Multirate Signal Processing Concepts in Digital Communications

Multirate systems are building blocks commonly used in digital signal processing (DSP). Their function is to alter the rate of the discrete-time signals, which is achieved by adding or deleting a portion of the signal samples. Multirate systems play a central role in many areas of signal processing, such as filter bank theory and multiresolution theory. They are essential in various standard signal processing techniques such as signal analysis, denoising, compression and so forth. During the last decade, however, they have increasingly found applications in new and emerging areas of signal processing, as well as in several neighboring disciplines such as digital communications. The main contribution of this thesis is aimed towards better understanding of multirate systems and their use in modern communication systems. To this end, we first study a property of linear systems appearing in certain multirate structures. This property is called biorthogonal partnership and represents a terminology introduced recently to address a need for a descriptive term for such class of filters. In the thesis we especially focus on the extensions of this simple idea to the case of vector signals (MIMO biorthogonal partners) and to accommodate for nonintegral decimation ratios (fractional biorthogonal partners). Some of the main results developed here pertain to a better understanding of the biorthogonal partner relationship. These include the conditions for the existence of stable and of finite impulse response (FIR) biorthogonal partners. A major result that we establish states that under some generally mild conditions, MIMO and fractional biorthogonal partners exist. Moreover, when they exist, FIR solutions are not unique. We develop the parameterization of FIR solutions, which makes the search for the best partner in a given application analytically tractable. This proves very useful in the central application of biorthogonal partners, namely, channel equalization in digital communications with signal oversampling at the receiver. Sampling the received signal at a rate higher than that defined by the transmitter provides some flexibility in the design of the equalizer. A good channel equalizer in this context is one that helps neutralize the distortion on the signal introduced by the channel propagation but not at the expense of amplifying the channel noise. This presents the rationale behind the partner design problem which is formulated and solved. The performance of such equalizers is then compared to several other equalization methods by computer simulations. These findings point to the conclusion that the communication system performance can be improved at the expense of an increased implementational cost of the receiver. While the multirate DSP in the aforementioned communication systems serves to provide additional degrees of freedom in the design of the receiver, another important class of multirate structures is used at the transmitter side in order to introduce the redundancy in the data stream. This redundancy generally serves to facilitate the equalization process by forcing certain structure on the transmitted signal. If the channel is unknown, this procedure helps to identify it; if the channel is ill-conditioned, additional redundancy helps v avoid severe noise amplification at the receiver, and so forth. In the second part of the thesis, we focus on this second group of multirate systems, derive some of their properties and introduce certain improvements of the communication systems in question. We first consider the transmission systems that introduce the redundancy in the form of a cyclic prefix. The examples of such systems include the discrete multitone (DMT) and the orthogonal frequency division multiplexing (OFDM) systems. The cyclic prefix insertion helps to effectively divide the channel in a certain number of nonoverlaping frequency bands. We study the problem of signal precoding in such systems that serves to adjust the signal properties in order to fully take advantage of the channel and noise properties across different bands. Our ultimate goal is to improve the overall system performance by minimizing the noise power at the receiver. The special case of our general solution corresponds to the white channel noise and the best precoder under these circumstances simply performs the optimal power allocation. Finally, we study a different class of communication systems with induced signal redundancy, namely, the multiuser systems based on code division multiple access (CDMA). We specifically focus on the special class of CDMA systems called ‘a mutually orthogonal usercode receiver’ (AMOUR). These systems use the transmission redundancy to facilitate the user separation at the receiver regardless of the (different) communication channels. While the method also guarantees the existence of the zero-forcing equalizers irrespective of the channel zero locations, the performance of these equalizers can be further improved by exploiting the inherent flexibility in their design. We show how to find the best equalizer from the class of zero-forcing solutions and then increase the size of this class by employing alternative sampling strategies at the receiver. Our method retains the separability properties of AMOUR systems while improving their robustness in the noisy environment.