A Detection Algorithm for MIMO Transmission Using Poly-Diagonalization and Trellis Decoding

Abstract

A MIMO decoding algorithm utilizing polydiagonalization and tail-biting trellis is proposed. Linear MIMO decoding, such as zero-forcing equalization, is a channel diagonalization technique, where all interferences from other data streams are suppressed for separate decoding. It is well known, however, that such decoders suffer from the noise enhancement. In the proposed scheme, interferences are partially allowed, in order to alleviate the noise enhancement and, then, post trellis decoding is used for the joint detection utilizing the poly-diagonal structure of the effective channel. Under the proposed framework, the zero-forcing equalizer can be regarded as special cases of poly-diagonalization, i.e., of the first order. And the proposed scheme can provide a tradeoff between the complexity and performance by choosing an appropriate order of poly-diagonalization. According to the simulation results, considerable gain can be obtained even with the second order, i.e., bi-diagonalization, for which the decoding complexity is far less than that of the maximum likelihood decoding.

A Low Complexity MIMO Detection Based on Pair-Wise Markov Random Fields

“…One difference between the proposed scheme and the one in [16] is that, in our approach, the potential function is obtained by marginalizing the posterior joint probability density under the Gaussian assumption resulting in the bi-truncation in MMSE sense as in [6] while, in [16], it is similar to the bi-truncation in ZF sense, as also discussed in [6].…”

“…Pruning via linear processing: An alternative strategy to prune edges has been proposed in [5] and [6], where the channel is first transformed into a "poly-diagonal" form and, then, utilizing the poly-diagonal structure of the underlying channel matrix, a tail-biting trellis decoding (known also as forward-backward algorithm) is applied to produce the posterior likelihoods. In this approach, the edge degree, d f , could be as small as 2 for a reasonable performance degradation.…”

“…In this approach, the edge degree, d f , could be as small as 2 for a reasonable performance degradation. The idea in [6] is to use a multi-modal estimator, c Φ(j) for j = 1,2,…,M, either in zero-forcing (ZF) sense or in minimum mean squared error (MMSE) sense, where Φ(j) is the indices set consisting of ordered numbers {(j−l) M +1; l =1,…,L} with L defined as the order of poly-diagonalization. By applying c Φ(j) to the received vector y, we have n h c h c y c…”

“…Message passing rule 1 [6] Denote the message emanating from the variable node x j±1 and destined to x j (via y' j±1 ) as λ j±1→j (x j±1 ), which are all initially zero. Given this message, it is first translated into…”

“…Another type of MIMO detectors, which has not been received much attention, is the channel truncation approach [5] [6]. It is also a two stage detector, where the channel is first converted into a bi-diagonal or, more generally, a polydiagonal form [6] and, utilizing the effective channel structure, a trellis search, e.g., Viterbi algorithm or the forwardbackward algorithm [7], is used for post-joint detection.…”