Aye Aung

Sequency-Ordered Complex Hadamard Transform: Properties, Computational Complexity and Applications

In this paper, the generation of sequency-ordered complex Hadamard transform (SCHT) based on the complex Rademacher matrices is presented. The exponential form of SCHT is also derived, and the proof for the unitary property of SCHT is given. Using the sparse matrix factorization, the fast and efficient algorithm to compute the SCHT transform is developed, and its computation load is described. Certain properties of the SCHT matrices are derived and analyzed with the discussion of SCHT applications in spectrum analysis and image watermarking. Relations of SCHT with fast Fourier transform (FFT) and unified complex Hadamard transform (UCHT) are discussed.

Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform

A new transform known as conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT) is presented in this paper. The transform matrix of this transform possesses sequency ordering and the spectrum obtained by the CS-SCHT is conjugate symmetric. Some of its important properties are discussed and analyzed. Sequency defined in the CS-SCHT is interpreted as compared to frequency in the discrete Fourier transform. The exponential form of the CS-SCHT is derived, and the proof of the dyadic shift invariant property of the CS-SCHT is also given. The fast and efficient algorithm to compute the CS-SCHT is developed using the sparse matrix factorization method and its computational load is examined as compared to that of the SCHT. The applications of the CS-SCHT in spectrum estimation and image compression are discussed. The simulation results reveal that the CS-SCHT is promising to be employed in such applications.

Performance of SCHT Sequences in Asynchronous CDMA System

In this letter, the performance of a new set of spreading sequences for a direct sequence (DS) code division multiple access (CDMA) system is examined. These new sequences are derived from sequency-ordered complex Hadamard transform (SCHT). Various correlation properties are presented and the performance of the new sequence is analyzed by comparing it with the other well-known existing spreading sequences, such as UCHT, WHT, Gold, small set of Kasami and m-sequences. According to the simulation results, it is shown that the SCHT sequences provide smaller mean square cross correlation values and offer better average bit error rate for an asynchronous CDMA system over the multipath fading channel.

A Robust Watermarking Scheme Using Sequency-ordered Complex Hadamard Transform

This paper presents a robust phase watermarking scheme for still digital images based on the sequency-ordered complex Hadamard transform (SCHT). The transform matrix of the SCHT exhibits sequency ordering which is analogous to frequency in the discrete Fourier transform (DFT). Hence, sequency-based image analysis can be performed for image watermarking while providing simple implementation and with less computational complexity for computation of the transform. As the SCHT coefficients are complex numbers which consist of both magnitudes and phases, they are suited to adopt phase modulation techniques to embed the watermark. In this proposed scheme, the phases of the SCHT coefficients in the sequency domain are altered to convey the watermark information using the phase shift keying (PSK) modulation. Low amplitude block selection (LABS) is used to enhance the imperceptibility of digital watermark, and amplitude boost (AB) method is employed to improve the robustness of the watermarking scheme. Spread spectrum (SS) technique is adopted to increase the security of watermark against various unintentional or intentional attacks. In order to demonstrate the effectiveness of the proposed watermarking scheme, simulations are conducted under various kinds of attacking operations. The results show that the proposed scheme is able to sustain a series of attacks including common geometric transformations such as scaling, rotating, cropping, painting, and common image-processing operations such as JPEG compression, low-pass filtering, sharpening, noising and phase perturbation, etc. Comparisons of the simulation results with the other schemes are also mentioned and the results reveal that the proposed scheme shows better robustness.

Pipelined Hardware Structure for Sequency-Ordered Complex Hadamard Transform

This letter presents a fast algorithm for the sequency-ordered complex Hadamard transform (SCHT) based on the decomposition method of decimation-in-sequency. To support high-speed real-time applications, a pipelined hardware structure is also proposed to deal with sequentially presented input/output data streams. This structure achieves a full hardware utilization and requires only complex adder/subtracters and complex data stores for an N-point SCHT.

Natural-ordered complex Hadamard transform

This paper presents a new transform known as natural-ordered complex Hadamard transform (NCHT) which is derived from the Walsh-Hadamard transform (WHT) through the direct block matrix operation. Some of its properties, including the exponential property of the NCHT and the shift invariant property of the NCHT power spectrum, are presented. The relationship of the NCHT with the sequency-ordered complex Hadamard transform (SCHT) is discussed. In fact, it is shown that NCHT is a natural-ordered version of complex Hadamard transform whereas SCHT shows the sequency ordering. This is parallel to their real-valued counterparts, the WHT and the sequency-ordered Walsh transform (SOWT). A fast algorithm for computing the NCHT is also developed using sparse matrix factorization and its computational complexity is examined.

Detection of Unknown Multitone Interference Using the AR Method in Slow FH/BFSK Systems over Rayleigh Fading Channels

In this paper, we propose a detection algorithm to detect unknown multitone interference (MTI) encountered in frequency-hopped spread spectrum (FH-SS) systems over a Rayleigh fading channel and additive white Gaussian noise by using autoregressive (AR) spectral estimation method. The proposed algorithm is performed in the AR coefficient domain. The incoming received data is separated into non-overlapping data segments, and the Yule-Walker (YW) AR method is applied on each data segment to obtain the AR coefficient vector. The resultant coefficient vectors are used in the averaging process to obtain the spectrum estimate of the MTI. Computer simulations are conducted in order to investigate detection performance of the proposed AR spectral averaging technique and comparisons are made between the proposed scheme and the fast Fourier transform (FFT) based scheme. Numerical results show that the proposed technique is able to detect the MTI accurately under such a channel environment even at low signal-to-noise power ratio (SNR) condition. The comparisons reveal that the proposed AR detection technique is promising to be employed in slow FH-SS systems to detect the MTI due to higher estimation accuracy and better reliability as compared to the FFT- detection technique.

Multitone interference detection after dehopping process in slow FH/BFSK systems over Rayleigh fading channels

This paper presents an algorithm to detect unknown multitone interference (MTI) which is commonly encountered in slow frequency-hopped spread spectrum (FH-SS) systems over a Rayleigh fading channel. The least-squares (LS) autoregressive (AR) spectral estimation method is used in our algorithm. The proposed algorithm performs the detection process after dehopping, hence, it can be used to provide the side information whether the MTI is present or absent for optimum maximum-likelihood (ML) FH-SS receivers. The fast Fourier transform (FFT) can also be used to implement this detection algorithm. Computer simulations are conducted to evaluate detection performance of both algorithms and comparisons are presented. Numerical results show that the MTI can be detected by both algorithms even at very low interference power (10 dB lower than signal power). Performance comparisons reveal that the proposed algorithm using the AR method is able to locate the MTI within the desired FH band more precisely than the FFT-based algorithm.

Full length article: Detection and countermeasure of interference in slow FH/MFSK systems over fading channels

In this paper, we present an algorithm to detect unknown interference in slow frequency-hopped M-ary frequency-shift-keying (SFH/MFSK) systems over fading channels. Both partial-band noise interference (PBNI) and multitone interference (MTI) are considered. The proposed algorithm performs the detection process after dehopping by making use of square-law detectors. We first analyze the statistical property of the outputs of the square-law detectors over one hop duration, and an appropriate threshold level is derived for detecting the interference based on a binary hypothesis testing. We also formulate the closed-form expressions for the probabilities of detection of both types of interference experienced in any particular frequency hop. The analytical results are validated by the simulation results and they reveal that the proposed algorithm is able to provide good detection performance for both types of interference and outperforms the conventional ratio-threshold test (RTT) method.

Interference detection in slow frequency-hopped quadrature phase-shift-keying systems over fading channels

In this study, the authors present an algorithm to detect unknown interference in slow frequency-hopped quadrature phase-shift-keying systems. Both partial-band noise interference and multitone interference are considered. The algorithm is developed based on the correlator outputs over one hop. A suitable threshold level is derived for detection. The authors formulate the analytical expressions for probability of detection for both interference models. Numerical results reveal that the proposed algorithm can detect both interference types even at low interference power.