Estimation over MIMO Fading Channels: Outage and Diversity Analysis
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In this thesis, estimation of signals over fading channels for analog uncoded transmission is considered. In communication settings with tight delay requirements, e.g. in real-time control over wireless fading channels and vehicle-to-vehicle communication, the use of efficient and therefore long channel codes for reliability is not possible. Without channel codes, one needs to seek out alternative techniques. One such technique is to send uncompressed discrete-time source samples directly over the channel and then estimate the source signals from the channel outputs at the receiver. It is then required that the estimation quality is assessed with respect to source and system parameters, such that suitable system parameters can be selected for a given setting. This work begins by considering scalar Gauss-Markov sources and communication over scalar Rayleigh fading channels. For estimation, the optimal minimum mean square filter, i.e. the Kalman filter, is used in order to estimate the signal at the receiver. In order to evaluate the performance of the Kalman filter, the estimation error outage probability is selected as a measure of quality. For random fading channels, the instantaneous estimation error variance for the Kalman filter is also random. Principally, the outage probability criterion measures the probability that the instantaneous estimation error variance of the Kalman filter exceeds a certain threshold. This measure is most meaningful in settings where delay is of concern. The presented results in this thesis include characterization of the estimation outage probability, derivation of the upper and lower bounds for a certain range of outage thresholds, and characterization of the behavior of the outage probability in the high signal-to-noise ratio regime. Next, the channel model is extended to include multiple receivers in order to obtain a diversity gain and improve the estimation quality. Due to lack of coding, diversity is a very a suitable way to obtain extra reliability when needed. For this setting too, upper and lower bounds are obtained for the outage probability. It is then shown that in the high signal-to-noise ratio regime, the estimation error outage probability decreases inversely polynomially with the signal-to-noiseratio to the power of the number of receivers. Afterwards, the source is extended to be a vector of arbitrary dimension and the channel to be a general MIMO Rayleigh fading channel. A joint Kalman filter and space-time coding scheme is proposed to allow for transmission of sources with any dimensions over the channel. The spacetime codes are incorporated in order to parallelize the channels and obtain full diversity for the estimation outage probability. Finally, two special scenarios are considered. The first is when the source dimension grows large. In this case, the source may be considered as a collection of users in a sensor network who transmit their measurements over a general MIMO fading channel without compression or other extra processing. The performance is analyzed in terms of the high signal-to-noise-ratio behavior of the average mean squared error. The second scenario, considers a case when source samples are not correlated in time, and are sent over parallel MIMO channels. The estimation quality is then improved by transmission over a larger number of channels than the source dimension.