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)

It is well known that communication systems employing multiple transmit and multiple receive antennas provide high data rates along with increased reliability. It has been shown that coding across both spatial and temporal domains together, called Space-Time Coding (STC), achieves, a diversity order equal to the product of the number of transmit and receive antennas. Space-Time Block Codes (STBC) achieving the maximum diversity is called full-diversity STBCs. An STBC is called information-lossless, if the structure of it is such that the maximum mutual information of the resulting equivalent channel is equal to the capacity of the channel. This thesis deals with high-rate and information-lossless STBCs obtained from certain matrix algebras called Crossed-Product Algebras. First we give constructions of high-rate STBCs using both commutative and non-commutative matrix algebras obtained from appropriate representations of extensions of the field of rational numbers. In the case of commutative algebras, we restrict ourselves to fields and call the STBCs obtained from them as STBCs from field extensions. In the case of non-commutative algebras, we consider only the class of crossed-product algebras. For the case of field extensions, we first construct high-rate; full-diversity STBCs for arbitrary number of transmit antennas, over arbitrary apriori specified signal sets. Then we obtain a closed form expression for the coding gain of these STBCs and give a tight lower bound on the coding gain of some of these STBCs. This lower bound in certain cases indicates that some of the STBCs from field extensions are optimal m the sense of coding gain. We then show that the STBCs from field extensions are information-lossy. However, we also show that the finite-signal-set capacity of the STBCs from field extensions can be improved by increasing the symbol rate of the STBCs. The simulation results presented show that our high-rate STBCs perform better than the rate-1 STBCs in terms of the bit error rate performance. Then we proceed to present a construction of high-rate STBCs from crossed-product algebras. After giving a sufficient condition on the crossed-product algebras under which the resulting STBCs are information-lossless, we identify few classes of crossed-product algebras that satisfy this sufficient condition and also some classes of crossed-product algebras which are division algebras which lead to full-diversity STBCs. We present simulation results to show that the STBCs from crossed-product algebras perform better than the well-known codes m terms of the bit error rate. Finally, we introduce the notion of asymptotic-information-lossless (AILL) designs and give a necessary and sufficient condition under which a linear design is an AILL design. Analogous to the condition that a design has to be a full-rank design to achieve the point corresponding to the maximum diversity of the optimal diversity-multiplexing tradeoff, we show that a design has to be AILL to achieve the point corresponding to the maximum multiplexing gain of the optimal diversity-multiplexing tradeoff. Using the notion of AILL designs, we give a lower bound on the diversity-multiplexing tradeoff achieved by the STBCs from both field extensions and division algebras. The lower bound for STBCs obtained from division algebras indicates that they achieve the two extreme points, 1 e, zero multiplexing gain and zero diversity gain, of the optimal diversity-multiplexing tradeoff. Also, we show by simulation results that STBCs from division algebras achieves all the points on the optimal diversity-multiplexing tradeoff for n transmit and n receive antennas, where n = 2, 3, 4.

The phenomenon of fading constitutes a fundamental problem in wireless communications. Researchers have proposed many methods to improve the reliability of communication over wireless channels in the presence of fading. Many studies on this topic have focused on diversity techniques. Transmit diversity is a common diversity type in which multiple antennas are employed at the transmitter. Space-time coding is a technique based on transmit diversity introduced by Tarokh et alii in 1998. In this thesis, various types of space-time codes are examined. Since they were originally introduced in the form of trellis codes, a major part is devoted to space-time trellis codes where the fundamental design criteria are established. Then, space-time block coding, which presents a different approach, is introduced and orthogonal spacetime block codes are analyzed in some detail. Lastly, rank codes from coding theory are studied and their relation to space-time coding are investigated.