Nonlinear Precoding Design for MIMO Amplify-and-Forward Two-Way Relay Systems

This paper investigates the problem of joint design of relay precoders and receivers based on the minimum mean-square-error (MMSE) criterion in multi-hop bi-directional multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay systems. In contrast to the conventional research on two-way relay systems, we combine a multi-hop relay system with a bi-directional relay system which further enhances the system performance. By decoupling the original highly non-convex problem into three sub-problems, we propose an iterative algorithm to alternatively optimize relay precoders and receivers. Numerical simulation results show that the proposed iterative algorithm outperforms other algorithms in terms of bit-error-rate (BER).

In this paper, the problem of precoder design and node power allocation in a three node cooperative multiple-input multiple-output (MIMO) relay system is discussed. All the nodes are assumed to be equipped with multiple antennas and the source and the relay nodes are subject to a total transmit power constraint. We first introduce an upper bound on the received mean square error (MSE), then we suggest suboptimal structures to the source and the relay precoders to minimize this bound. Unlike the previous works in this area, the proposed precoders are easy to calculate and does not involve in computationally costly iterative methods. Next, based on the precoder structures, it is shown that proper transmit power assignment to the source and relay nodes can further improve the system performance and the optimal power allocation for the special case of single symbol transmission is derived. Simulation results show significant improvement in the received mean square error (MSE) by applying the proposed precoding and node power allocation schemes. The node power allocation scheme is also shown to be most effective when the relay and destination nodes have different noise levels.

In recent times, there has been growing interests in integration of voice, data and video traffic in wireless communication networks. With these growing interests, WCDMA has immerged as an attractive access technique. The performance of WCDMA system is deteriorated in presence of multipath fading environment. The paper presents space-time coded minimum mean square error (MMSE) Decision Feedback Equalizer (DFE) for wideband code division multiple access (WCDMA) in a frequency selective channel. The filter coefficients in MMSE DFE are optimized to suppress noise, intersymbol interference (ISI), and multiple access interference (MAI) with reasonable system complexity. For the above structure, we have presented the estimation of BER for a MMSE DFE using computer simulation experiments. The simulation includes the effects of additive white Gaussian noise, multipath fading and multiple access interference (MAI). Furthermore, the performance is compared with standard linear equalizer (LE) and RAKE receiver. Numerical and simulation results show that the MMSE DFE exhibits significant performance improvement over the standard linear equalizer (LE) and RAKE receiver.

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically.

Block data transmission is an efficient scheme to mitigate the inter-symbol interference (ISI) caused by dispersive channels. Recent research work attempt to obtain optimal designs of precoders given various linear and non-linear receivers. In this paper we focus on the systems with optimal precoder designs based on the minimization of bit error rate (BER) which is the more meaningful criterion in data communications. The linear receivers employed in these systems include zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Recently, block decision feedback equalization (DFE) has also been suggested to be used in the design of such block data transmission systems. We also revisit the jointly optimum designs of the precoder coupled with the DFE receivers. First we derive the block-data error rate for all of these different systems with their corresponding optimal precoders. Then we rank their performance accordingly. Simulation results are also obtained to verify our analysis. Later, we evaluate the computational complexity on the various systems and draw some conclusions on their relative merits. Finally, we derive the lower and upper bounds of bit error rate (BER) considering error propagation for systems employing nonlinear equalizers.

In this paper, we design a zero-forcing (ZF) Tomlinson-Harashima precoding (THP) and a minimum mean square error (MMSE) THP for multiuser MIMO relay system with direct link. Based on these precoding structures, we propose the optimal combining weights of the ZF THP and the MMSE THP in half duplex relay system, and the sub-optimal weights of MMSE THP to reduce feedback channel state information (CSI). Through the Monte Carlo simulation, we verify that the optimal weights combining method outperforms the constant weights combining method. In addition, we confirm that the performance of the sub-optimal weights combining method is close to the optimal method, while reducing the feedback CSI simultaneously.

The performance of linear filters degrade drastically when applied to mitigate intersymbol interference caused by channels with frequent nulls in their spectral characteristics like, e.g., time-dispersive radio channels. In such cases, the well-known decision feedback equalizer (DFE) is one possible nonlinear approach to improve the quality of the receiver. However, adapting the DFE filter coefficients to equalize time-varying channels is computationally intense, especially if the dimension of the observation vector is very high. In this paper, we apply the conjugate gradient (CG) algorithm to a conventional minimum mean square error (MMSE) DFE in order to reduce its computational complexity. Moreover, we compare its performance to the one of MMSE DFE versions which are based on the computationally efficient least-mean-square (LMS) or recursive least-squares (RLS) algorithm, respectively. The analysis additionally includes a detailed investigation of computational complexity with respect to the required number of floating point operations (FLOPs). Simulation results when applied to a digital communications system show the ability of the CG based MMSE DFE to outperform either the LMS and the RLS based MMSE DFE although its computational complexity is even smaller in most of the cases.

Adopting the amplify-and-forward (AF) relay protocol, this paper focuses on the design of a multiuser multiple-input multiple-output (MIMO) multi-relay system with direct source-destination links taken into consideration. In order to improve the quality of signal detection at the receiver, we make use of the minimal mean-squared error (MMSE)-decision feedback equalization (DFE) technique. With the constraints of the signal transmission power at both source and relay nodes, the minimization of the sum mean-squared error (MSE) for the signal waveform estimation of all users' data streams is employed as our design criterion. Through the block coordinate descent (BCD) method of Gauss-Seidel type, we develop an iterative algorithm with guaranteed convergence to conduct the joint optimization of all the source precoding, relay amplifying, feed-forward and decision feedback matrices, where each step we take is to solve a convex problem. It is shown from simulation results that, in comparison to the linear MMSE receiver-based algorithm, the proposed nonlinear one achieves better performance in terms of both MSE and bit-error-rate (BER). Moreover, the system reliability can be significantly improved when the signal-to-noise ratios (SNRs) of direct links become relatively good.

We investigate the equalization and channel identification for space-time block coded signals over a frequency-selective multiple-input multiple output (MIMO) channels. The equalization is considered by taking into account the cyclostationarity of space-time block coded signals. The minimum mean square error (MMSE) solutions are derived for linear and decision feedback (DF) equalizers. Due to the redundancy induced by space-time block coding, a blind estimation for MIMO channels is investigated by using the subspace method. Together with pilot symbols, the semi-blind channel estimation can be used and it can result in less (bit error rate) performance degradation of the MMSE linear and DF equalizers.

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 $$M$$ M -ary amplitude shift-keying ( $$M$$ 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.

In this paper, we propose a set of joint transmit diversity selection (TDS) and relay selection (RS) algorithms based on discrete iterative stochastic optimization for the uplink of cooperative multiple-input-multiple-output (MIMO) systems. Decode-and-forward (DF) and amplify-and-forward (AF) multirelay systems with linear minimum mean square error (MSE), successive interference cancelation, and adaptive reception are considered. The problems of TDS and RS are expressed as MSE and mutual information (MI) joint discrete optimization problems and solved using iterative discrete stochastic algorithms. Such an approach circumvents the need for exhaustive searching and results in a range of procedures with low complexity and increased speed of convergence that can track the optimal selection over an estimated channel. The proposed schemes are analyzed in terms of their complexity, convergence, and diversity benefits and are shown to be both stable and computationally efficient. Their performance is then evaluated via MSE, MI, and bit error rate comparisons and shown to outperform conventional cooperative transmission and, in the majority of scenarios, match that of the optimal exhaustive solution.

Mobile edge caching (MEC) has received much attention as a promising technique to overcome the stringent latency and data hungry requirements in future generation wireless networks. Meanwhile, full-duplex (FD) transmission can potentially double the spectral efficiency by allowing a node to receive and transmit in the same time/frequency block simultaneously. In this paper, we investigate the delivery time performance of full-duplex enabled MEC (FD-MEC) systems, in which the users are served by distributed edge nodes (ENs), which operate in FD mode and are equipped with a limited storage memory. Firstly, we analyse the FD-MEC with different levels of cooperation among the ENs and take into account a realistic model of self-interference cancellation. Secondly, we propose a framework to minimize the system delivery time of FD-MEC under both linear and optimal precoding designs. Thirdly, to deal with the non-convexity of the formulated problems, two iterative optimization algorithms are proposed based on the inner approximation method, whose convergence is analytically guaranteed. Finally, the effectiveness of the proposed designs are demonstrated via extensive numerical results. It is shown that the cooperative scheme mitigates inter-user and self interference significantly better than the distributed scheme at an expense of inter-EN cooperation. In addition, we show that minimum mean square error (MMSE)-based precoding design achieves the best performance-complexity trade-off, compared with the zero-forcing and optimal designs.

Compared to wired channels, time dispersive radio channels possess more frequent nulls in their spectral characteristics. Thus, the performance of linear filters to compensate intersymbol interference degrades dramatically. The well-known nonlinear decision feedback equalizer (DFE) is one approach to improve this behavior. However, in systems with observations of high dimensionality, the optimum DFE structure is computational intensive. In this paper, we apply the method of the multi-stage Wiener filter (MSWF) to a conventional minimum mean square error (MMSE) DFE in order to reduce computational complexity. The application of the new algorithm to an Enhanced Data rates for GSM Evolution (EDGE) system demonstrates the ability to outperform the even more computational intensive linear Wiener filter (WF).

In this paper, we investigate the optimization problem of joint source and relay beamforming matrices for a two-way amplify-and-forward (AF) multi-input multi-output (MIMO) relay system. The system, consisting of two source nodes and two relay nodes, is considered, and the linear minimum mean-square-error (MMSE) is employed at both receivers. We assume individual relay power constraints and study an important design problem, a so-called determinant maximization (DM) problem. Since this DM problem is nonconvex, we consider an efficient iterative algorithm by using an MSE balancing result to obtain at least a locally optimal solution. The proposed algorithm is developed based on QL, QR, and Choleskey decompositions which differ in complexity and performance. Analytical and simulation results show that the proposed algorithm can significantly reduce computational complexity compared with their existing two-way relay systems and have equivalent bit-error-rate (BER) performance to the singular value decomposition (SVD) based on a regular block diagonal (RBD) scheme.

An adaptive distributed space-time coding (DSTC) scheme is proposed for two-hop cooperative MIMO networks. Linear minimum mean square error (MMSE) receive filters and adjustable code matrices are considered subject to a power constraint with an amplify-and-forward (AF) cooperation strategy. In the proposed adaptive DSTC scheme, an adjustable code matrix obtained by a feedback channel is employed to transform the space-time coded matrix at the relay node. The effects of the limited feedback and the feedback errors are assessed. Linear MMSE expressions are devised to compute the parameters of the adjustable code matrix and the linear receive filters. Stochastic gradient (SG) and least-squares (LS) algorithms are also developed with reduced computational complexity. An upper bound on the pairwise error probability analysis is derived and indicates the advantage of employing the adjustable code matrices at the relay nodes. An alternative optimization algorithm for the adaptive DSTC scheme is also derived in order to eliminate the need for the feedback. The algorithm provides a fully distributed scheme for the adaptive DSTC at the relay node based on the minimization of the error probability. Simulation results show that the proposed algorithms obtain significant performance gains as compared to existing DSTC schemes.