On Secrecy Rate Analysis of MIMO Wiretap Channels Driven by Finite-Alphabet Input

This work investigates the effect of finite-alphabet source input on the secrecy rate of a multi-antenna wiretap system. Existing works have characterized maximum achievable secrecy rate or secrecy capacity for single and multiple antenna systems based on Gaussian source signals and secrecy code. Despite the impracticality of Gaussian sources, the compact closed-form expression of mutual information between linear channel Gaussian input and corresponding output has led to broad application of Gaussian input assumption in physical secrecy analysis. For practical considerations, we study the effect of finite discrete-constellation on the achievable secrecy rate of multiple-antenna wire-tap channels. Our proposed precoding scheme converts the multi-antenna system into a bank of parallel channels. Based on this precoding strategy, we propose a decentralized power allocation algorithm based on dual decomposition for maximizing the achievable secrecy rate. In addition, we analyze the achievable secrecy rate for finite-alphabet inputs in low and high SNR cases. Our results demonstrate substantial difference in secrecy rate between systems given finite-alphabet inputs and systems with Gaussian inputs.Comment: 21 pages, 5 figures, Submitted to IEEE Transactions on Communications, April 4, 2011. Revision submitted on December 21, 201

Free Deterministic Equivalents for the Analysis of MIMO Multiple Access Channel

In this paper, a free deterministic equivalent is proposed for the capacity analysis of the multi-input multi-output (MIMO) multiple access channel (MAC) with a more general channel model compared to previous works. Specifically, a MIMO MAC with one base station (BS) equipped with several distributed antenna sets is considered. Each link between a user and a BS antenna set forms a jointly correlated Rician fading channel. The analysis is based on operator-valued free probability theory, which broadens the range of applicability of free probability techniques tremendously. By replacing independent Gaussian random matrices with operator-valued random variables satisfying certain operator-valued freeness relations, the free deterministic equivalent of the considered channel Gram matrix is obtained. The Shannon transform of the free deterministic equivalent is derived, which provides an approximate expression for the ergodic input-output mutual information of the channel. The sum-rate capacity achieving input covariance matrices are also derived based on the approximate ergodic input-output mutual information. The free deterministic equivalent results are easy to compute, and simulation results show that these approximations are numerically accurate and computationally efficient.Comment: 26 pages, 7 figures, Accepted by IEEE Transactions on Information Theor

On the Linear Precoder Design for MIMO Channels with Finite-Alphabet Inputs and Statistical CSI

This paper investigates the linear precoder design that maximizes the average mutual information of multiple-input multiple-output channels with finite-alphabet inputs and statistical channel state information known at the transmitter. This linear precoder design is an important open problem and is extremely difficult to solve: First, average mutual information lacks closed-form expression and involves complicated computations; Second, the optimization problem over precoder is nonconcave. This study explores the solution to this problem and provides the following contributions: 1) A closed-form lower bound of average mutual information is derived. It achieves asymptotic optimality at low and high signal-to-noise ratio regions and, with a constant shift, offers an accurate approximation to the average mutual information; 2) The optimal structure of the precoder is revealed, and a unified two-step iterative algorithm is proposed to solve this problem. Numerical examples show the convergence and the efficacy of the proposed algorithm. Compared to its conventional counterparts, the proposed linear precoding method provides a significant performance gain.Comment: 5 pages, 3 figures, accepted by IEEE Global Communications Conference (GLOBECOM) 2011, Houston, T

Performance Analysis of Wireless Systems with Doubly Selective Rayleigh Fading

Theoretical error performances of wireless communication systems suffering from both doubly selective (time varying and frequency selective) Rayleigh fading and sampler timing offset are analyzed in this paper. Single-input-single-output systems with doubly selective fading channels are equivalently represented as discrete-time single-input-multiple-output (SIMO) systems with correlated frequency-flat fading channels, with the correlation information being determined by the combined effects of sampler timing phase, maximum Doppler spread, and power delay profile of the physical fading. Based on the equivalent SIMO system representation, closed-form error-probability expressions are derived as tight lower bounds for linearly modulated systems with fractionally spaced equalizers. The information on the sampler timing offset and the statistical properties of the physical channel fading, along with the effects of the fractionally spaced equalizer, are incorporated in the error-probability expressions. Simulation results show that the new analytical results can accurately predict the error performances of maximum-likelihood sequence estimation and maximum a posteriori equalizers for practical wireless communication systems in a wide range of signal-to-noise ratio. Moreover, some interesting observations about receiver oversampling and system timing phase sensitivity are obtained based on the new analytical results

Optimal Diversity Combining Based on Linear Estimation of Rician Fading Channels

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of pilot-assisted least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. Exact analytical expressions for the symbol error rates of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counter-example to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results

Soft-decision Feedback Turbo Equalization for Multilevel Modulations

Error propagation phenomena is the major drawback for existing hard-decision feedback turbo equalizers. in this paper, we propose a new soft-decision feedback equalizer (SDFE) suitable for multilevel modulation systems employing turbo equalization. the proposed SDFE offers a low computational complexity growing only linearly with the number of equalizer coefficients, as opposed to the quadratic complexity of MMSE-Based linear turbo equalizer with time-varying coefficients (Exact-MMSE-LE). the performance and convergence property of the proposed SDFE are analyzed using extrinsic information transfer (EXIT) chart and verified by simulations in a severe InterSymbol interference channel set by Proakis. Results show that our approach performs close to Exact-MMSE-LE for BPSK/QPSK modulation. and for 8PSK/16QAM modulations, the proposed SDFE performs much better. It exhibits lower SNR threshold (SNR required for \u27waterfall\u27 BER) and much faster convergence than Exact-MMSE-LE. © 1991-2012 IEEE

On Linear Precoding of Non-regenerative MIMO Relays for QAM Inputs

Recent works have established that MIMO systems optimized for Gaussian source signals may suffer unexpected performance loss when practical inputs are in fact discrete QAM sources. There is a practical need in the optimization of MIMO related systems of various networking scenarios to specifically target source signals of finite QAM alphabet. in this work, we investigate the precoding optimization of wireless two-hop non-regenerative three-node MIMO relay networks driven by finite-alphabet inputs. Exploiting a known optimal structure for the precoder at relay and a special convexity property, we propose an iterative two-step numerical optimization algorithm. This algorithm is a general solution, not only for arbitrary source signals but also for cooperative networks with or without direct link. Simulation results demonstrate substantial performance improvement by the new precoder over precoders optimized under the Gaussian input assumption. © 2012 IEEE

On Linear Precoding of Nonregenerative MIMO Relay Networks for Finite-alphabet Source

Multiple input and multiple output (MIMO) relay could provide broader wireless coverage, better diversity, and higher throughput. Most existing precoder designs for either source or relay node are based on the assumption of Gaussian input signals. However, recent works have revealed possible performance loss of MIMO systems originally optimized for Gaussian source signals when applied to practical finite-alphabet source signals. In this work, we investigate the design problem of joint MIMO precoding for wireless two-hop nonregenerative cooperative relay networks under finite-alphabet source signals. We identify several structural properties of optimal precoders. Specifically, we provided the optimal left singular vectors of the relay precoder and proved the convexity of mutual information with respect to the square of relay precoder singular value. These results generalize the two-hop relay networks in Gaussian input assumption to the cooperative relay networks in arbitrary finite-alphabet input signals. Furthermore, we propose gradient-based numerical iterative optimization algorithms not only for arbitrary finite-alphabet source signal precoding but also for cooperative relay networks which may or may not have a direct source to destination link. Our results demonstrate substantial performance improvement over existing precoder designed traditionally under Gaussian input assumption, which indicates that the water filling based precoding strategy is not suitable for finite-alphabet constellation source inputs

Optimized Power Allocation for Packet Retransmissions of Non-Gaussian Inputs through Sequential AWGN Channels

This work investigates the optimization of power allocation for hybrid-ARQ (H-ARQ) retransmissions of non-Gaussian inputs over a bank of independent parallel Gaussian channels. We establish a general solution for maximizing generic transceiver objective utility functions that are monotonically non-decreasing and concave function with respect to the accumulated signal to noise ratio (SNR). Specifically, we investigate optimized solutions under two performance metrics, namely, the mutual information (MI) and the union bound of symbol error rate (UBSER) under maximal ratio combining (MRC) reception. We establish that efficient utilization of parallel channels in H-ARQ retransmissions requires sequential updating of signal-channel pairing as well as optimizing power allocation. Applying geometric analysis of power loading for H-ARQ retransmission, we show that for i.i.d. inputs that are not necessarily Gaussian, the optimum pairing policy should match signals of the lowest cumulative signal-to-noise ratio with channels of the best quality in each transmission, which is consistent with a similar result of, for Gaussian input signals. We further propose a generalized mercury/water filling algorithm for the optimal power assignment problem in H-ARQ. Simulation results illustrate substantial improvements over designs based on Gaussian input assumptions. © 1972-2012 IEEE