Reduced-state soft-output equalization for MIMO-ISI systems employing HOM

A reduced complexity soft-output joint equalization scheme is proposed for MIMO-ISI systems employing Higher Order Modulation (HOM). Multi-dimensional set partitioning proposed by Zhang et.al. [1] is applied to form a reduced-state trellis or the subset trellis. The Max-Log-MAP algorithm is modified to operate on the subset trellis in order to generate soft information at reduced complexity. The backward recursion can often be avoided since the forward recursion of the Max-LogMAP algorithm is capable of providing reliable soft information when some fixed decision delay is introduced. This idea is leveraged in the equalization scheme proposed in this paper. It generates soft information using only the forward recursion of the Max-Log-MAP algorithm and is referred to as the Forward-Only algorithm. A key requirement of reduced-state equalization is the ability to decide winners of parallel transitions using low-complexity slicing operations, which is accomplished via a novel flexible-complexity algorithm, viz., Reduced-State Tree Detection. Due to set partitioning, soft decision failure can occur in the forward-only algorithm and in such an event, a general approach to regenerate soft information using delayed decision feedback is proposed. The low complexity and memory requirements of the forward-only algorithm makes it attractive for MIMO-ISI equalization.