Single-symbol and Double-symbol Decodable STBCs for MIMO Fading Channels

For a communication system operating in a fading environment, receive antenna diversity is a widely applied technique to reduce the detrimental effects of multi path fading. But as this makes the receiver complex and costly, is generally used exclusively at the base station. Recently a combination of transmit and receive diversity has been suggested as a more effective solution to the above problem resulting in a MIMO (Multiple Input Multiple Output) fading channel which has been shown to have the potential of supporting large data rates as compared to SISO (Single Input Single Output) channels. Signal design for such a MIMO channel is known as Space-Time Codes (STC), which take advantage of both space and time diversity available with time varying fading by coding both in space and time. Space-Time Block Codes (STBC) are promising in this regard as there exist fast decoding algorithms like sphere decoding, etc. Further there exist classes of codes among STBCs that have very simple decoding properties like STBCs from orthogonal designs (ODs) and quasi-orthogonal designs (QODs). This simplicity of decoding for ODs and QODs is due to the fact that the Maximum Likelihood (ML) decoding metric can be written as sum of squares of terms each depending on only one variable in the case of OD and two variables in the case of QODs; as a result each variable can be decoded separately for ODs and pairs of variables for QODs. However the rates of ODs and QODs are restrictive; resulting in search of other codes. It is in this context that STBCs are investigated in this thesis where we classify and characterize all STBCs that have decoding properties similar to ODs and QODs; calling them “single-symbol decodable (SD)” and “double-symbol decodable (DSD)” respectively, for quasi-static and fast-fading channels when channel state information (CSI) is known at the receiver. The characterization of single-symbol decodable STBCs shows that full-rank singlesymbol decodable designs can exist outside the well-known Generalized Linear Processing Complex Orthogonal Designs. In particular, we present single-symbol decodable, fullrank, rate 1, space-time block codes (STBCs) for 2 and 4 antennas that are not-obtainable from GLCODs. The characterization of single-symbol decodable STBCs proceeds in two steps: first, we characterize all linear STBCs, that allow single-symbol ML decoding (not necessarily fulldiversity) over quasi-static fading channels-calling them single-symbol decodable designs (SDD). The class SDD includes GLCOD as a proper subclass. Among the SDD those that offer full-diversity, called Full-rank SDD (FSDD), are characterized. For square FSDD, complete classification and construction of maximal rate designs are presented. As a consequence, we show that full-rank, rate-one, square SDD exist only for 2 and 4 transmit antennas and GLCODs are not maximal rate FSDD except for N = 2. For non-square FSDD we present a class of non-GLCOD, STBCs called Generalized Co-ordinate Interleaved Orthogonal Designs (GCIODs). Construction of various high rate (>1/2) designs within this class of codes is presented and the coding gain and maximum mutual information (MMI) of these codes is evaluated and compared with known STBCs. We then show that the class of GLCODs and GCIODs arise naturally when all maximal SNR STBCs are characterized. A characterization of all double-symbol decodable STBCs is then presented, in particular we present a double-symbol decodable, full-rank, rate 1, STBCs for 8 antennas. Next, we propose designs for fast-fading channels and derive maximal rates of single, double symbol decodable designs for fast-fading channels. Of particular interest is the uniqueness of CIOD for 2 Tx. which has single-symbol decodability for both quasi-static and fast-fading channels. It turns out that co-ordinate interleaving of complex constellations is an effective tool to improve the diversity performance of MIMO fading channels without accruing any complexity penalty at the receiver.