Azadeh Vosoughi

Everything you always wanted to know about training: guidelines derived using the affine precoding framework and the CRB

In this paper, affine precoding is used to investigate the tradeoffs that exist while using the transmitter resources on training versus information symbols. The channel input is a training vector superimposed on a linearly precoded vector of symbols. A block-fading frequency-selective multi-input multi-output (MIMO) channel is considered. To highlight the tradeoffs between training and data symbols, the Fisher information matrix (FIM) is derived under two circumstances: the random parameter vector to be estimated contains 1) only fading channel coefficients and 2) unknown data symbols as well as the channel coefficients. While strategy 1 corresponds to the receiver structure in which the channel is estimated initially and the channel measurement is utilized to retrieve the data symbols, strategy 2 corresponds to the structure in which channel and symbol estimations are performed jointly. The interesting outcome of the study in this paper is that minimizing the channel Cramer-Rao bound (CRB) for strategies 1 and 2 under a total average transmit power constraint leads to different affine precoder design guidelines.

Impact of channel estimation error on decentralized detection in bandwidth constrained wireless sensor networks

In this paper we consider the problem of fusing decisions in a distributed detection system when the local binary decisions made at the sensors are transmitted over wireless links subject to fading and noise. We consider a training based channel estimator with which the fusion center (FC) estimates the complex channels between the sensors and the FC. We derive the likelihood-ratio-test (LRT) fusion rules that incorporate the complex channel estimates for the cases where the sensors employ BPSK, OOK, binary FSK, and binary PPM signaling to modulate their binary local decisions. We study the effect of channel estimation error on the system performance. As a benchmark we compare it with a fusion rule that assumes perfect channel state information (CSI). Performance evaluation shows that as SNR increases the channel estimation error decreases and the system performance approaches to the clairvoyant scenario where perfect CSI is assumed at the FC.

On the effect of receiver estimation error upon channel mutual information

Our goal in this paper is to study the effect of the receiver structure upon the achievable data rates. We consider transmission of linearly precoded data symbols over a frequency selective block fading multiple input multiple output (MIMO) wireless channel. To encompass a number of transmission schemes, we study this problem utilizing affine precoding, which is a unified model of linearly precoded data symbols with superimposed training. We focus on Bayesian receivers that estimate both the unknown fading coefficients and the data symbols. The receiver may adopt either of the following strategies to retrieve the data symbols: strategy (i) the receiver obtains joint Bayesian channel and symbol estimates, strategy, (ii) the receiver obtains a Bayesian channel estimate initially and the channel measurement is utilized to estimate the data symbols. For both strategies, we provide lower bounds on the mutual information between the data symbols and their corresponding estimates, and we relate these bounds to the symbol Cramer-Rao bound (CRB) matrices. In contrast to strategy (ii), for strategy (i) the lower bound does not depend on either the channel estimate or the covariance of the channel estimation error. For strategy (ii) we show that asymptotically (as the size of the transmission block grows) there is no loss of information after the maximum a posteriori (MAP) estimate of Gaussian symbols. We also provide guidelines to design affine precoders that maximize the derived lower bounds under the total average transmit power constraint.

Outage Probability and Power Allocation of Two-Way Amplify-and-Forward Relaying with Channel Estimation Errors

We consider a two-way amplify-and-forward (AF) relaying system consisting of two source nodes and a half-duplex relay. We assume that the source nodes are equipped with the linear minimum mean squared error (LMMSE) channel estimators. We investigate the effect of uncertainty due to channel estimation error on the system outage probability, considering the imposed bandwidth and energy costs of channel estimation. For a fixed transmission block length and a total transmit power constraint, we provide a compact-form expression for the system outage probability upper bound and we explore the optimal number of training symbols, the optimal power allocation between data and training, and the optimal power allotment between the two users and the relay, such that this bound is minimized. Our numerical results show that channel estimation error does not limit the performance in high signal-to-noise ratio (SNR). Also, the optimal power allocation between data and training and between the users and the relay provides a significant SNR improvement, compared with the suboptimal schemes, including fixed power allocation. The optimization gain increases as the relay moves away from the middle point.

How Does Channel Estimation Error Affect Average Sum-Rate in Two-Way Amplify-and-Forward Relay Networks?

This paper studies the impact of channel estimation error on the performance of a two-way amplify-and-forward (AF) relay network and investigates the optimal transmit resource allocation that minimizes the impact. In particular, we consider a three node network, consisting of two user terminals \mathbb{T}_A and \mathbb{T}_B and a half duplex relay node \mathbb{R}, where only \mathbb{T}_A and \mathbb{T}_B are equipped with channel estimators. Assuming block flat fading channel model, we adopt two estimation theoretic performance metrics, namely the Bayesian Cramer-Rao lower bound (CRLB) and the mean-squared error (MSE) of the linear minimum mean square error (LMMSE) channel estimate, and an information theoretic performance metric, namely the average sum-rate lower bound, as our optimality criteria. For a fixed transmission block length and under the total transmit power constraint, we investigate the optimal training vector design, the optimal number of training symbols in the training vector, the optimal power allocation between training and data in a transmission block, and the optimal power allotment between three nodes, such that these performance metrics are optimized, via utilizing bi-objective optimization methods. Our simulation results demonstrate that the optimal solutions corresponding to each performance metric vary, as the relay location and the system signal-to-noise ratio (SNR) change. They also reveal interesting symmetry relationship between these optimal solutions and the relay location.

Turbo estimation of channel and symbols in precoded MIMO systems

We consider a block fading frequency selective multi-input multi-output (MIMO) channel in additive white Gaussian noise (AWGN). The channel input is a training vector superimposed on a linearly precoded vector of Gaussian symbols. To achieve a better performance over the conventional least-squares (LS), we utilize the linear mean square error (LMMSE) symbol estimate to improve the initial LS estimate and update the symbol estimation accordingly. We provide the guidelines to design training which minimizes the MSE of the initial LS estimate.

Precoding and Decoding Paradigms for Distributed Vector Data Compression

In this paper, we consider the problem of lossy coding of correlated vector sources with uncoded side information available at the decoder. In particular, we consider lossy coding of vector source xisinRN which is correlated with vector source yisinRN, known at the decoder. We propose two compression schemes, namely, distributed adaptive compression (DAC) and distributed universal compression (DUC) schemes. The DAC algorithm is inspired by the optimal solution for Gaussian sources and requires computation of the conditional Karhunen-Loegraveve transform (CKLT) of the data at the encoder. The DUC algorithm, however, does not require knowledge of the CKLT at the encoder. The DUC algorithms are based on the approximation of the correlation model between the sources y and x through a linear model y=Hx+n in which H is a matrix and n is a random vector and independent of x. This model can be viewed as a fictitious communication channel with input x and output y. Utilizing channel equalization at the receiver, we convert the original vector source coding problem into a set of manageable scalar source coding problems. Furthermore, inspired by bit loading strategies employed in wireless communication systems, we propose for both compression schemes a rate allocation policy which minimizes the decoding error rate under a total rate constraint. Equalization and bit loading are paired with a quantization scheme for each vector source entry (a slightly simplified version of the so called DISCUS scheme). The merits of our work are as follows: 1) it provides a simple, yet optimized, implementation of Wyner-Ziv quantizers for correlated vector sources, by using the insight gained in the design of communication systems; 2) it provides encoding schemes that, with or without the knowledge of the correlation model at the encoder, enjoy distributed compression gains

Transmission Resource Allocation for Training Based Amplify-and-Forward Relay Systems

For a three node amplify-and-forward (AF) relay system in which only destination D is equipped with a channel estimator, we derive lower bound on training-based mutual information per transmission block. For a given transmission block length and a fixed total transmit power constraint between source S and relay R, we investigate jointly optimal number of training symbols, optimal power allocation between training and data, and optimal power allotment between S and R, such that the mutual information lower bound is maximized. For the AF relay system without direct link we provide analytical solutions to the joint optimization problem and relate the solutions to the relay location. For the AF relay system with direct link we resort to numerical evaluations to find the optimal solutions.

Channel estimation for precoded MIMO systems

We consider a block fading frequency selective multi-input multi-output (MIMO) channel in additive white Gaussian noise (AWGN). The channel input is a training vector superimposed on a linearly precoded vector of Gaussian symbols. This form of precoding is referred to as affine precoding. We derive the channel Cramer-Rao bound (CRB) and we show that tr(CRB) can be lowered if we design the precoder and training such that the channel estimation through the training component is not affected by the precoded symbols. We propose a deterministic channel estimation algorithm which combines a second order blind estimator capitalized on the redundant precoding, with a standard linear estimator which exploits only training. The simulation results show a performance improvement over the least square (LS) which utilizes only training to obtain the channel estimate.

Optimal Training and Data Power Allocation in Distributed Detection With Inhomogeneous Sensors

We consider a binary distributed detection problem in a wireless sensor network with inhomogeneous sensors, in which sensors send their binary phase shift keying (BPSK) modulated decisions to the fusion center (FC) over orthogonal channels that are subject to pathloss, Rayleigh fading, and Gaussian noise. Assuming training based channel estimation, we consider a linear fusion rule which employs imperfect channel state information (CSI) to form the global decision at the FC. Under the constraint that the total transmit power of training and decision symbols at each sensor is fixed, we analytically derive the optimal power allocation between training and data at each sensor such that the deflection coefficient at the FC is maximized. Our analysis shows that the proposed optimal power allocation scheme is a function of signal-to-noise (SNR) and local detection indices, and at high SNR regime, the proposed scheme outperforms the uniform power allocation.