Throughput analysis and design of fixed and adaptive ARQ/diversity systems for slow fading channels

We study the performance of a fixed diversity (FD) ARQ system in which no error correction coding is used, and only second order transmitter diversity is used. In the system two spatially separated antennas are used to transmit the same information signal in a staggered fashion. In an FD system with two transmitting antennas, due to the staggered nature of transmission, the information rate of the FD system is 1/2, and we compare this system with the block-coded hybrid ARQ system of rate 1/2 used by Sayeed (see International Journal of Wireless Information Networks, 1997, Doctoral Disseration, University of Pennsylvania, 1996), and by Weerackody (1993). Due to the lower information rate of the transmitter diversity system, we do not wish to diversify at all times, but only when diversity is required. Thus we propose an adaptive ARQ/diversity (AD) system, in which the transmitter adaptively switches between the single antenna and dual antenna mode using the implicit channel state information contained in the number of consecutive ACKs and NACKs. Using analytical techniques we show that the performance of the adaptive diversity system equals the performance of adaptive ARQ/FEC techniques that have been used by Kallel (1994), by Sayeed and Weerackody (see Proceedings of Conference on Information Sciences and Systems, CISS '96, 1996), and by Deng and Lin (see IEEE Transactions on Communications, vol.-43, no.2/3/4, p.733-7, 1995) which uses the uncoded and a rate half maximum distance separable code (MDS).