Spatially Modulated Non Orthogonal Space Time Block Code: Construction and design from cyclic codes over Galois Field

A new class of non-binary Spatially Modulated Non-orthogonal Space Time Block Code designs (SM-NSTBC) has been proposed. These designs employ full rank, length n,(n|qm−1,m≤n) cyclic codes defined over GF(qm). The underlying cyclic code constructions have the property that the codewords when viewed as m×n matrices over GF(q) have rank equal to m (Full rank). These codes are punctured to yield m×m full rank matrices over GF(q). Rank preserving transformations are used to map the codewords of full rank codes over a finite field to full rank Space Time Block Codes. The proposed scheme can be generalized to handle any number of transmit antenna greater than two. Due to the characteristics of Full rank cyclic codes employed, a coding gain of approximately 1.5 dB to 5 dB is obtained over conventional STBC-SM and SM-OSTBC schemes. This is demonstrated for spectral efficiencies of 4, 5, 7 and 8 bpcu. Analytical as well as Monte-Carlo simulations show that proposed SM-NSTBC outperforms STBC-SM and its variants. The upper bound on average bit error rate has been derived and the computation complexity for ML detection has been estimated.