We develop practical time- and frequency-domain adaptive equalizers for distributed time-reversal space-time block-coded (TR-STBC) systems. The adaptive equalizers eliminate the need for explicit channel impulse response estimation at the receiver. The length of the time-domain adaptive equalizer is also independent of the data block length, making it particularly suitable for frequency selective fading channels with short delay spreads. We derive the block minimum mean square error solutions for both time- and frequency-domain distributed TR-STBC systems and from these we develop recursive least squares adaptive algorithms for the block structures. We use computer simulations to compare both the time- and frequency-domain adaptive equalizers for amplify-and-forward relay networks. We show that the adaptive algorithms work well for Protocols I and III proposed by Nabar et al. The time-domain adaptive algorithms perform better than the frequency-domain algorithms, and overall the Protocol I receivers outperform the Protocol III receivers. We also show that, if only the Protocol III receiver is used, it can be susceptible to noise amplification due to a weaker source-to-relay link compared to the relay-to-destination link. This problem can be mitigated by using the Protocol I receivers with some extra complexity but much superior diversity performance.
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