Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners

Doctor of Philosophy

dissertationThe demand for high speed communication has been increasing in the past two decades. Multicarrier communication technology has been suggested to address this demand. Orthogonal frequency-division multiplexing (OFDM) is the most widely used multicarrier technique. However, OFDM has a number of disadvantages in time-varying channels, multiple access, and cognitive radios. On the other hand, filterbank multicarrier (FBMC) communication has been suggested as an alternative to OFDM that can overcome the disadvantages of OFDM. In this dissertation, we investigate the application of filtered multitone (FMT), a subset of FBMC modulation methods, to slow fading and fast fading channels. We investigate the FMT transmitter and receiver in continuous and discrete time domains. An efficient implementation of FMT systems is derived and the conditions for perfect reconstruction in an FBMC communication system are presented. We derive equations for FMT in slow fading channels that allow evaluation of FMT when applied to mobile wireless communication systems. We consider using fractionally spaced per tone channel equalizers with different number of taps. The numerical results are presented to investigate the performance of these equalizers. The numerical results show that single-tap equalizers suffice for typical wireless channels. The equalizer design study is advanced by introducing adaptive equalizers which use channel estimation. We derive equations for a minimum mean square error (MMSE) channel estimator and improve the channel estimation by considering the finite duration of channel impulse response. The results of optimum equalizers (when channel is known perfectly) are compared with those of the adaptive equalizers, and it is found that a loss of 1 dB or less incurs. We also introduce a new form of FMT which is specially designed to handle doubly dispersive channels. This method is called FMT-dd (FMT for doubly dispersive channels). The proposed FMT-dd is applied to two common methods of data symbol orientation in the time-frequency space grid; namely, rectangular and hexagonal lattices. The performance of these methods along with OFDM and the conventional FMT are compared and a significant improvement in performance is observed. The FMT-dd design is applied to real-world underwater acoustic (UWA) communication channels. The experimental results from an at-sea experiment (ACOMM10) show that this new design provides a significant gain over OFDM. The feasibility of implementing a MIMO system for multicarrier UWA communication channels is studied through computer simulations. Our study emphasizes the bandwidth efficiency of multicarrier MIMO communications .We show that the value of MIMO to UWA communication is very limited

A Review on Advancements in Optical Communication System

Communication systems are revolutionized by the tremendous research being done in this direction. The need is the mother of the invention. The need of data transfer in increasing every day. There is the big demand for the fast optical communication systems. The optical fibers have the big potential of carrying the different channels which can transmit the data at amazing speed. In this work we have studied the research done in the field of technological development taking place in fiber communication system. The focus is on the use of fiber link as a modern medium of communication in the optical range.Communication system, Optical data transfer, Channel, Fiber link, Optical range

A low-complexity eigenfilter design method for channel shortening equalizers for DMT systems

We present a new low-complexity method for the design of channel shortening equalizers for discrete multitone (DMT) modulation systems using the eigenfilter approach. In contrast to other such methods which require a Cholesky decomposition for each delay parameter value used, ours requires only one such decomposition. Simulation results show that our method performs nearly optimally in terms of observed bit rate

Semi-blind adaptive spatial equalisation for MIMO systems with high-order QAM signalling

This contribution investigates semi-blind adaptive spatial filtering or equalisation for multiple-input multiple-output (MIMO) systems that employ high-throughput quadrature amplitude modulation (QAM) signalling. A minimum number of training symbols, equal to the number of receivers (we assume that the number of transmitters is no more than that of receivers), are first utilized to provide a rough least squares channel estimate of the system's MIMO channel matrix for the initialization of the spatial equalizers' weight vectors. A constant modulus algorithm aided soft decision-directed blind algorithm, originally derived for blind equalization of single-input single-output and single-input multiple-output systems employing high-order QAM signalling, is then extended to adapt the spatial equalizers for MIMO systems. This semi-blind scheme has a low computational complexity, and our simulation results demonstrate that it converges fast to the minimum mean-square-error spatial equalization solution

Estimation and detection techniques for doubly-selective channels in wireless communications

A fundamental problem in communications is the estimation of the channel. The signal transmitted through a communications channel undergoes distortions so that it is often received in an unrecognizable form at the receiver. The receiver must expend significant signal processing effort in order to be able to decode the transmit signal from this received signal. This signal processing requires knowledge of how the channel distorts the transmit signal, i.e. channel knowledge. To maintain a reliable link, the channel must be estimated and tracked by the receiver. The estimation of the channel at the receiver often proceeds by transmission of a signal called the 'pilot' which is known a priori to the receiver. The receiver forms its estimate of the transmitted signal based on how this known signal is distorted by the channel, i.e. it estimates the channel from the received signal and the pilot. This design of the pilot is a function of the modulation, the type of training and the channel. [Continues.

Performance Analysis of Wireless Systems with Doubly Selective Rayleigh Fading

Theoretical error performances of wireless communication systems suffering from both doubly selective (time varying and frequency selective) Rayleigh fading and sampler timing offset are analyzed in this paper. Single-input-single-output systems with doubly selective fading channels are equivalently represented as discrete-time single-input-multiple-output (SIMO) systems with correlated frequency-flat fading channels, with the correlation information being determined by the combined effects of sampler timing phase, maximum Doppler spread, and power delay profile of the physical fading. Based on the equivalent SIMO system representation, closed-form error-probability expressions are derived as tight lower bounds for linearly modulated systems with fractionally spaced equalizers. The information on the sampler timing offset and the statistical properties of the physical channel fading, along with the effects of the fractionally spaced equalizer, are incorporated in the error-probability expressions. Simulation results show that the new analytical results can accurately predict the error performances of maximum-likelihood sequence estimation and maximum a posteriori equalizers for practical wireless communication systems in a wide range of signal-to-noise ratio. Moreover, some interesting observations about receiver oversampling and system timing phase sensitivity are obtained based on the new analytical results

Adaptive Blind Channel Equalization for Mobile Multimedia Communication

In the last decade much research effort has been dedicated to deal with the issues of wireless multimedia communications, in particular bandwidth limitation and channel impairment. We have recently proposed a new scheme for blind equalization called sinusoidally-distributed dither signed-error constant modulus algorithm (S-DSE-CMA). In this paper, we test this scheme for wireless image transmission. Simulation showed that the low complexity of implementation and fast convergence rate are the major advantages of employing the new scheme for multimedia applications. It is also shown, from perceptual-based analysis as well as objective measurements using peak signal-to-noise ratio (PSNR) of the recovered image, that the recently-proposed blind adaptive equalization algorithm outperforms existing methods, e.g., uniformly-distributed DSE-CMA