In this paper, we first present two tight upper bounds for the normalized diversity products (or product distances) of2 × 2diagonal space-time block codes from quadratic extensions on\BBQ (i)and\BBQ ( \mmbzeta6), where i=radic{-1}and\mmbzeta6=exp(i2pi/6). Two such codes are shown to reach the tight upper bounds and therefore have the maximal normalized diversity products. We present two new diagonal space-time block codes from higher order algebraic extensions on\BBQ (i)and\BBQ ( \mmbzeta6)for three and four transmit antennas. We also present a nontight upper bound for normalized diversity products of2 × 2diagonal space-time block codes with QAM information symbols, i.e., in\BBZ [i], from general2 × 2complex-valued generating matrices. We then present ann×n-diagonal space-time code design method directly from2nreal integers based on extended complex lattices (of generating matrix sizen× 2n) that are shown to have better normalized diversity products than the optimal diagonal cyclotomic codes do. We finally use the optimal2 × 2diagonal space-time codes from the optimal quadratic extensions to construct two2 × 2full-rate space-time block codes and find that both of them have better normalized diversity products than the Golden code does.

In this paper, we show that the diversity products of the full transmit diversity space-time block codes proposed by Lu-Kumar (we call them Lu-Kumar's codes) with quadratic-amplitude modulation (QAM) constellations are lower bounded by 4. We present a sufficient condition on the minimum Hamming weight of the linear binary full-rank space-time code such that this lower bound is met. We show that the special Lu-Kumar codes does satisfy the sufficient condition, and therefore, the diversity products of the special Lu-Kumar codes are 4, where ldquospecialrdquo means that the linear binary full-rank space-time codes are not general but specially constructed by Lu-Kumar.

A generalized Chinese remainder theorem (CRT) for multiple integers from residue sets has been studied recently, where the remainders in a residue set are not ordered. In this correspondence, we first propose a majority method and then based on the proposed majority method we present a sharpened dynamic range of multiple integers that can be uniquely determined from their residue sets

In this correspondence, we first present a transformation technique to improve the normalized diversity product for a full rate algebraic space-time block code (STBC) by balancing the signal mean powers at different transmit antennas. After rewriting a cyclic division algebra structure into a multilayer structure for a full rate code, we show that the normalized diversity product of the transformed code with the multilayer structure is better than the one of the transformed code with the cyclic division algebra structure. We then present a new full rate algebraic STBC with multilayer structure with nonvanishing determinant (NVD) for three transmit antennas when signal constellation is carved from QAM. We show that the new code has larger normalized diversity product than the existing 3 times 3 NVD full rate STBC for quadrature amplitude modulation (QAM) signals, and we also show that it has the largest normalized diversity product in a family of full rate STBC.

Based on the normalized diversity product criterion of space-time code designs, we present two optimal 2/spl times/2 diagonal algebraic space-time block codes based on field extensions. We then present an n/spl times/n diagonal space-time code design method directly from 2n real integers based on extended complex lattices. We also present a non-tight upper bound for normalized diversity products of 2/spl times/2 diagonal space-time block codes with QAM information symbols from general 2/spl times/2 complex-valued matrices. We finally use the optimal 2/spl times/2 algebraic diagonal space-time codes to construct two 2/spl times/2 full rate space-time block codes and find that both of them have better normalized diversity products than the Golden code does.

In this correspondence, a new and systematic design of cyclotomic lattices with full diversity is proposed by using some algebraic number theory. This design provides infinitely many full diversity cyclotomic lattices for a given lattice size. Based on the packing theory and the concrete form of the design, optimal cyclotomic lattices are presented by minimizing the mean transmission signal power for a given minimum (diversity) product (or equivalently maximizing the minimum product for a given mean transmission signal power). The newly proposed cyclotomic lattices can be applied to both space-time code designs for multi-antenna systems and linear precode design for signal space diversity in single antenna systems over fast Rayleigh fading channels. Although there are some cyclotomic lattices/space-time codes existing in the literature, most of them are not optimal.

A systematic diagonal space-time block code (cyclotomic space-time code) design is proposed by using high dimensional cyclotomic lattices and some algebraic number theory. This design can be applied to any number of transmit antennas and for a fixed number of transmit antennas, there are infinitely many cyclotomic space-time codes. It is shown that all the cyclotomic space-time codes from the design have full diversity. Furthermore, optimal cyclotomic space-time codes from the design for different numbers of transmit antennas are obtained, where the optimality is in the sense that, for a fixed mean transmission signal power, its diversity product is maximized, or for a fixed diversity product, its mean transmission signal power is minimized. Although there are some cyclotomic space-time codes existed in the literature, most of them are not optimal.