Gröbner bases and wavelet design

AbstractIn this paper, we detail the use of symbolic methods in order to solve some advanced design problems arising in signal processing. Our interest lies especially in the construction of wavelet filters for which the usual spectral factorization approach (used for example to construct the well-known Daubechies filters) is not applicable. In these problems, we show how the design equations can be written as multivariate polynomial systems of equations and accordingly how Gröbner algorithms offer an effective way to obtain solutions in some of these cases

DSP compensation for distortion in RF filters

There is a growing demand for the high quality TV programs such as High Definition TV (HDTV). The CATV network is often a suitable solution to address this demand using a CATV modem delivering high data rate digital signals in a cost effective manner, thereby, utilizing a complex digital modulation scheme is inevitable. Exploiting complex modulation schemes, entails a more sophisticated modulator and distribution system with much tighter tolerances. However, there are always distortions introduced to the modulated signal in the modulator degrading signal quality. In this research, the effect of distortions introduced by the RF band pass filter in the modulator will be considered which cause degradations on the quality of the output Quadrature Amplitude Modulated (QAM) signal. Since the RF filter's amplitude/group delay distortions are not symmetrical in the frequency domain, once translated into the base band they have a complex effect on the QAM signal. Using Matlab, the degradation effects of these distortions on the QAM signal such as Bit Error Rate (BER) is investigated. In order to compensate for the effects of the RF filter distortions, two different methods are proposed. In the first method, a complex base band compensation filter is placed after the pulse shaping filter (SRRC). The coefficients of this complex filter are determined using an optimization algorithm developed during this research. The second approach, uses a pre-equalizer in the form of a Feed Forward FIR structure placed before the pulse shaping filter (SRRC). The coefficients of this pre-equalizer are determined using the equalization algorithm employed in a test receiver, with its tap weights generating the inverse response of the RF filter. The compensation of RF filter distortions in base band, in turn, improves the QAM signal parameters such as Modulation Error Ratio (MER). Finally, the MER of the modulated QAM signal before and after the base band compensation is compared between the two methods, showing a significant enhancement in the RF modulator performance

Optimal digital filter design for dispersed signal equalization

Any signal a satellite receives from Earth has traveled through the ionosphere. Transmission through the ionosphere results in a frequency dependent time-delay of the signal frequency components. This effect of the medium on the signal is termed dispersion, and it increases the difficulty of pulse detection. A system capable of compensating for the dispersion would be desirable, as pulsed signals would be more readily detected after compression. In this thesis, we investigate the derivation of a digital filter to compensate for the dispersion caused by the ionosphere. A transfer function model for the analysis of the ionosphere as a system is introduced. Based on the signal model, a matched filter response is derived. The problem is formulated as a group delay compensation effort. The Abel-Smith algorithm is employed for the synthesis of a cascaded allpass filter bank with desired group delay characteristics. Extending this work, an optimized allpass filter is then derived using a pole location approach. A mean-square error metric shows that the optimized filter can reproduce, and even improve upon, the results of the Abel-Smith design with a significantly lower order filter. When compared against digital filters produced with the least p-th minimax algorithm, we find that the new method exhibits significantly lower error in the band of interest, as well as lower mean squared error overall. The result is a simple optimized equalization filter that is stable, robust against cascading difficulties, and applicable to arbitrary waveforms. This filter is the cornerstone to a new all-digital electromagnetic pulse detection system

Efficient reconstruction of band-limited sequences from nonuniformly decimated versions by use of polyphase filter banks

An efficient polyphase structure for the reconstruction of a band-limited sequence from a nonuniformly decimated version is developed. Theoretically, the reconstruction involves the implementation of a bank of multilevel filters, and it is shown that how all these reconstruction filters can be obtained at the cost of one Mth band low-pass filter and a constant matrix multiplier. The resulting structure is therefore more general than previous schemes. In addition, the method offers a direct means of controlling the overall reconstruction distortion T(z) by appropriate design of a low-pass prototype filter P(z). Extension of these results to multiband band-limited signals and to the case of nonconsecutive nonuniform subsampling are also summarized, along with generalizations to the multidimensional case. Design examples are included to demonstrate the theory, and the complexity of the new method is seen to be much lower than earlier ones

Carrier frequency offset recovery for zero-IF OFDM receivers

As trends in broadband wireless communications applications demand faster development cycles, smaller sizes, lower costs, and ever increasing data rates, engineers continually seek new ways to harness evolving technology. The zero intermediate frequency receiver architecture has now become popular as it has both economic and size advantages over the traditional superheterodyne architecture. Orthogonal Frequency Division Multiplexing (OFDM) is a popular multi-carrier modulation technique with the ability to provide high data rates over echo ladened channels. It has excellent robustness to impairments caused by multipath, which includes frequency selective fading. Unfortunately, OFDM is very sensitive to the carrier frequency offset (CFO) that is introduced by the downconversion process. The objective of this thesis is to develop and to analyze an algorithm for blind CFO recovery suitable for use with a practical zero-Intermediate Frequency (zero-IF) OFDM telecommunications system. A blind CFO recovery algorithm based upon characteristics of the received signal's power spectrum is proposed. The algorithm's error performance is mathematically analyzed, and the theoretical results are verified with simulations. Simulation shows that the performance of the proposed algorithm agrees with the mathematical analysis. A number of other CFO recovery techniques are compared to the proposed algorithm. The proposed algorithm performs well in comparison and does not suffer from many of the disadvantages of existing blind CFO recovery techniques. Most notably, its performance is not significantly degraded by noisy, frequency selective channels

Orthogonal transmultiplexers : extensions to digital subscriber line (DSL) communications

An orthogonal transmultiplexer which unifies multirate filter bank theory and communications theory is investigated in this dissertation. Various extensions of the orthogonal transmultiplexer techniques have been made for digital subscriber line communication applications. It is shown that the theoretical performance bounds of single carrier modulation based transceivers and multicarrier modulation based transceivers are the same under the same operational conditions. Single carrier based transceiver systems such as Quadrature Amplitude Modulation (QAM) and Carrierless Amplitude and Phase (CAP) modulation scheme, multicarrier based transceiver systems such as Orthogonal Frequency Division Multiplexing (OFDM) or Discrete Multi Tone (DMT) and Discrete Subband (Wavelet) Multicarrier based transceiver (DSBMT) techniques are considered in this investigation. The performance of DMT and DSBMT based transceiver systems for a narrow band interference and their robustness are also investigated. It is shown that the performance of a DMT based transceiver system is quite sensitive to the location and strength of a single tone (narrow band) interference. The performance sensitivity is highlighted in this work. It is shown that an adaptive interference exciser can alleviate the sensitivity problem of a DMT based system. The improved spectral properties of DSBMT technique reduces the performance sensitivity for variations of a narrow band interference. It is shown that DSBMT technique outperforms DMT and has a more robust performance than the latter. The superior performance robustness is shown in this work. Optimal orthogonal basis design using cosine modulated multirate filter bank is discussed. An adaptive linear combiner at the output of analysis filter bank is implemented to eliminate the intersymbol and interchannel interferences. It is shown that DSBMT is the most suitable technique for a narrow band interference environment. A blind channel identification and optimal MMSE based equalizer employing a nonmaximally decimated filter bank precoder / postequalizer structure is proposed. The performance of blind channel identification scheme is shown not to be sensitive to the characteristics of unknown channel. The performance of the proposed optimal MMSE based equalizer is shown to be superior to the zero-forcing equalizer

Interference Suppression in WCDMA with Adaptive Thresholding based Decision Feedback Equaliser

WCDMA is considered as one of the 3G wireless standards by 3GPP. Capacity calculation shows that WCDMA systems have more capacity compared to any other multiple access technique such as time division multiple access (TDMA) or frequency division multiple access (FDMA). So it is widely used. Rake receivers are used for the detection of transmitted data in case of WCDMA communication systems due to its resistance to multipath fading. But rake receiver treat multiuser interference (MUI) as AWGN and have limitation in overcoming the effect of multiple access interference (MAI) when the SNR is high. A de-correlating matched filter has been used in this thesis, which eliminates and improves system performance. But the given receiver works well only in the noise free environment. A DFE, compared to linear equaliser, gives better performance at severe ISI condition. The only problem in this equalisation technique is to select the number of symbols that are to be fed back. This thesis gives an idea on multiple symbol selection, based on sparity where an adaptive thresholding algorithm is used that computes the number of symbols to feedback. Simulated results show a significant performance improvement for Regularised Rake receiver along with thresholding in terms of BER compared to a rake receiver, de-correlating rake receiver and regularised rake receiver. The performance of the receiver in different channels is also analysed