Turbo Coded Space-time Block codes for four transmit antennas with linear precoding

In this paper, we combine Turbo Codes (TC) and Space-Time Block Coding (STBC) in order to exploit channel coding and spatio-temporal diversities. Moreover, linearprecoding matrices are combined to efficiently improve the space-t ime diversity order of the multiple antenna system. In addition of these good performance results, the proposed system implemnts a simple linear decoder at the reception side, which has very low complexity compared to the Maximum Likelihood (ML) detectors currently used in such systems. Performance results, obtai ned by simulations are given for a 4 transmit antenna system, with different precoding matrix sizes over flat Rayleigh fading channels, for a global system including turbo channel codin g. The described scheme can easily and efficiently be adapted to a two transmit antenna system. The results are compared to oth er schemes given in literature. I. I NTRODUCTION Since 1993, Turbo codes are demonstrated to be very efficient to exploit the coding diversity, performing close to the Shannon limit [1]. In 1996, Foschini demonstrated that the spectral efficiency increases linearly with the minimum of transmit or receive antennas [2] when using multiple antenn a systems. Another way to exploit multiple antennas is to use STBC. The initial two-transmit antenna Orthogonal STBC (OSTBC) proposed by Alamouti [3] is merely decoded with a linear operation. Another advantage of this code is its unitary rate. Then, Tarokh [4] extended OSTBC to 3 or 4 transmit antennas with linear decoding as well, but resulti ng in lower 1/2 and 3/4 rate codes. Since, many studies have been carried out to find out space-time codes with more than two antennas and rate one, all resulting in Quasi Orthogonal STB C (QOSTBC) [5, 6, 7], thus requiring more complex than linear detector such as Maximum Likelihood (ML) detector. In parallel, linear precoding also called constellation ro tati n was demonstrated to efficiently exploit time diversity for Single Input Single Output (SISO) systems [8]. In [9], a syst em combining the STBC proposed in [5] with linear precoding is presented, but the complexity of its ML detector varies exponentially with the length of the precoding matrix. In this paper, we tested the influence of the channel coding for the system pesented in [10], where linear precoding and OSTBC are efficiently combined. As channel coding scheme, we have implemented the robust duo binary turbo channel encoder that is proposed in DVB-RCT standard [11]. This scheme is compared to linear precoded QOSTBC described in [9]. As we will show, the diversity order increases with the s ize of the precoding matrix. We will focus our attention on linea r precoding matrices based on Hadamard matrix construction. This specific combination of turbo coded linear precoding an d OSTBC has the effect of increasing the overall diversity of * France Telecom R&D, Rennes, France. E-mail: vincent.lenir@rd.francetelecom. com the system by scattering the information in the space, time or frequency domains. At the receiver, before turbo decodin g a simple linear detector offers a good trade-off between performance and complexity thanks to low interference term s. First, in session II, we recall the channel representation o f OSTBC. In session III, we focus on the state of the art of 4 transmit existing systems and especially on QOSTBC channel representation. In session IV, we introduce our new scheme for 4 antennas, which is based on the combination of one particular linear precoding technique with OSTBC. Formula s are given, highlighting the importance of the interference terms that must be minimized in order to increase the performance. Before concluding, we give simulation results of the propos ed system for different precoding matrix sizes, with and witho ut duo binary turbo channel coding. We compare the obtained performance to existing four antennas systems. For this study, frequency non-selective flat Rayleigh fadin g channel and time invariance during T symbol durations are assumed as well as perfect channel estimation. Hence, the th eoretical channel response, from transmit antenna t to receive antennar can be estimated by htr = ρtretr . Moreover, we consider uncorrelated channels from each transmit antenna t to each receive antenna r. II. GENERAL OSTBCDESCRIPTION In this section an OSTBC description based on channel r presentation is given. The Alamouti code [3] can be represented as follows: G2 = [ s1 −s ∗ 2 s2 s ∗ 1 ] (1) Under the assumption that the fading coefficients are constant overT = 2 consecutive symbol durations, the Alamouti OSTBC code forNt = 2 transmit andNr = 1 receive antenna is represented by: r = H.s + n (2) wherer = [r1 r2] is the received signal over two consecutive symbol durations, s = [s1 s2] is the transmitted signal, n = [n1 n2] T is the additive white gaussian noise, H = [