On Full Diversity Space-Time Block Codes with Partial Interference Cancellation Group Decoding

In this paper, we propose a partial interferencecancellation (PIC) group decoding strategy/scheme for linear dis-persive space-time block codes (STBC) and a design criterion forthe codes to achieve full diversity when the PIC group decoding isused at the receiver. A PIC group decoding decodes the symbolsembedded in an STBC by dividing them into several groupsand decoding each group separately after a linear PIC operationis implemented. It can be viewed as an intermediate decodingbetween the maximum likelihood (ML) receiver that decodes allthe embedded symbols together, i.e., all the embedded symbolsare in a single group, and the zero-forcing (ZF) receiver thatdecodes all the embedded symbols separately and independently,i.e., each group has and only has one embedded symbol, afterthe ZF operation is implemented. The PIC group decodingprovides a framework to adjust the complexity-performancetradeoff by choosing the sizes of the information symbol groups.Our proposed design criterion (group independence) for thePIC group decoding to achieve full diversity is an intermediatecondition between the loosest ML full rank criterion of codewordsand the strongest ZF linear independence condition of thecolumn vectors in the equivalent channel matrix. We also proposeasymptotic optimal (AO) group decoding algorithm which is anintermediate decoding between the MMSE decoding algorithmand the ML decoding algorithm. The design criterion for thePIC group decoding can be applied to the AO group decodingalgorithm because of its asymptotic optimality. It is well-knownthat the symbol rate for a full rank linear STBC can be full, i.e.,nt, for nt transmit antennas. It has been recently shown thatits rate is upper bounded by 1 if a code achieves full diversitywith a linear receiver. The intermediate criterion proposed inthis paper provides the possibility for codes of rates between ntand 1 that achieve full diversity with the PIC group decoding.This therefore provides a complexity-performance-rate tradeoff.Some design examples are given.