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The primary focus of the codes that we have discussed so far has been on the case when only the receiver knows the channel. This is the case for most practical systems. The transmitter sends pilot signals and the receiver uses them to estimate the channel . Then, the receiver uses the estimated path gains to coherently decode the data symbols during the same frame. In such a coherent system, the underlying assumption is that the channel does not change during one frame of data. In other words, the frame length is chosen such that the path gain change during one frame is negligible. This is basically the quasi-static fading assumption that we have used so far. There is a bandwidth penalty due to the number of transmitted pilot symbols. Of course, choosing a longer frame reduces this bandwidth penalty; however, on the other hand, the quasi-static assumption is less valid for longer frames. Therefore, there is a trade-off between the frame length and the accuracy of the channel estimation. This is an interesting research topic and the interested reader is referred to  and the references therein.
For one transmit antenna, differential detection schemes exist that neither require the knowledge of the channel nor employ pilot symbol transmission. These differential decoding schemes are used, for instance, in the IEEE IS-54 standard . This motivates the generalization of differential detection schemes for the case of multiple transmit antennas.
Trellis-coded modulation (TCM) [144, 14] combines modulation and coding to achieve higher coding gains. It provides significant coding gain and a better performance for a given bandwidth compared to uncoded modulation schemes. Space-time trellis codes (STTCs) combine modulation and trellis coding to transmit information over multiple transmit antennas and MIMO channels. Therefore, one can think of STTCs as TCM schemes for MIMO channels. We start this chapter with a brief description of TCM design and the corresponding encoding and decoding. The main idea behind coding is to use structured redundancy to reduce the effects of noise. One approach is to restrict the transmitted symbols to a subset of constellation points to have a larger minimum Euclidean distance. This approach, however, results in a rate reduction due to a decrease in the size of available constellation points. To compensate for the rate reduction, one may expand the constellation and use a subset of the expanded constellation at each time slot. A finite-state machine represented by a trellis is utilized to decide which subset should be used at each time slot. The goal is to maximize the coding gain for a given rate. This is the main idea behind TCM and in such a structure the transmitted symbols at different time slots are not independent.
Let us assume that we use a trellis with I states such that 2l branches leave every state. We enumerate the states from top to bottom starting from zero.
We introduced space-time block coding in Chapter 4. The space-time block codes in Chapters 4 and 5 have interesting structures that can be utilized to simplify the ML decoding. The orthogonality of OSTBCs makes it possible to decouple the decoding of different symbols. Similarly, a pairwise decoding is possible for QOSTBCs. Such simple ML decoding methods restrict the cardinality of transmitted symbols. It may also impose a limit on the performance of the code. On the other hand, there is no restriction on the number of receive antennas and even one receive antenna is enough. In addition to simple ML decoding and full diversity, the nice structure of these codes makes it possible to combine them with other blocks of the system. In fact, the transmission of an orthogonal STBC over a MIMO channel usually translates into N parallel SISO channels. As a result many wireless communication methods and building blocks that have been developed for SISO channels can be easily generalized using an orthogonal STBC. In many wireless communication systems the above advantages and disadvantages makes OSTBC a very attractive candidate, especially at low transmission bit rates.
As discussed in Chapter 4, OSTBCs are more restrictive for channels with higher number of antennas. When decoding complexity is not an issue, one may design codes that provide higher rates or better performance compared to OSTBCs.
Using multiple antennas can result in a smaller probability of error for the same throughput because of the diversity gain. The main objective of space-time codes is to achieve the maximum possible diversity. As we have shown in previous chapters, space-time codes provide a diversity gain equal to the product of the number of transmit and receive antennas NM. Also, we have demonstrated that the maximum throughput of the space-time codes is one symbol per channel use for any number of transmit antennas. The use of multiple antennas results in increasing the capacity of MIMO channels as shown in Chapter 2. Therefore, one may transmit at a higher throughput, compared to SISO channels, for a given probability of error. The capacity analysis of Chapter 2 shows that when the number of transmit and receive antennas are the same, the capacity grows at least linearly by the number of antennas. Instead of utilizing the multiple antennas to achieve the maximum possible diversity gain, one can use multiple antennas to increase the transmission rate. In fact, as we discussed in Chapter, there is a trade-off between these two gains from multiple antennas.
One approach to achieve the higher possible throughput is spatial multiplexing (SM). One simple example of spatial multiplexing is when the input is demultiplexed into N separate streams, using a serial-to-parallel converter, and each stream is transmitted from an independent antenna.
A code is mapping from the input bits to the transmitted symbols. As discussed in Chapter 2, we assume that symbols are transmitted simultaneously from different antennas. In this chapter, we study the performance of different codes by deriving some bounds on them. Then, we use the bounds to provide some guidance to design codes with “good” performance. Such guidance is called the design criterion. Most of the analyses in this chapter are asymptotic analysis. Therefore, different asymptotic assumptions may result in different code criteria. We concentrate on a quasi-static Rayleigh fading wireless channel and some of the important design criteria that result in achieving maximum diversity and good performance at high SNRs.
A good code follows a design criterion that adds some notion of optimality to the code. In fact, the goal of defining a design criterion is to have a guideline for designing good codes. For example let us consider transmission over a binary symmetric channel using a linear binary block channel code. The bit error rate of the system depends on the Hamming distances of the codeword pairs. Defining the set of all possible codeword pairs and the corresponding set of Hamming distances, we denote the minimum Hamming distance by dmin. It can be shown that a code with minimum Hamming distance dmin can correct all error patterns of weight less than or equal to ⌊(dmin – 1)/2⌋, where ⌊x⌋ is the largest integer less than or equal to x.
In this section, we study the design of space-time block codes (STBCs) to transmit information over a multiple antenna wireless communication system. We assume that fading is quasi-static and flat as explained in Chapter 2. We consider a wireless communication system where the transmitter contains N transmit antennas and the decoder contains M receive antennas. We follow our notations in Equation (2.1) for the input–output relation of the MIMO channel. The goal of space-time coding is to achieve the maximum diversity of N M, the maximum coding gain, and the highest possible throughput. In addition, the decoding complexity is very important. In a typical wireless communication system the mobile transceiver has a limited available power through a battery and should be a small physical device. To improve the battery life, low complexity encoding and decoding is very crucial. On the other hand, the base station is not as restricted in terms of power and physical size. One can put multiple independent antennas in a base station. Therefore, in many practical situations, a very low complexity system with multiple transmit antennas is desirable. Space-time block coding is a scheme to provide these properties. Despite the name, a STBC can be considered as a modulation scheme for multiple transmit antennas that provide full diversity and very low complexity encoding and decoding.
Recent advances in wireless communication systems have increased the throughput over wireless channels and networks. At the same time, the reliability of wireless communication has been increased. As a result, customers use wireless systems more often. The main driving force behind wireless communication is the promise of portability, mobility, and accessibility. Although wired communication brings more stability, better performance, and higher reliability, it comes with the necessity of being restricted to a certain location or a bounded environment. Logically, people choose freedom versus confinement. Therefore, there is a natural tendency towards getting rid of wires if possible. The users are even ready to pay a reasonable price for such a trade-off. Such a price could be a lower quality, a higher risk of disconnection, or a lower throughput, as long as the overall performance is higher than some tolerable threshold. The main issue for wireless communication systems is to make the conversion from wired systems to wireless systems more reliable and if possible transparent. While freedom is the main driving force for users, the incredible number of challenges to achieve this goal is the main motivation for research in the field. In this chapter, we present some of these challenges. We study different wireless communication applications and the behavior of wireless channels in these applications. We provide different mathematical models to characterize the behavior of wireless channels. We also investigate the challenges that a wireless communication system faces.
STBCs provide full diversity and small decoding complexity. STBCs can be considered as modulation schemes for multiple transmit antennas and as such do not provide coding gains. As we discussed earlier in Chapters 4 and 5, full rate STBCs do not exist for every possible number of transmit antennas. On the other hand, STTCs are designed to achieve full diversity and high coding gains while requiring a higher decoding complexity. The STTCs presented in Chapter 6 are designed either manually or by computer search. In this chapter, we provide a systematic method to design space-time trellis codes.
Another way of achieving high coding gains is to concatenate an outer trellis code that has been designed for the AWGN channel with a STBC. Let us view each of the possible orthogonal matrices generated by a STBC as a point in a high dimensional space. The outer trellis code's task is to select one of these high dimensional signal points to be transmitted based on the current state and the input bits. In , it is shown that for the slow fading channel, the trellis code should be based on the set partitioning concepts of “Ungerboeck codes” for the AWGN channel.
The main idea behind super-orthogonal space-time trellis codes (SOSTTCs) is to consider STBCs as modulation schemes for multiple transmit antennas. We assign a STBC with specific constellation symbols to transitions originating from a state.
This book covers the fundamental principles of space-time coding for wireless communications over multiple-input multiple-output (MIMO) channels, and sets out practical coding methods for achieving the performance improvements predicted by the theory. Starting with background material on wireless communications and the capacity of MIMO channels, the book then reviews design criteria for space-time codes. A detailed treatment of the theory behind space-time block codes then leads on to an in-depth discussion of space-time trellis codes. The book continues with discussion of differential space-time modulation, BLAST and some other space-time processing methods and the final chapter addresses additional topics in space-time coding. The theory and practice sections can be used independently of each other. Written by one of the inventors of space-time block coding, this book is ideal for a graduate student familiar with the basics of digital communications, and for engineers implementing the theory in real systems.
OFDM is an efficient technique for transmitting data over frequency selective channels. The main idea behind OFDM is to divide a broadband frequency channel into a few narrowband sub-channels. Then, each sub-channel is a flat fading channel despite the frequency selective nature of the broadband channel. To generate these parallel sub-carriers in OFDM, an inverse fast Fourier transform (IFFT) is applied to a block of L data symbols. To avoid ISI due to the channel delay spread, a few “cyclic prefix” (CP) symbols are inserted in the block. The cyclic prefix samples are also called guard intervals. Basically, the last g samples of the block are duplicated in front of the block as the cyclic prefix. The number of these cyclic prefix samples, g, should be bigger than the length of the channel impulse response. The effects of the cyclic prefix samples eliminate ISI and convert the convolution between the transmit symbols and the channel to a circular convolution. These cyclic pre-fix samples are removed at the receiver. Then, a fast Fourier transform (FFT) is utilized at the receiver to recover the block of L received symbols. Figure 11.1 shows the block diagram of a wireless communication system using OFDM over a SISO channel. In this section, we study how to use OFDM in a system designed for MIMO channels. This is usually called MIMO-OFDM.
The use of multiple antennas in most future wireless communication systems seems to be inevitable. Today, the main question is how to include multiple antennas and what are the appropriate methods for specific applications. The academic interest in space-time coding and multiple-input multiple-output (MIMO) systems has been growing for the last few years. Recently, the industry has shown a lot of interest as well. It is amazing how fast the topic has emerged from a theoretical curiosity to the practice of every engineer in the field. It was just a few years ago, when I started working at AT&T Labs – Research, that many would ask “who would use more than one antenna in a real system?” Today, such skepticism is gone.
The fast growth of the interest and activities on space-time coding has resulted in a spectrum of people who actively follow the field. The range spans from mathematicians who are only curious about the interesting mathematics behind space-time coding to engineers who want to build it. There is a need for covering both the theory and practice of space-time coding in depth. This book hopes to fulfill this need. The book has been written as a textbook for first-year graduate students and as a reference for the engineers who want to learn the subject from scratch. An early version of the book has been used as a textbook to teach a course in space-time coding at the University of California, Irvine.
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