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In this paper, we consider the signal detection for multiple input-multiple output intersymbol interference (MIMO-ISI) channels with diverse assumptions on the channel knowledge: perfect, blind, trained, etc. This general problem is cast into a unifying Bayesian statistics framework. With this formulation, the optimal detector is the one maximizing the posterior signal density [marginal maximum a posteriori (MAP)]. Since the marginal MAP is hard to deal with, a joint MAP formulation is proposed as a reasonable substitute that maximizes the posterior joint signal and channel density. It is also shown that for independent and identically distributed (i.i.d.) signals, the two formulations will lead to very close results. The joint MAP formulation leads to an iterative projection algorithm that alternates between the optimization over channel parameters and signaling matrices. The bottleneck of iterative projections is on the finite-alphabet constrained quadratic minimization. We show that the notion of error decomposition can be bridged with greedy optimizations to construct iterative greedy search algorithms and examine their performance. A particularization, called full greedy search, is shown to be able to reach the global optimum (maximum likelihood solutions) starting with any initialization. Since potential constraints in computational complexity may prohibit the application of this version of greedy search, we explore the performance (loss) for greedy search implementations with complexity constraints, arriving at deterministic performance bounds and a bit-error rate (BER) upper bound. The effect of model imprecision is also theoretically characterized. Based on the theoretical development, an iterative local optimization with interference cancellation (LOIC) algorithm is proposed to achieve low complexity and exploit the finite alphabet constraint. Motivated by the Sylvester structure, it approximates the full greedy search by focusing on local error sequences. It can also be regarded as a flexible interference cancellation strategy with noncausal information and iterative computations. An empirical comparison of detectors with perfect channel knowledge demonstrated that the proposed LOIC algorithms can offer very attractive BER/complexity tradeoffs.