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A generic model of bit-interleaved coded modulation (BICM) on a multipath Rayleigh fading multiple-input multiple-output (MIMO) channel is derived. A practical low-complexity trellis-based receiver performing iteratively channel estimation, multilayer coded data detection and channel decoding is introduced. The inner multilayer data detector, employing reduced-state techniques together with generalized per-survivor processing, presents two-fold advantages. It enables one to cope with severe channel intersymbol interference and allows the use of more transmit antennas than receive antennas. Simulations show that our approach can dramatically improve the downlink performance of time division multiple access (TDMA) systems with high order modulation, such as EDGE, keeping a reasonable complexity at the receiver side.