N ° d’ordre: 2011-20-TH THÈSE DE DOCTORAT SPECIALITE: PHYSIQUE Ecole Doctorale « Sciences et Technologies de l’Information des

The last few years witnessed a dramatic increase in the demand on high-rate reliable wireless communications due to the incorporation of broadband internet access and demanding multimedia services such as high-definition audio and video streaming to modern wireless devices. In order to meet these new requirements, resorting to Multiple-Input Multiple-Output (MIMO) techniques was inevitable as they may offer high-rate reliable wireless communications without any additional bandwidth. In the open loop case where the transmitter does not have any prior knowledge about the channel state information, space-time coding techniques have proved to efficiently exploit the MIMO channel degrees of freedom while taking advantage of the maximum diversity gain. As indicated by its name, a Space-Time Code (STC) refers to the coding of the information symbols over two dimensions namely time and space. On the other hand, the ML decoding complexity of STCs generally increases exponentially with the rate which imposes an important challenge to the incorporation of STCs in recent communications standards due to power consumption restrictions. In the present thesis, we focus on Space-Time Block Codes (STBCs) where the code matrix is expressed as a linear combination of the transmitted real symbols. Several families of STBCs that admit a reduced ML decoding complexity have been proposed in the literature, namely the g-group-decodable, fast-decodable and fast-group-decodable codes. The g-group decodable STBCs are codes where the ML metric may be expressed as a sum of g terms depending on disjoint sets of the transmitted symbols thus enabling separate detection of these disjoint sets and te l-0 07 71 98 2, v er si on 1 9 Ja n 20 13 significantly reducing the detection complexity. If the number of real symbols in each group is restricted to be one, the g-group-decodable codes coincide with the well-known orthogonal codes. However, for a STBC to be g-group decodable, a certain number of conditions must be satisfied which reduces the achievable rates. Moreover, the proposed construction methods for the g-group-decodable codes are based on sufficient but not necessary conditions which may reduce further the attainable rates. In Chapter 4, we investigate the maximal achievable rates of g-group-decodable STBCs for a specific type of code matrices that subsumes the majority of the STBCs proposed in the literature. We propose a new numerical approach based on necessary and sufficient conditions for g-group-decodable codes and present the maximal-rate symmetric g = 2 code and g = 3 code in the case of four transmit antennas. In order to remedy the rate limitation of the g-group-decodable codes, another family of codes has been proposed, namely the fast decodable codes. A fast-decodable STBC encloses a g-group-decodable code and makes use of the conditional detection approach to decode the transmitted symbols in two steps. The first step consists of evaluating the conditional ML estimation of the symbols belonging to the g-groupdecodable code. In the second step, the decoder has only to decode the rest of the symbols. In Chapter 5, we focus on the multiplexing of two orthogonal STBCs in the case of four transmit antennas by the means of a unitary matrix. We derive an upper bound for the rate of the proposed code structure in order to satisfy the cubic shaping property and then we prove that this rate is indeed achievable. Fast-group-decodable STBCs are g-group-decodable codes such that each group of symbol is fast-decodable. In Chapter 6, we propose a systematic approach to obtain fast-group-decodable rate-1 STBCs for an arbitrary number of transmit antennas. Applying the proposed method in the case of four transmit antennas, we obtain a new rate-1 fast-groupdecodable STBC that has to the best of our knowledge the least worstxii te l-0 07 71 98 2, v er si on 1 9 Ja n 20 13 case decoding complexity among comparable STBCs in the literature. The rate is then increased through multiplexing two rate-1 codes giving rise to a new fast-decodable rate-2 STBC that has the least worstcase decoding complexity. xiii te l-0 07 71 98 2, v er si on 1 9 Ja n 20 13