It is well known that communication systems employing multiple transmit and multiple receive antennas provide high data rates along with increased reliability. Some of the design criteria of the space-time block codes (STBCs) for multiple input multiple output (MIMO)communication system are that these codes should attain large transmit diversity, high data-rate, low decoding-complexity, low decoding –delay and low peak-to-average power ratio (PAPR). STBCs based on real orthogonal designs (RODs) and complex orthogonal designs (CODs) achieve full transmit diversity and in addition, these codes are single-symbol maximum-likelihood (ML) decodable. It has been observed that the data-rate (in number of information symbols per channel use) of the square CODs falls exponentially with increase in number of antennas and it has led to the construction of rectangular CODs with high rate. We have constructed a class of maximal-rate CODs for n transmit antennas with rate if n is even and if n is odd. The novelty of the above construction is that they 2n+1 are constructed from square CODs. Though these codes have a high rate, this is achieved at the expense of large decoding delay especially when the number of antennas is 5or more. Moreover the rate also converges to half as the number of transmit antennas increases. We give a construction of rate-1/2 CODs with a substantial reduction in decoding delay when compared with the maximal- rate codes. Though there is a significant improvement in the rate of the codes mentioned above when compared with square CODs for the same number of antennas, the decoding delay of these codes is still considerably high. For certain applications, it is desirable to construct codes which are balanced with respect to both rate and decoding delay. To this end, we have constructed high rate and low decoding-delay RODs and CODs from Cayley-Dickson Algebra. Apart from the rate and decoding delay of orthogonal designs, peak-to-average power ratio (PAPR) of STBC is very important from implementation point of view. The standard constructions of square complex orthogonal designs contain a large number of zeros in the matrix result in gin high PAPR. We have given a construction for square complex orthogonal designs with lesser number of zero entries than the known constructions. When a + 1 is a power of 2, we get codes with no zero entries. Further more, we get complex orthogonal designs with no zero entry for any power of 2 antennas by introducing co- ordinate interleaved variables in the design matrix. These codes have significant advantage over the existing codes in term of PAPR. The only sacrifice that is made in the construction of these codes is that the signaling complexity (of these codes) is marginally greater than the existing codes (with zero entries) for some of the entries in the matrix consist of co-ordinate interleaved variables. Also a class of maximal-rate CODs (For mathematical equations pl see the pdf file)

In this thesis, we focus on interference cancelling (IC) detectors for advanced communication systems. The contents of this thesis is divided into the following four parts: 1. Multiuser interference (MUI) cancellation in uplink orthogonal frequency division multiple access (OFDMA). 2. Inter-carrier interference (ICI) and inter-symbol interference (ISI) cancellation in space-frequency block coded OFDM (SFBC-OFDM). 3. Single-symbol decodability (SSD) of distributed space-time block codes (DSTBC) in partially-coherent cooperative networks with amplify-and-forward protocol at the relays 4. Interference cancellation in cooperative SFBC-OFDM networks with amplify-and-forward (AF) and decode-and-forward (DF) protocols at the relays. In uplink OFDMA systems, MUI occurs due to different carrier frequency offsets of different users at the receiver. In the first part of the thesis, we present a weighted multistage linear parallel interference cancellation approach to mitigate the effect of this MUI in uplink OFDMA. We also present a minimum mean square error (MMSE) based approach to MUI cancellation in uplink OFDMA. We present a recursion to approach the MMSE solution and show structure-wise and performance-wise comparison with other detectors in the literature. Use of SFBC-OFDM signals is advantageous in high-mobility broadband wireless access, where the channel is highly time- as well as frequency-selective because of which the receiver experiences both ISI as well as ICI. In the second part of the thesis, we are concerned with the detection of SFBC-OFDM signals on time- and frequency-selective MIMO channels. Specifically, we propose and evaluate the performance of an interference cancelling receiver for SFBC-OFDM, which alleviates the effects of ISI and ICI in highly time- and frequency-selective channels The benefits of MIMO techniques can be made possible to user nodes having a single transmit antenna through cooperation among different nodes. In the third part of the thesis, we derive a new set of conditions for a distributed DSTBC to be SSD for a partially-coherent relay channel (PCRC), where the relays have only the phase information of the source-to-relay channels. We also establish several properties of SSD codes for PCRC. In the last part of the thesis, we consider cooperative SFBC-OFDM networks with AF and DF protocols at the relays. In cooperative SFBC-OFDM networks that employ DF protocol, i) ISI occurs at the destination due to violation of the `quasi-static' assumption because of the frequency selectivity of the relay-to-destination channels, and ii) ICI occurs due to imperfect carrier synchronization between the relay nodes and the destination, both of which result in error-floors in the bit error performance at the destination. We propose an interference cancellation algorithm for this system at the destination node, and show that the proposed algorithm effectively mitigates the ISI and ICI effects.

It is well known that communication using multiple antennas provides high data rate and reliability. Coding across space and time is necessary to fully exploit the gains offered by multiple input multiple output (MIMO) systems. One such popular method of coding for MIMO systems is space-time block coding. In applications where the terminals do not have enough physical space to mount multiple antennas, relaying or cooperation between multiple single antenna terminals can help achieve spatial diversity in such scenarios as well. Relaying techniques can also help improve the range and reliability of communication. Recently it has been shown that certain space-time block codes (STBCs) can be employed in a distributed fashion in single antenna relay networks to extract the same benefits as in point to point MIMO systems. Such STBCs are called distributed STBCs. However an important practical issue with STBCs and DSTBCs is its associated high maximum likelihood (ML) decoding complexity. The central theme of this thesis is to systematically construct STBCs and DSTBCs applicable for various scenarios such that are amenable for low decoding complexity. The first part of this thesis provides constructions of high rate STBCs from crossed product algebras that are minimum mean squared error (MMSE) optimal, i.e., achieves the least symbol error rate under MMSE reception. Moreover several previous constructions of MMSE optimal STBCs are found to be special cases of the constructions in this thesis. It is well known that STBCs from orthogonal designs offer single symbol ML decoding along with full diversity but the rate of orthogonal designs fall exponentially with the number of transmit antennas. Thus it is evident that there exists a tradeoff between rate and ML decoding complexity of full diversity STBCs. In the second part of the thesis, a definition of rate of a STBC is proposed and the problem of optimal tradeoff between rate and ML decoding complexity is posed. An algebraic framework based on extended Clifford algebras is introduced to study the optimal tradeoff for a class of multi-symbol ML decodable STBCs called ‘Clifford unitary weight (CUW) STBCs’ which include orthogonal designs as a special case. Code constructions optimally meeting this tradeoff are also obtained using extended Clifford algebras. All CUW-STBCs achieve full diversity as well. The third part of this thesis focusses on constructing DSTBCs with low ML decoding complexity for two hop, amplify and forward based relay networks under various scenarios. The symbol synchronous, coherent case is first considered and conditions for a DSTBC to be multi-group ML decodable are first obtained. Then three new classes of four-group ML decodable full diversity DSTBCs are systematically constructed for arbitrary number of relays. Next the symbol synchronous non-coherent case is considered and full diversity, four group decodable distributed differential STBCs (DDSTBCs) are constructed for power of two number of relays. These DDSTBCs have the best error performance compared to all previous works along with low ML decoding complexity. For the symbol asynchronous, coherent case, a transmission scheme based on orthogonal frequency division multiplexing (OFDM) is proposed to mitigate the effects of timing errors at the relay nodes and sufficient conditions for a DSTBC to be applicable in this new transmission scheme are given. Many of the existing DSTBCs including the ones in this thesis are found to satisfy these sufficient conditions. As a further extension, differential encoding is combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full diversity in symbol asynchronous, non-coherent relay networks with no knowledge of the timing errors at the relay nodes. The DDSTBCs in this thesis are proposed for application in the proposed transmission scheme for symbol asynchronous, non-coherent relay networks. As a parallel to the non-coherent schemes based on differential encoding, we also propose non-coherent schemes for symbol synchronous and symbol asynchronous relay networks that are based on training. This training based transmission scheme leverages existing coherent DSTBCs for non-coherent communication in relay networks. Simulations show that this training scheme when used along with the coherent DSTBCs in this thesis outperform the best known DDSTBCs in the literature. Finally, in the last part of the thesis, connections between multi-group ML decodable unitary weight (UW) STBCs and groups with real elements are established for the first time. Using this connection, we translate the necessary and sufficient conditions for multi-group ML decoding of UW-STBCs entirely in group theoretic terms. We discuss various examples of multi-group decodable UW-STBCs together with their associated groups and list the real elements involved. These examples include orthogonal designs, quasi-orthogonal designs among many others.

Space-Time Block Coding is an efficient communication technique used in multiple-input multiple-output wireless systems. The complexity with which a Space-Time Block Code (STBC) can be decoded is important from an implementation point of view since it directly affects the receiver complexity and speed. In this thesis, we address the problem of designing low complexity decoding techniques for STBCs, and constructing STBCs that achieve high rate and full-diversity with these decoders. This thesis is divided into two parts; the first is concerned with the optimal decoder, viz. the maximum-likelihood (ML) decoder, and the second with non-ML decoders. An STBC is said to be multigroup ML decodable if the information symbols encoded by it can be partitioned into several groups such that each symbol group can be ML decoded independently of the others, and thereby admitting low complexity ML decoding. In this thesis, we first give a new framework for constructing low ML decoding complexity STBCs using codes over the Klein group, and show that almost all known low ML decoding complexity STBCs can be obtained by this method. Using this framework we then construct new full-diversity STBCs that have the least known ML decoding complexity for a large set of choices of number of transmit antennas and rate. We then introduce the notion of Asymptotically-Good (AG) multigroup ML decodable codes, which are families of multigroup ML decodable codes whose rate increases linearly with the number of transmit antennas. We give constructions for full-diversity AG multigroup ML decodable codes for each number of groups g > 1. For g > 2, these are the first instances of g-group ML decodable codes that are AG or have rate more than 1. For g = 2 and identical delay, the new codes match the known families of AG codes in terms of rate. In the final section of the first part we show that the upper triangular matrix R encountered during the sphere-decoding of STBCs can be rank-deficient, thus leading to higher sphere-decoding complexity, even when the rate is less than the minimum of the number of transmit antennas and the number receive antennas. We show that all known AG multigroup ML decodable codes suffer from such rank-deficiency, and we explicitly derive the sphere-decoding complexities of most known AG multigroup ML decodable codes. In the second part of this thesis we first study a low complexity non-ML decoder introduced by Guo and Xia called Partial Interference Cancellation (PIC) decoder. We give a new full-diversity criterion for PIC decoding of STBCs which is equivalent to the criterion of Guo and Xia, and is easier to check. We then show that Distributed STBCs (DSTBCs) used in wireless relay networks can be full-diversity PIC decoded, and we give a full-diversity criterion for the same. We then construct full-diversity PIC decodable STBCs and DSTBCs which give higher rate and better error performance than known multigroup ML decodable codes for similar decoding complexity, and which include other known full-diversity PIC decodable codes as special cases. Finally, inspired by a low complexity essentially-ML decoder given by Sirianunpiboon et al. for the two and three antenna Perfect codes, we introduce a new non-ML decoder called Adaptive Conditional Zero-Forcing (ACZF) decoder which includes the technique of Sirianunpiboon et al. as a special case. We give a full-diversity criterion for ACZF decoding, and show that the Perfect codes for two, three and four antennas, the Threaded Algebraic Space-Time code, and the 4 antenna rate 2 code of Srinath and Rajan satisfy this criterion. Simulation results show that the proposed decoder performs identical to ML decoding for these five codes. These STBCs along with ACZF decoding have the best error performance with least complexity among all known STBCs for four or less transmit antennas.

This thesis addresses the design of low-complexity coding schemes for wireless relay networks and multiple access channels. The first part of the thesis is on wireless relay networks and the second part is on multiple access channels. Distributed space-time coding is a well known technique to achieve spatial diversity in wireless networks wherein, several geographically separated nodes assist a source node to distributively transmit a space-time block code (STBC) to the destination. Such STBCs are referred to as Distributed STBCs (DSTBCs). In the first part of the thesis, we focus on designing full diversity DSTBCs with some nice properties which make them amenable for implementation in practice. Towards that end, a class of full diversity DST-BCs referred to as Co-ordinate Interleaved DSTBCs (CIDSTBCs) are proposed for relay networks with two-antenna relays. To construct CIDSTBCs, a technique called co-ordinate vector interleaving is introduced wherein, the received signals at different antennas of the relay are processed in a combined fashion. Compared to the schemes where the received signals at different antennas of the relay are processed independently, we show that CIDSTBCs provide coding gain which comes in with negligible increase in the processing complexity at the relays. Subsequently, we design single-symbol ML decodable (SSD) DSTBCs for relay networks with single-antenna nodes. In particular, two classes of SSD DSTBCs referred to as (i) Semi-orthogonal SSD Precoded DSTBCs and (ii) Training-Symbol Embedded (TSE) SSD DSTBCs are proposed. A detailed analysis on the maximal rate of such DSTBCs is presented and explicit DSTBCs achieving the maximal rate are proposed. It is shown that the proposed codes have higher rates than the existing SSD DSTBCs. In the second part, we study two-user Gaussian Multiple Access Channels (GMAC). Capacity regions of two-user GMAC are well known. Though, capacity regions of such channels provide insights into the achievable rate pairs in an information theoretic sense, they fail to provide information on the achievable rate pairs when we consider finitary restrictions on the input alphabets and analyze some real world practical signal constellations like QAM and PSK signal sets. Hence, we study the capacity aspects of two-user GMAC with finite input alphabets. In particular, Constellation Constrained (CC) capacity regions of two-user SISO-GMAC are computed for several orthogonal and non-orthogonal multiple access schemes (abbreviated as O-MA and NO-MA schemes respectively). It is first shown that NO-MA schemes strictly offer larger capacity regions than the O-MA schemes for finite input alphabets. Subsequently, for NO-MA schemes, code pairs based on Trellis Coded Modulation (TCM) are proposed such that any rate pair on the CC capacity region can be approached. Finally, we consider a two-user Multiple-Input Multiple-Output (MIMO) fading MAC and design STBC pairs such that ML decoding complexity is reduced.

One of the most popular ways to exploit the advantages of a multiple-input multiple-output (MIMO) system is using space time block coding. A space time block code (STBC) is a finite set of complex matrices whose entries consist of the information symbols to be transmitted. A linear STBC is one in which the information symbols are linearly combined to form a two-dimensional code matrix. A well known method of maximum-likelihood (ML) decoding of such STBCs is using the sphere decoder (SD). In this thesis, new constructions of STBCs with low sphere decoding complexity are presented and various ways of characterizing and reducing the sphere decoding complexity of an STBC are addressed. The construction of low sphere decoding complexity STBCs is tackled using irreducible matrix representations of Clifford algebras, cyclic division algebras and crossed-product algebras. The complexity reduction algorithms for the STBCs constructed are explored using tree based search algorithms. Considering an STBC as a vector space over the set of weight matrices, the problem of characterizing the sphere decoding complexity is addressed using quadratic form representations. The main results are as follows. A sub-class of fast decodable STBCs known as Block Orthogonal STBCs (BOSTBCs) are explored. A set of sufficient conditions to obtain BOSTBCs are explained. How the block orthogonal structure of these codes can be exploited to reduce the SD complexity of the STBC is then explained using a depth first tree search algorithm. Bounds on the SD complexity reduction and its relationship with the block orthogonal structure are then addressed. A set of constructions to obtain BOSTBCs are presented next using Clifford unitary weight designs (CUWDs), Coordinate-interleaved orthogonal designs (CIODs), cyclic division algebras and crossed product algebras which show that a lot of codes existing in literature exhibit the block orthogonal property. Next, the dependency of the ordering of information symbols on the SD complexity is discussed following which a quadratic form representation known as the Hurwitz-Radon quadratic form (HRQF) of an STBC is presented which is solely dependent on the weight matrices of the STBC and their ordering. It is then shown that the SD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization). It is also shown that the SD complexity is completely captured into a single matrix obtained from the HRQF. Also, for a given set of weight matrices, an algorithm to obtain a best ordering of them leading to the least SD complexity is presented using the HRQF matrix.