Robust FIR precoder design with imperfect channel knowledge for broadband MIMO wireless systems

We study how to design a worst-case robust training sequence for multiple-input multiple-output (MIMO) channel estimation. We consider mean-squared error of channel estimates as the figure of merit which is a function of second-order statistics of the MIMO channel, i.e., channel covariance matrix, in order to optimize training sequences under a total power constraint. In practical applications, the channel covariance matrix is not known perfectly. Thus the main aspect of our design is to improve robustness of the training sequences against possible uncertainties in the available channel covariance matrix. Using a deterministic uncertainty model, we formulate a robust training sequence design as a minimax optimization problem where we take such imperfections into account. We investigate the robust design problem assuming the general case of an arbitrarily correlated MIMO channel and a non-empty compact convex uncertainty set. We prove that such a problem admits a globally optimal solution by exploiting the convex-concave structure of the objective function, and propose numerical algorithms to address the robust training design problem. We proceed the analysis by considering multiple-input single-output (MISO) channels and Kronecker structured MIMO channels along with unitarily-invariant uncertainty sets. For these scenarios, we show that the problem is diagonalized by the eigenvectors of the nominal covariance matrices so that the robust design is significantly simplified from a complex matrix-variable problem to a real vector-variable power allocation problem. For the MISO channel, we provide closed-form solutions for the robust training sequences with the uncertainty sets defined by the spectral norm and nuclear norm.

Accurate channel state information (CSI) is a prerequisite for diversity and multiplexing gains in multiple-input multiple-output (MIMO) wireless systems. More refined CSI can be attained by bootstrapping channel estimation techniques. We propose adaptive filtering-based iterative channel estimators with the incorporation of an iterative receiver over a flat-fading MIMO wireless link. The performance of three different algorithms with the aid of hard decision feedback is evaluated and compared through simulations. We show that the least-mean-square algorithm is a reasonable choice among the other considered algorithms in terms of performance and feasibility.

Multiple transmit-receive antenna based wireless communication system is a well investigated area in the literature. However, within the scope of author’s knowledge there are few analytical frameworks which facilitate communication system design engineers to select the required transmit-receive antenna combination for a given quality of service (QoS) in terms of Bit Error Rate (BER) or Symbol Error Rate (SER). Most of such frameworks for Multiple-Input Multiple-Output (MIMO) wireless systems in the existing literature are lacking tightness between theoretical approximation and actual simulation results. The aim of investigation in this study is to provide theoretical expectation of receiver performance with MIMO wireless communication system within a given channel. In this study, new analytical performance bound frameworks with tighter lower bounds have been presented for different receivers for MIMO systems. On the basis of the presented analytical framework, a simulation platform has been established. The channel state information as well as expected quality of service is assumed to be known for simplicity. Rayleigh fading channel has been considered within simulation platform. Simulation results show that the proposed frameworks provide degree of tightness up to 100 times at Signal to Noise Ratio (SNR) 20 dB for (2x2) MIMO system in comparison to the existing frameworks. Few other MIMO antenna combinations have been considered in the evaluation process of the proposed framework.

Multiple-input multiple-output (MIMO) wireless communication systems can achieve higher throughput through interference alignment. For a small number of users, determining the maximum possible degrees of freedom as well as the feasibility of interference alignment in MIMO systems is well studied. However, the issues of scheduling in systems employing interference alignment and serving a large number of users have received little attention so far. In this paper, we study the problem of joint scheduling, interference alignment, and packet admission control in MIMO wireless systems with the goal of maximizing system throughput subject to stability constraints. We formulate a stochastic network optimization problem and propose a scheduling and interference alignment (SIA) algorithm. In each time slot, SIA schedules some users among many competing ones to transmit data, and determines encoding and decoding matrices for the selected users. Packet admission control is performed in each time slot. In addition, we propose a heuristic semi-distributed algorithm (SDSIA), which has a lower computational complexity than the SIA algorithm. Via simulation, we evaluate the performance of SIA and SDSIA for different algorithm parameters and different numbers of users. We also compare the performance of SDSIA with other approaches which do not simultaneously exploit interference alignment and scheduling and find that the combination of these two techniques increases the achievable data rate dramatically.

The use of multiple antennas at both ends of a wireless link such as multiple-input multiple-output (MIMO) systems are now expected to hold the potential to drastically improve the spectral efficiency and link reliability in the future wireless communications. This is due to the fact that a MIMO channel can offer a capacity gain over a traditional single-input single-output (SISO) channel. These spectral efficiency gains often require accurate knowledge of the channel at the receiver, and some times at the transmitter as well. In this paper, we present the concept and discuss some ongoing research directions on the channel capacity of a MIMO wireless system. Preliminary simulations show linear increasing results in spectral efficiency of MIMO with an arbitrary number of transmit or receive antennas.

Multipath fading is one of the primary factors for degrading the performance in a wireless network. Information theoretic and past research suggest the use various diversity techniques to combat fading in wireless networks. Antenna diversity, a form of diversity technique, when incorporated in a wireless transceiver increases the system capacity and is one of the effective methods to combat fading in wireless systems. Also, recent research by Laneman et.al., Sendonaris et.al. suggests that cooperation among users in a wireless networks is an effective approach for a better signal reception in multipath fading environments. The diversity gains obtained by cooperation among the users of a wireless network is termed as cooperative diversity . Although, prior research in cooperative diversity considers users equipped with single antenna, in practical scenarios users may be able to accommodate multiple antennas due to the recent advanced research in semiconductor industry. Hence, the primary purpose of this thesis is to design, simulate and analyze an end-end performance of multi-antenna wireless systems employing cooperative multi antenna relay nodes so as to exploit the cooperative diversity and antenna diversity simultaneously in a wireless networks. Three main contributions to the area of cooperative multiple-input multiple-output (MIMO) wireless systems is presented in this thesis. First, we perform information theoretic analysis to study the impact of antenna arrays on cooperative wireless networks and propose the best possible distribution of antenna arrays among the three terminals of a simple three terminal cooperative relay network. Second, we design, simulate, and analyze a cooperative multiple-input multiple-output (MIMO) wireless systems employing orthogonal space-time block codes as proposed by Alamouti in 1998 with a decode-and-forward (DF) relay terminal. We implement a maximal ratio combining receiver that provides almost twice the diversity gain with respect to point-point multiple input multiple output link. Finally, we implement a practical receiver for cooperative reception using multiple antennas at all nodes based on Bell-Labs Layered Space Time architecture (BLAST). We incorporate a practical adaptive decode-and-forward (DF) relaying technique for reliable signal retransmission for both Alamouti space-time coding and the BLAST schemes. Results presented in terms of bit error rates and throughput show that remarkable performance gains are achievable by combining the concepts drawn from space-time coding, cooperative relaying and array processing.

The Taguchi robust design method traditionally deals with single‐characteristic problems. Various methods have been developed for extending the Taguchi single‐characteristic robust design method to the case of multi‐characteristic robust design problems. However, most of those methods have shortcomings in that they do not properly consider the variance–covariance structures among performance characteristics and/or do not preserve the original properties of the Taguchi signal‐to‐noise ratio for single‐characteristic robust design problems. To overcome these shortcomings, this paper develops a multivariate loss function approach to multi‐characteristic robust design problems with an appropriately defined signal‐to‐noise ratio. Its performance is evaluated using simulated examples, and the results indicate that it generally outperforms existing representative methods for correlated as well as uncorrelated experimental data. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we propose a robust transceiver design for MIMO interfering broadcast channels taking imperfect channel knowledge at each base station into consideration. By considering the worst-case transceiver design which maximizes the minimum signal-to-interference-plus-noise ratio (SINR), the proposed design can provide better sum rate and worst user rate performance compared to the conventional schemes. From simulation results, we show the resilience of the proposed design against imperfect channel knowledge.

In this paper, the problem of MIMO signal detection based on the belief propagation (BP) algorithm has been addressed in the presence of channel and noise uncertainties at the receiver. We propose a robust detection approach that works on the basis of message passing algorithm on the best tree approximation of the posterior distribution of the received signal. Our approach to make the detector robust is to formulate a worst-case detector design as a min-max optimization problem with imperfect channel and noise knowledge at the receiver.

Robust design is an important method for improving product manufacturability and life, and for increasing manufacturing process stability and yield. In 1980 Genichi Taguchi introduced his approach to using statistically planned experiments in robust product and process design to U.S. industry. Since then, the robust design problem and Taguchi's approach to solving it has received much attention from product designers, manufacturers, statisticians and quality professionals. Although most agree on the importance of the robust design problem, controversy over some of the specific methods used to solve the problem has made this an active research area.Although the answers are not all in yet, the importance of the problem has led to development of a four‐step methodology for implementing robust design. The steps are (1) formulate the problem by stating objectives and then listing and classifying product or process variables, (2) plan an experiment to study these variables, (3) identify improved settings of controllable variables from the experiment's results and (4) confirm the improvement in a small follow‐up experiment.This paper presents a methodology for the problem formulation and experiment planning steps. We give practical guidelines for making key decisions in these two steps, including choice of response characteristics, and specification of interactions and test levels for variables. We describe how orthogonal arrays and interaction graphs can be used to simplify the process of planning an experiment. We also compare the experiment planning strategies we are recommending to those of Taguchi and to more traditional approaches.

This work examines the use of two-way training to efficiently discriminate the channel estimation performances at a legitimate receiver (LR) and an unauthorized receiver (UR) in a multiple-input multiple-output (MIMO) wireless system. This work improves upon the original discriminatory channel estimation (DCE) scheme proposed by Chang where multiple stages of feedback and retraining were used. While most studies on physical layer secrecy are under the information-theoretic framework and focus directly on the data transmission phase, studies on DCE focus on the training phase and aim to provide a practical signal processing technique to discriminate between the channel estimation performances (and, thus, the effective received signal qualities) at LR and UR. A key feature of DCE designs is the insertion of artificial noise (AN) in the training signal to degrade the channel estimation performance at UR. To do so, AN must be placed in a carefully chosen subspace, based on the transmitter's knowledge of LR's channel, in order to minimize its effect on LR. In this paper, we adopt the idea of two-way training that allows both the transmitter and LR to send training signals to facilitate channel estimation at both ends. Both reciprocal and nonreciprocal channels are considered and a two-way DCE scheme is proposed for each scenario. For mathematical tractability, we assume that all terminals employ the linear minimum mean square error criterion for channel estimation. Based on the mean square error (MSE) of the channel estimates at all terminals, we formulate and solve an optimization problem where the optimal power allocation between the training signal and AN is found by minimizing the MSE of LR's channel estimate subject to a constraint on the MSE achievable at UR. Numerical results show that the proposed DCE schemes can effectively discriminate between the channel estimation and, hence, the data detection performances at LR and UR.

In modern wireless communication systems, accurate characterization of wireless propagation channels remains a significant challenge. In multiple-input multiple-output (MIMO) wireless systems, a double-directional channel can be achieved by utilizing multipath components' spatial and temporal properties (MPCs). Grouping the MPC can simplify the parameters as a trade-off between complexity and accuracy. This paper implements k-Deep Auto Encoder (k-DAE), AE+k-means, and K Power Means (KPM) clustering approaches and compares their performance in clustering wireless propagation multipaths in indoor and outdoor scenarios. The results show that AE+k-means performs better than k-DAE in indoor scenarios by 25.48%, while k-DAE performs 24.60 % better in outdoor scenarios. The KPM algorithm performs best in all indoor scenarios among the three algorithms, with a significant increase of 4.38% and 11.062% to AE+k-means and k-DAE, respectively. However, both k-DAE and AE+k-means have quite similar performance in outdoor scenarios. The study also highlights the first use of autoencoders in clustering the MPCs. The results indicate that k-DAE can be used as an alternative clustering method in channel modeling. Future works envisioned applying the approach to other wireless channel models.

The purpose of robust design optimization is to minimize variations in design performances and therefore to make the design insensitive to uncertainties. Current robust design methods fall into two types — probabilistic robust design and worst-case (interval) robust design. The former method is used when random variables are involved. In this method, robustness is measure by standard deviations of design performances. The later method is used when uncertainties are represented by intervals. The widths of design performances are then used to measure robustness. In many engineering application, both random variables and interval variables may exist simultaneously. In this paper, a general approach to robust design optimization is proposed. The generality comes from the ability to handle both random and interval variables. To alleviate the computational burden, we employ a previously developed general robustness assessment method — semi-second-order Taylor expansion method, to evaluate the maximum and minimum standard deviations of a design performance. An efficient integration strategy of the general robustness assessment and optimization is proposed. With the integration strategy, the number of function calls can be reduced while good accuracy is maintained. A robust shaft design problem is given for demonstration.

Multicell coordinated beamforming (MCBF) has been recognized as a promising approach to enhancing the system throughput and spectrum efficiency of wireless cellular systems. In contrast to the conventional single-cell beamforming (SBF) design, MCBF jointly optimizes the beamforming vectors of cooperative base stations (BSs) (via a central processing unit (CPU)) in order to mitigate the intercell interference. While most of the existing designs assume that the CPU has the perfect knowledge of the channel state information (CSI) of mobile stations (MSs), this paper takes into account the inevitable CSI errors at the CPU, and study the robust MCBF design problem. Specifically, we consider the worst-case robust design formulation that minimizes the weighted sum transmission power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on MSs. The associated optimization problem is challenging because it involves infinitely many nonconvex SINR constraints. In this paper, we show that the worst-case SINR constraints can be reformulated as linear matrix inequalities, and the approximation method known as semidefinite relation can be used to efficiently handle the worst-case robust MCBF problem. Simulation results show that the proposed robust MCBF design can provide guaranteed SINR performances for the MSs and outperforms the robust SBF design.

This paper investigates the capacity of multiple-input multiple-output (MIMO) wireless systems when instantaneous channel state information (CSI) is available at both the transmitter and the receiver in a line-of-sight Rician fading environment. Specifically, an infinite series representation for the ergodic capacity of uncorrelated Rician fading MIMO channels is derived, assuming both transmitter and receiver CSI and a specular component of arbitrary rank. The ergodic capacity and its associated outage probability are expressed in terms of a cutoff level capturing the optimal eigen-mode power and rate adaptation. Moreover, an equation from which the cutoff value can be solved for numerically is derived for arbitrary numbers of transmit and receive antennas.