Symbol Error Rate Performance Analysis for Generalized Coordinate Interleaved Orthogonal Designs over Nakagami- $$m$$ m Fading Channels

Abstract

Space-time block codes (STBC) using generalized coordinate interleaved orthogonal designs (GCIOD) proposed by Khan and Rajan (IEEE Trans Inf Theory 52(5):2062---2091, 2006) allow single-complex symbol decoding and offer higher data rates than orthogonal STBC. In this paper, we present an exact closed-form formula (i.e., not in integral form) for the average symbol pair-wise error probability of GCIODs derived in quasi-static frequency-nonselective independent identically distributed Nakagami- $$m$$ m fading channels. By using the formula, a tight union bound (UB) on symbol error rate (SER) is presented. Extensive simulation results show that the curves for the UB are asymptotically tight with the simulated SER curves for various antenna configurations and different modulations. The UB thus can be used to accurately predict and optimize the performance of GCIODs without the need of time-consuming simulations.