  Non-orthogonal space-time block codes (STBC) from cyclic division algebras
(CDA) having large dimensions are attractive because they can simultaneously
achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST
for a given number of transmit antennas) {\em as well as} full transmit
diversity. Decoding of non-orthogonal STBCs with hundreds of dimensions has
been a challenge. In this paper, we present a probabilistic data association
(PDA) based algorithm for decoding non-orthogonal STBCs with large dimensions.
Our simulation results show that the proposed PDA-based algorithm achieves near
SISO AWGN uncoded BER as well as near-capacity coded BER (within about 5 dB of
the theoretical capacity) for large non-orthogonal STBCs from CDA. We study the
effect of spatial correlation on the BER, and show that the performance loss
due to spatial correlation can be alleviated by providing more receive spatial
dimensions. We report good BER performance when a training-based iterative
decoding/channel estimation is used (instead of assuming perfect channel
knowledge) in channels with large coherence times. A comparison of the
performances of the PDA algorithm and the likelihood ascent search (LAS)
algorithm (reported in our recent work) is also presented.
