Jamal Tuqan

A DSP Approach for Finding the Codon Bias in DNA Sequences

The detection of different forms of periodicities in DNA sequences has been an active area of research in recent years. Most of the signal processing based methods have primarily focussed on assigning numerical values to the symbolic DNA sequence and then applying spectral analysis tools such as the short-time discrete Fourier transform (ST-DFT) to locate these repeats. A key application of DNA periodicity finding has been in the identification of the protein coding regions in DNA sequences by tracking the so-called period-3 component using the DNA spectrum. The main problem with this gene detection approach is that it is successful for certain genes but does not work for others. An interesting open research problem is to therefore determine the underlying reasons behind this disparity in performance. This requires, in turn, a solid understanding of the working principles of the period-3 component and the DNA spectrum. In this paper, we present a DSP-based approach that provides a complete analysis of this phenomenon. Specifically, we derive a new DSP based model that 1) clearly explains the underlying mechanism of the period-3 component, 2) directly relates the identification of the period-3 component to the detection of nucleotide bias in the codon structure, and 3) completely characterizes the DNA spectrum by a set of numerical sequences termed the filtered polyphase sequences. Furthermore, by adhering to the specific structure of the derived model, we can show that standard signal processing tools such as digital filtering can substantially enhance the detection of the codon bias. Several performance measures of DNA periodicity detection are also proposed and experimental results are provided to illustrate the key findings of our work.

A Quadratic Programming Approach to Blind Equalization and Signal Separation

Blind equalization and signal separation are two well-established signal processing problems. In this paper, we present a quadratic programming algorithm for fast blind equalization and signal separation. By introducing a special non-mean-square error (MSE) objective function, we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem. Based on a clear geometric interpretation and a formal proof, we show that a perfect equalization solution is obtained at every local optimum of the quadratic program. Because blind source separation is, by nature and mathematically, a closely related problem, we also generalize the algorithm for blind signal separation. We show that by enforcing source orthogonalization through successive processing, the quadratic programming approach can be applied effectively. Moreover, the quadratic program is easily extendible to incorporate additional practical conditions, such as jamming suppression constraints. We also provide evidence of good performance through computer simulations.

Gene Identification Using the Z-Curve Representation

DSP based techniques have been recently proposed to identify the protein coding regions in a DNA strand by detecting the so-called period-3 component in the DNA spectrum. The DNA spectrum is computed after mapping the DNA symbolic sequence to numerical digital sequences. A typical choice of mapping is the Voss representation. In this paper, we propose the use of a more elaborate mapping scheme, namely the Z-curve representation. Using a multirate signal processing approach, we derive closed form expressions to compute the Z-curve based DNA spectrum as well as mathematical conditions that characterize the coding regions. The derived formulas also prove that the Z-curve representation yields essentially the same DNA spectrum as the one obtained using the Voss representation at a lower computational cost

Precoded STBC-VBLAST for MIMO Wireless Communication Systems

A degradation in the bit error rate (BER) performance of the vertical Bell-Labs layered space-time (VBLAST) MIMO system is often due to its low minimum diversity and decoders error propagation. To remedy this problem, a hybrid scheme that integrates orthogonal space time block codes (STBC) into the lower layers of a VBLAST system was recently introduced. However, if channel state information is available at the transmitter, this hybrid system does not necessarily outperform a precoded VBLAST. This, in turn, motivates our work in this paper, namely the joint design of a precoder and its corresponding decoder for the VBLAST-STBC hybrid system. We consider the two scenarios of a flat and frequency selective fading channels and derive complete analytical solutions for both cases. Our simulation results indicate that the BER performance of the proposed precoded hybrid system is better than all of the other schemes.

PAPR Reduction in Trigonometric-Based OFDM Systems

A key building block in any OFDM transceiver is the Fast Fourier Transform (FFT) and its inverse. A number of researchers have recently proposed the use of the discrete cosine transform (DCT) and the discrete sine transform (DST), and their inverses as alternative modulating/demodulating bases to improve the BER performance of OFDM schemes while maintaining a low implementation cost. In this paper, we consider the open problem of reducing the peak-to-average power ratio (PAPR) in OFDM systems that deploy these trigonometric transforms. In specific, we show that similar to the FFT case, the complex envelope of a bandlimited DCT/DST- OFDM signal has a chi-square distribution with one degree of freedom and hence converges weakly to a Gaussian random process as the number of sub-carriers becomes large. Using this result, we then derive closed form expressions for the complementary cumulative distribution functions (CCDF) of each system and show that OFDM systems with trigonometric transforms provide higher PAPR reduction than the standard FFT-based system. Simulation results that compare the CCDFs of the different transforms using the partial transmit sequences (PTS) technique confirm our theoretical findings.

A DSP perspective to the period-3 detection problem

Many signal processing techniques have been introduced in the past to identify the protein coding regions by detecting the so-called period-3 component in the DNA spectrum. However, a solid understanding of this observed phenomenon and its underlying mechanism from a DSP perspective has been missing from the literature. We therefore propose a novel DSP model that i) clearly explains the intricate operation of the DNA spectrum, ii) allows the derivation of new DNA spectrum expressions which, in turn, generalize and unify previous work and iii) suggests an efficient way to improve the detection of protein coding regions by computing a filtered spectrum.

The role of the symbolic-to-numerical mapping in the detection of DNA periodicities

The detection of many forms of periodicities in DNA sequences has been an active area of research in recent years. Most of the signal processing based methods have used the simple Voss mapping to map the symbolic DNA sequence into binary indicator ones before computing some form of the so-called DNA spectrum to locate these repeats. A key research issue that remains however open is whether the success of these techniques is Voss specific. In this paper, we first propose a new and generic matrix based framework that comprises most of the widely used mappings in the literature as special cases. By using this approach, we can then show that the standard DNA spectrum is in fact in variable under most of these mappings. Finally, we demonstrate that a number of potential new mappings naturally follow from the suggested framework.

Trigonometric transforms for finding repeats in DNA sequences

The detection of many forms of periodicities in DNA sequences has been an active area of research in recent years. Most of the signal processing based methods have primarily focussed on using the short-time discrete Fourier transform (ST-DFT) as the key tool in identifying such repeat sequences. In this paper, we propose to use different fast discrete transforms such as the discrete cosine transform (DCT), the discrete sine transform (DST), and the discrete Hartley transform (DHT), to locate these patterns. In specific, we derive a new unified multirate DSP model that i) allows the derivation of new closed form DNA spectrum expressions for the above trigonometric transforms, ii) includes the DFT model as a special case, and iii) suggests an efficient way to improve the detection of repeats by digital filtering.

The Filtered Spectral Rotation Measure

Many signal processing techniques were proposed in the past to identify the so-called period-3 component in the protein coding regions of DNA sequences. Most of these methods evaluate the magnitude of the output of an M-point sliding window DFT at the frequency k = M/3. In this paper, we introduce a new multirate DSP approach that computes the phase of the output of the sliding window DFT at the above frequency. We first show that, similar to the magnitude case, the phase component is completely denned by the so-called filtered polyphase sequences. We then propose the filtered spectral rotation measure for detecting the periodicity in genetic regions by modifying the polyphase sequences using digital filters. Experimental results show that the new filtered measure performs better than the existing non-filtered approaches.

Multirate DSP models for gene detection

Digital filtering techniques such as the sliding window DFT and IIR anti-notch filters can be used as tools to identify the protein coding region in a DNA sequence. A multirate DSP model that emulates a complex anti-notch digital filter has been recently introduced. It was shown through simulations that this specific model is most effective in generating the so-called DNA spectrum when compared to previous digital filtering approaches. The improvement in performance is however offset by a higher computational cost. In this paper, we propose a new and efficient IIR implementation of this complex filtering process that does not sacrifice performance. The new implementation uses real causal stable IIR filters and removes the background noise in the DNA spectrum by a simple averaging operation. A mathematical analysis of the newly proposed scheme is also presented.