Maximum Diversity Space-Time Systems with Maximum Rate for Any Number of Antennas

Various multi-antenna designs have been developed in recent years targeting either highperformance, or, high rate. In this paper, we design a layered space-time (ST) scheme equipped with linear complex field (LCF) coding, which enables full diversity with full rate, for any number of transmitand receive-antennas. Our theoretical claims are confirmed by simulations. Main Results Existing multi-antenna designs have been developed targeting either high-performance, or, high rate (e.g., VBLAST [3]). Recently, designs enabling desirable performance-rate tradeoffs receive increasing attention (see e.g., [1]). However, with Nt(Nr) transmit(receive-)antennae none of these schemes achieves simultaneously full diversity (NtNr), and full rate (Nt) for any number of antennas. In this paper, we design a layered space-time coding (STC) scheme equipped with linear complex field (LCF) coding, which enables full diversity and full rate (FDFR). System model: The information bearing symbols {s(i)} are drawn from a finite alphabet As, and parsed into blocks of size N × 1 so that s := [s(1), . . . , s(N)] . Every block s is split in sub-blocks (groups) {sg} g=1, each of length Nsub. Hence, N = NsubNg, where Ng is the number of groups. The LCF encoder {Θg} g=1 per group is an Nsub × Nsub matrix with entries drawn from the complex field. Each sub-block sg is coded linearly (via Θg) to obtain each LCF coded sub-block as: ug := Θgsg. Define an LCF coded group ug as one layer, and Ng as the number of layers per information block. The layers {ug} g=1 are further mapped to space-time matrix C, and transmitted through Nt antennas. Let hν,μ be the Rayleigh independent flat fading channel associated with the μth transmitantenna, and the νth receive-antenna. Selecting Nsub = Nt and Ng = Nt, our LCF-ST coded symbols transmitted per time slot from the Nt transmit-antennas are given by: C =   u1(1) uNt(2) · · · u2(Nt) u2(1) u1(2) · · · uNt−1(Nt) .. .. · · · .. uNt(1) uNt−1(2) · · · u1(Nt)   . (1) The matrix input-output relationship is Y = HC + W , (2) ∗The work in this paper was supported by the ARL/CTA Grant No. DAAD19-01-2-011.