the receiver using training symbols. With perfect CSIR, under a short-term power constraint, we determine: (a) the outage probability for beamforming with imperfect CSIT (BF-IC) analytically, and (b) the optimal spatial power allocation (OSPA) scheme that minimizes outage numerically. Results show that, for delayed CSIT, BF-IC is close to optimal for low SNR and uniform spatial power allocation (USPA) is close to optimal at high SNR. Similarly, under a longterm power constraint, we show that BF-IC is better for low SNR and USPA is better at high SNR. With imperfect CSIR, we obtain an upper bound on the outage probability with USPA and BF-IC. Results show that the loss in performance due to imperfection in CSIR is not significant, if the training power is chosen appropriately.     

User clustering and robust beamforming design in multicell MIMO-NOMA system for 5G communications

In this paper, we present a robust beamforming design to tackle the weighted sum-rate maximization (WSRM) problem in a multicell multiple-input multiple-output (MIMO) – non-orthogonal multiple access (NOMA) downlink system for 5G wireless communications. This work consider the imperfect channel state information (CSI) at the base station (BS) by adding uncertainties to channel estimation matrices as the worst-case model i.e., singular value uncertainty model (SVUM). With this observation, the WSRM problem is formulated subject to the transmit power constraints at the BS. The objective problem is known as non-deterministic polynomial (NP) problem which is difficult to solve. We propose an robust beamforming design which establishes on majorization minimization (MM) technique to find the optimal transmit beamforming matrix, as well as efficiently solve the objective problem. In addition, we also propose a joint user clustering and power allocation (JUCPA) algorithm in which the best user pair is selected as a cluster to attain a higher sum-rate. Extensive numerical results are provided to show that the proposed robust beamforming design together with the proposed JUCPA algorithm significantly increases the performance in term of sum-rate as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme.     

Joint Beamforming and Power Allocation for Multiple Access Channels in Cognitive Radio Networks

A cognitive radio (CR) network refers to a secondary network operating in a frequency band originally licensed/allocated to a primary network consisting of one or multiple primary users (PUs). A fundamental challenge for realizing such a system is to ensure the quality of service (QoS) of the PUs as well as to maximize the throughput or ensure the QoS, such as signal-to-interference-plus-noise ratios (SINRs), of the secondary users (SUs). In this paper, we study single-input multiple output multiple access channels (SIMO-MAC) for the CR network. Subject to interference constraints for the PUs as well as peak power constraints for the SUs, two optimization problems involving a joint beamforming and power allocation for the CR network are considered: the sum-rate maximization problem and the SINR balancing problem. For the sum-rate maximization problem, zero-forcing based decision feedback equalizers are used to decouple the SIMO-MAC, and a capped multi-level (CML) water-filling algorithm is proposed to maximize the achievable sum-rate of the SUs for the single PU case. When multiple PUs exist, a recursive decoupled power allocation algorithm is proposed to derive the optimal power allocation solution. For the SINR balancing problem, it is shown that, using linear minimum mean-square-error receivers, each of the interference constraints and peak power constraints can be completely decoupled, and thus the multi-constraint optimization problem can be solved through multiple single-constraint sub-problems. Theoretical analysis for the proposed algorithms is presented, together with numerical simulations which compare the performances of different power allocation schemes.     

认知MIMO MAC最优迭代注水算法

研究发送功率以及干扰温度约束下的认知多入多出多址接入信道(MIMO MAC)的速率和最大化问题。通过部分对偶分解技术松弛干扰温度约束,原始问题被分解为较易处理的子问题,并提出一种迭代算法,通过交替进行对偶变量更新与迭代注水运算求解使得速率和最大的最优发送协方差矩阵。最后通过仿真表明算法的有效性。     

Joint user pairing and power allocation in uplink virtual MIMO with imperfect CSI

User pairing strategy for virtual multi-input multi-output （VMIMO） has been widely studied to improve system throughput, but most studies are based on perfect channel state information （CSI） and uniform power allocation. However, perfect CSI is very difficult or even impossible to obtain in practical system. Moreover power allocation has significant impact on algorithm performance. Therefore, in this paper, a low-complex joint user pairing and power allocation algorithm based on aggressive discrete stochastic optimization and Lagrangian dual solution is proposed for uplink VMIMO with imperfect CSI. Simulation results show that the proposed algorithm can achieve desirable throughput performance, and restrict inter-user interference （IUI） efficiently.     

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.     

Optimized BD‐ZF Precoder for Multiuser MIMO‐VFDM Cognitive Transmission

In this paper, we study an optimized block‐diagonal zero‐forcing (BD‐ZF) precoder in a two‐tiered cognitive network consisting of a macro cell (MC) and a small cell (SC). By exploiting multiuser multiple‐input and multiple‐output Vandermonde‐subspace frequency‐division multiplexing (VFDM) transmission, a cognitive SC can coexist with an MC. We first devise a cross‐tier precoder based on the idea of VFDM to cancel the interference from the SC to the MC. Then, we propose an optimized BD‐ZF intra‐tier precoder (ITP) to suppress multiuser interference and maximize the throughput in the SC. In the case where the dimension of a provided null space is larger than that required by the BD‐ZF ITP, the optimized BD‐ZF ITP can collect all limited channel gain by optimizing rotating and selecting matrices. Otherwise, the optimized BD‐ZF ITP is validated to be equivalent to the conventional BD‐ZF ITP in terms of throughput. Numerical results are presented to demonstrate the throughput improvement of the proposed optimized BD‐ZF ITP and to discover the impact of imperfect channel state information.     

Joint Detection and Diversity Techniques in CDMA Mobile Radio Systems

CDMA mobile radio systems suffer from intersymbol interference (ISI) and multiple access interference (MAI) which can be combated by using joint detection (JD) techniques. Furthermore, the time variation of the radio channels leads to degradations of the receiver performance due to fading. These degradations can be reduced by applying diversity techniques. Three suboptimum detection techniques based on matched filters (MF), zero forcing (ZF) and minimum mean square-error (MMSE) equalization are considered. For further improvements, switched and equal gain diversity techniques are employed to combat fading. The performance is depicted in terms of the average bit error probability versus the average SNR per bit in a single cell environment showing an appreciable improvement over the non diversity situation. Theoretical results for the SNR at the front end of the receiver and the BER for ideal channel are obtained and compared with the simulation results.     

多用户MIMO系统最优发送策略研究

研究一个收发双方都采用多天线的K用户MIMO系统的前向链路的几种最优发送策略.利用矢量广播信道和矢量多接入信道之间的对偶性交换两类信道的发送协方差矩阵以达到快速优化;分析了在各用户功率受限时总的信道容量最大的算法;研究在假定基站采用理想的线性多用户MMSE接收时的最优发送.在总功率受限时通过调整各用户的协方差矩阵实现平均标准MSE最优,采用自适应功率分配可以进一步优化MSE.分析最优化问题与KKT条件的关系,通过迭代计算单用户平均最小均方误差,利用内点法计算互协方差矩阵优化问题.     

Capacity regions and optimal power allocation for groupwise multiuser detection

In this letter, optimal power allocation and capacity regions are derived for groupwise successive interference cancellation (GSIC) systems operating in multipath fading channels, under imperfect channel estimation conditions. It is shown that the impact of channel estimation errors on the system capacity is two-fold: It affects the receiver performance within a group of users, as well as the cancellation performance (through cancellation errors). An iterative power allocation algorithm is derived, based on which it can be shown that that the total required received power is minimized when the groups are ordered according to their cancellation errors, and the first detected group has the smallest cancellation error. Performance/complexity tradeoff issues are also discussed by directly comparing the system capacity for different implementations: GSIC with linear minimum-mean-square error (LMMSE) receivers within the detection groups; GSIC with matched filter (MF) receivers; multicode LMMSE systems; and simple all MF receivers systems.     

一种下行多用户MIMO系统中的鲁棒波束形成算法

提出了一种下行多用户MIMO系统中的鲁棒性线性处理算法.该算法利用了信道均值和天线相关矩阵等信道统计信息,在总发射功率不大于目标值的约束条件下,能够使所有用户的均方误差(total mean square error,TMSE)在随机信道上的平均值最小.该算法不明显依赖瞬时信道信息(channel state information,CSI),当信道估计得到的CSI不准确时,它能够有效降低由CSI偏差带来的性能损失.仿真结果表明提出的算法能够有效地降低由于不准确CSI带来的误码率和平均MSE的损失.     

Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI

The capacity of a massive MIMO cellular network depends on user and antenna selection algorithms, and also on the acquisition of perfect Channel State Information (CSI). Low computational cost algorithms for user and antenna selection significantly may enhance the system capacity, as it would consume a smaller bandwidth out of the total bandwidth for downlink transmission. The objective of this paper is to maximize the system sum-rate capacity with efficient user and antenna selection algorithms and linear precoding. We consider in this paper, a slowly fading Rayleigh channel with perfect acquisition of CSI to explore the system sum-rate capacity of a massive MIMO network. For user selection, we apply three algorithms, namely Semi-orthogonal user selection (SUS), Descending Order of SNR-based User Scheduling (DOSUS), and Random User Selection (RUS) algorithm. In all the user selection algorithms, the selection of Base Station (BS) antenna is based on the maximum Signal-to-Noise Ratio (SNR) to the selected users. Hence users are characterized by having both Small Scale Fading (SSF) due to slowly fading Rayleigh channel and Large-Scale Fading (LSF) due to distances from the base station. Further, we use linear precoding techniques, such as Zero Forcing (ZF), Minimum Mean Square Error (MMSE), and Maximum Ratio Transmission (MRT) to reduce interferences, thereby improving average system sum-rate capacity. Results using SUS, DOSUS, and RUS user selection algorithms with ZF, MMSE, and MRT precoding techniques are compared. We also analyzed and compared the computational complexity of all the three user selection algorithms. The computational complexities of the three algorithms that we achieved in this paper are O(1) for RUS and DOSUS, and O(M²N) for SUS which are less than the other conventional user selection methods.     

Rate-optimal fair power allocation in complex field network coded relay communications

In this paper, we consider the complex field network coded relay assisted communication (CFNC-RAC) channel. Although CFNC-RAC is spectrally efficient, its bit error rate performance is degraded by multi-access interference, which can be improved by appropriately allocating the user and relay powers. Since the fairness is an important factor for a practical multi-user communication system, we have proposed a rate-optimal fair power adaptation (ROFPA) technique in this work. The proposed ROFPA policy not only aims to maximize the average achievable sum-rate of CFNC-RAC under the use of the decode and forward relaying but also intends to satisfy the average rate-fairness restriction while taking the total power constraint and the network topology into account. We formulate the ROFPA as a non-convex optimization program and then derive an analytical solution for it. Extensive performance evaluation and numerical simulations validate that ROFPA method can provide significant sum-rate with considerable user fairness when compared to symbol-error-rate optimized (SER-OPT) policy proposed by Eritmen et al. (Wirel Netw, 2015. doi:10.1007/s11276-015-0924-1).     

Coordinated User Scheduling Based on Hybrid CSI in Multi-User MIMO Relay System with Limited Feedback

This paper considers coordinated user scheduling in a multi-user two-hop multi-input multi-output relay system with limited feedback. The proposed scheme utilizes a quantized transmit correlation and channel quality information, enabling to achieve both interference mitigation and multi-user diversity (MUD) gain. To this end, we first investigate the effect of quantization error on the statistical characteristics of co-channel interference (CCI) cased by the relay. Then, the coordinated user-scheduling strategy is designed with the use of eigen-beamforming to maximize the desired signal power in an instantaneous manner while minimizing the CCI in an average sense. Analytic and numerical results show that the proposed scheme can maximize the achievable sum-rate by handling a tradeoff between interference mitigation and MUD gain according to the number of quantization bits, providing a large sum-rate performance in the presence of quantization error.     

Robust Interference Management via Linear Precoding and Linear/Non-Linear Equalization

This work studies the robust design of linear precoding and linear/ non-linear equalization for multi-cell MIMO systems in the presence of imperfect channel state information (CSI). A worst-case design approach is adopted whereby the CSI error is assumed to lie within spherical sets of known radius. First, the optimal robust design of linear precoders is tackled for a MIMO interference broadcast channel (MIMO-IBC) with general unicast/multicast messages in each cell and operating over multiple time-frequency resources. This problem is formulated as the maximization of the worst-case sum-rate assuming optimal detection at the mobile stations (MSs). Then, symbol-by-symbol non-linear equalization at the MSs is considered. In this case, the problem of jointly optimizing linear precoding and decision-feedback (DF) equalization is investigated for a MIMO interference channel (MIMO-IC) with the goal of minimizing the worst-case sum-mean squared error (MSE). Both problems are addressed by proposing iterative algorithms with descent properties. The algorithms are also shown to be implementable in a distributed fashion on processors that have only local and partial CSI by means of the Alternating Direction Method of Multipliers (ADMM). From numerical results, it is shown that the proposed robust solutions significantly improve over conventional non-robust schemes in terms of sum-rate or symbol error rate. Moreover, it is seen that the proposed joint design of linear precoding and DF equalization outperforms existing separate solutions.     

Iterative joint optimization of minimal transmit redundancy FIR zero-forcing precoder-equalizer system for MIMO-ISI channel

An iterative joint finite-impulse response (FIR) zero-forcing (ZF) precoder-equalizer optimization algorithm for multiple-input multiple-output intersymbol interference (MIMO-ISI) channel is proposed. The existing joint precoder-equalizer design algorithms for MIMO-ISI channels require a guard period, which is longer than or equal to the channel order to avoid the interblock interference (IBI). This longer guard period is a kind of unnecessary redundancy consuming the valuable channel bandwidth. Based on space-time-modulated codes (STMC), this paper proposes the first algorithm for jointly optimizing the FIR precoder and equalizer without the guard-period constraint. Hence, the precoder-equalizer pairs obtained can achieve minimal transmit redundancy ISI-free communications for complex-valued signals. This greatly enhances the spectral efficiency for wide-band communications. The proposed algorithm is performed in an iterative basis. Sufficient conditions and convergence analysis of this algorithm are presented. The resultant precoder and equalizer are proved to be a least-square (LS) optimal solution for each other. The simulation results show that substantial performance gain is obtained with the proposed joint optimization algorithm.     

Energy-efficient power allocation for NOMA heterogeneous networks with imperfect CSI

In this paper, an optimal user power allocation scheme is proposed to maximize the energy efficiency for downlink non-orthogonal multiple access (NOMA) heterogeneous networks (HetNets). Considering channel estimation errors and inter-user interference under imperfect channel state information (CSI), the energy efficiency optimization problem is formulated, which is non-deterministic polynomial (NP)-hard and non-convex. To cope with this intractable problem, the optimization problem is converted into a convex problem and address it by the Lagrangian dual method. However, it is difficult to obtain closed-form solutions since the variables are coupled with each other. Therefore, a Lagrangian and sub-gradient based algorithm is proposed. In the inner layer loop, optimal powers are derived by the sub-gradient method. In the outer layer loop, optimal Lagrangian dual variables are obtained. Simulation results show that the proposed algorithm can significantly improve energy efficiency compared with traditional power allocation algorithms.     

Cognitive Radio MIMO Gaussian Broadcast Channels with the Power Constraint

The cognitive radio multiple-input multiple-output Gaussian broadcast channels are studied where multiple antennas are available for both primary users and secondary users in a spectrum sharing environment, and the sum-rate capacity is also obtained under both the SUs’ transmit power constraint and interference power constraint at the primary receivers. The paper principally consists of two steps. First, a duality technique and dirty paper coding are adopted to simplify the channels. Second, we propose an iterative power allocation algorithm to obtain the maximum sum-rate capacity and examine the effects of the constraint parameters on the concerned quantities. Finally, numerical simulation results are presented to validate the proposed theoretical analysis.