Optimized Power Allocation and Signal Shaping for Interference-Limited Multi-antenna “Ad Hoc” Networks

This paper reports on investigations into the effects of spatial correlation on channel estimation and capacity of a multiple input multiple output (MIMO) system. Minimum mean square error (MMSE) method is applied for channel estimation under a correlated channel scenario. Simulation results for a 4 times 4 MIMO system with the Jakes model describing a channel between a base station and a mobile station demonstrate a trade-off between the effects of spatial correlation, channel estimation and capacity. For low values of signal to noise ratio (SNR), spatial correlation decreases channel estimation errors and improves capacity. For high values of SNR, spatial correlation has a less pronounced effect on improving channel estimation and thus the MIMO capacity is adversely affected by the decreased channel matrix rank.

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.

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as “massive MIMO”. Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.

This paper considers the design of a practical low-density parity check (LDPC)-coded multiple-input multiple-output (MIMO) system composed of M transmit and N receive antennas operating in a flat-fading environment where channel state information (CSI) is assumed to be unavailable both to the transmitter and the receiver. A soft iterative receiver structure is developed, which consists of three main blocks: a soft MIMO detector and two LDPC component soft decoders. We first propose at the component level several soft-input soft-output MIMO detectors whose performances are much better than the conventional minimal mean square error (MMSE)-based detectors. In particular, one optimal soft MIMO detector and two simplified suboptimal detectors are developed that do not require an explicit channel estimate and offer an effective tradeoff between complexity and performance. In addition, a modified expectation maximization (EM)-based MIMO detector is developed that completely removes positive feedback between input and output extrinsic information and provides much better performance compared with the direct EM-based detector that has strong correlations especially in fast-fading channels. At the structural level, the LDPC-coded MIMO receiver is constructed in an unconventional manner where the soft MIMO detector and LDPC variable node decoder form one super soft-decoding unit, and the LDPC check node decoder forms the other component of the iterative decoding scheme. By exploiting the proposed receiver structure, tractable extrinsic information transfer functions of the component soft decoders are obtained, which further lead to a simple and efficient LDPC code degree profile optimization algorithm with proven global optimality and guaranteed convergence from any initialization. Finally, numerical and simulation results are provided to confirm the advantages of the proposed design approach for the coded MIMO system.

After a few decades’ evolution of wireless communication systems, to ensure reliable highspeed communication over unreliable wireless channels is still one of the major challenges facing researchers and engineers. The use of multiple antennas at transmitter and receiver, known as multiple-input multiple-output (MIMO) communications, is one promising technology delivering desired wireless services. The main goal of this thesis is to study two important issues in wireless MIMO communication systems: receiver design for coded MIMO systems, and diversity-multiplexing tradeoff analysis in general fading channels. In the first part of this thesis, we decompose the receiver design problem into two subproblems: MIMO channel estimation and MIMO detection. For the MIMO channel estimation, we develop an expectation-maximization (EM) based semi-blind channel and noise covariance matrix estimation algorithm for space-time coding systems under spatially correlated noise. By incorporating the proposed channel estimator into the iterative receiver structure, both the channel estimation and the error-control decoding are improved significantly. We also derive the modified Cramer-Rao bounds (MCRB) for the unknown parameters as the channel estimation performance metric, and demonstrate that the proposed channel estimation algorithm can achieve the MCRB after several iterations. For the MIMO detection, we propose a novel lowcomplexity MIMO detection algorithm, which has only cubic order computational complexity, but with near-optimal performance. For a 4×4 turbo-coded system, we show that the proposed detector had the same performance as the maximum a posteriori (MAP) detector for BPSK modulation, and 0.1 dB advantage over the approximated MAP detector (list sphere decoding algorithm) for 16-QAM modulation at BER = 10−4. In the second part of this thesis, we derive the optimal diversity-multiplexing tradeoff for

Space-time techniques for multiple-input multiple-output (MIMO) systems potentially provide vast increases in capacity. In order to achieve the quoted capacity gains the MIMO channel impulse response (CIR) must be known or estimated. Thus far, existing MIMO channel estimation techniques have been limited to the narrowband case or cater specifically for coded space-time systems. In this paper, we present a novel training-based MIMO channel estimation scheme for an uncoded layered space-time system that operates in the wideband frequency-selective fading environment. The method uses a pilot matrix consisting of pilot symbols derived from the Paley-Hadamard matrix in order to jointly estimate the individual CIR of the MIMO channel. The orthogonal property of the pilot matrix is utilized to resolve both intersymbol interference and intercarrier interference of the multiple transmit and received signals. The Paley Toeplitz structure is also exploited in order to minimise the length of the pilot sequence for a given length of CIR and thus maximise the effective data throughput. Results are presented which demonstrate the accuracy of the proposed channel estimation scheme and its performance in a layered space-time system.

In recent years, multiple-input multiple-output (MIMO) systems, which use several transmit and receive antennas, have attracted much attention for high performance radio systems. In MIMO systems, the channel estimation is important to distinguish transmit signals from multiple transmit antennas. While the space-alternating generalized expectation-maximization (SAGE) algorithm is known to offer good channel estimation and data detection. We proposed earlier the minimum mean square error (MMSE)-based SAGE algorithm for MIMO systems where the MMSE estimation is used for channel estimation. We showed that the proposed MMSE-based SAGE algorithm can achieve the better bit error rate (BER) than the maximum likelihood (ML) detection with training symbols. The MMSE channel estimation needs the knowledge of the maximum Doppler frequency F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> for deriving the covariance matrix of the channel and the variance sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of additive white Gaussian noise (AWGN). Additionally, the computation of the MMSE channel estimation requires O(L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where L is the transmitted frame length. Thus, its computational complexity is high. In this paper, we propose a zero-forcing (ZF)-based SAGE algorithm for channel estimation and data detection in MIMO systems that does not need the knowledge of Fd and sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Since the computation of the proposed ZF-based SAGE algorithm requires O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where N is the number of transmit antennas, its computational complexity is low. We show that the proposed ZF-based tracking SAGE algorithm with less computational complexity can achieve almost the same BER as that of the MMSE-based tracking SAGE algorithm

This paper presents a novel iterative detection and channel estimation scheme that combines the effort of superimposed training (ST) and pilot-aided training (PAT) for multiple-input multiple-output (MIMO) flat fading channels. The proposed method, hereafter known as joint mean removal ST and PAT (MRST-PAT), implements an iterative detection and channel estimation that achieves the performance of data-dependent ST (DDST) algorithm, with the difference that the data arithmetic cyclic mean is estimated and removed from data at the receiver’s end. It is demonstrated that this iterative and cooperative detection and channel estimator algorithm surpasses the effects of data detection identifiability condition that DDST has shown when higher orders of modulation are used. Theoretical performance of the MRST-PAT scheme is provided and corroborated by numerical simulations. In addition, the performance comparison between the proposed method and different MIMO channel estimation techniques is analyzed. The joint effort between ST and PAT shows that MRST-PAT is a solid candidate in communications systems for multiamplitude constellations in Rayleigh fading channels, while achieving high-throughput data rates with manageable complexity and bit-error rate (BER) as a figure of merit.

This paper describes investigations into the antenna mutual coupling (MC) effect on channel estimation and capacity of a multiple-input multiple-output (MIMO) wireless communication system. The presented investigations close the gap existing in the previous works which assessed the effect of mutual coupling on MIMO capacity under the assumption of availability of perfect channel state information (CSI) at the receiver. The new approach assumes that the perfect CSI is not available due to channel estimation errors. The investigations are carried out for different spacing between array antenna elements producing a varying effect of mutual coupling on the channel estimation and the resulting MIMO channel capacity.

A novel training-based channel estimation scheme is presented for an uncoded layered space-time system that operates in a wideband frequency selective fading environment of a time-varying multiple-input multiple-output (MIMO) channel. The method uses a pilot matrix consisting of pilot symbols derived from the Paley-Hadamard matrix to estimate the MIMO channel impulse response. The orthogonality of the pilot matrix resolves both the intersymbol interference and the cochannel interference of the wideband MIMO channel. The Toeplitz-like structure of the Paley-Hadamard matrix is exploited to minimise the length of the pilot sequence, reducing pilot symbol overhead. A decision feedback algorithm is used to track the time-varying MIMO channel. Results are presented which demonstrate the performance of the proposed MIMO channel estimator in a layered space-time system for different mobile velocities and system configurations.

Multiple Input Multiple Output (MIMO) system with orthogonal frequency division multiplexing (OFDM) is a promising physical layer candidate for the current and future wireless standards. MIMO increases system throughput while OFDM maximizes spectrum efficiency. To reduce the impacts of frequency selective fading and increase the capacity, MIMO requires precise channel state information (CSI). The presence of carrier frequency offset (CFO) introduces intercarrier interference (ICI) among the subcarriers which degrades the system performance. MIMO channel estimation is done under the assumption of perfect frequency synchronisation between the transmitter and receiver, or zero CFO. However, such an assumption is incorrect for time-varying and frequency-selective wireless channels, and the presence of CFO has an impact on channel estimation accuracy. In the existing methods, CFO and channel estimations are carried out independently using separate training sequences which reduces the spectral efficiency. As a result, the pilot aided interpolation approach is proposed in this paper for the joint estimate and compensation of CFO and channel effects using the same set of pilot tones. Theresults show that the proposed method offers precise CFO and channel estimation which improves the bit error rate performance and carrier to interference power ratio (CIR) of MIMO-OFDM system.

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 investigates iterative frequency domain techniques for the reception of spatially multiplexed single carrier signals transmitted over frequency-selective multiple input multiple output (MIMO) channels. The investigated equalizers are based on the soft-cancellation (SC) and minimum mean square error (MMSE) altering technique for turbo-coded single carrier point-to-point MIMO systems. We consider two different transmit antenna separation techniques in the frequency domain: (1) antenna-by-antenna (AA) and (2) joint over antenna techniques (JA). (1) aims to separate signals in different layers by MMSE filtering antenna-by-antenna, whereas (2) aims to detect the composite signal comprised of the signals transmitted from the multiple antennas. In (2) the composite received signal is decomposed by using the spatial maximum a posteriori probability (MAP) algorithm. We evaluate performances in terms of frame error rate (FER) and throughput in point-to-point MIMO frequency-selective fading channels. Impacts of spatial correlation on performance of the two detectors are also investigated in this paper.

In this thesis we consider the performance degradation of three telecommunication transceivers with respect to parameters uncertainties. The major contribution of our analysis is the derivation of simple and informative approximations to the excess mean square error, which uncover the basic factors that determine the performance of each transceiver under the pres- ence of parameter uncertainties. In Chapter 1, we brie°y present the channel models and the transceiver structures used in this thesis. In Chapters 2 and 3, we consider the case of the Multiple-Input Multiple-Output (MIMO) °at fading channel and two widely known transceiver schemes, i.e., the trans- mit MIMO Wiener ?ltering and the Tomlinson-Harashima (TH) precoding. For the case of the transmit MIMO Wiener ?ltering, degradation is due to channel estimation errors and time-variations, and noise second-order statistics estimation errors. For the case of the TH precoder, degradation is due to channel estimation errors and time-variations. For both cases, our ?nal expressions uncover the factors that determine the performance degradation in practice, and the relative importance between di®erent error sources. In Chapter 4, we consider the case of the Single-Input Single-Output (SISO) frequency selective channel and the minimum mean square error (MMSE) linear equalizer. The error sources that cause the system degradation is the channel and CFO estimation errors. Our aim is to uncover the relative importance of these error sources. It turns out that the CFO estimation error is much more important than the channel estimation error. This fact leads to useful conclusions concerning the optimal training sequence design for joint CFO and channel estimation.

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.