The present paper introduces a new construction of a class of binary sequence set having a zero-correlation zone (hereafter binary zcz sequence set). The cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence set is zero for the phase shifts within the zero-correlation zone. This paper shows that such a construction generates a binary zcz sequence set from an arbitrary pair of Hadamard matrices of common size. Since the proposed sequence construction generates a sequence set from an arbitrary pair of Hadamard matrices, many more types of sequence sets can be generated by the proposed sequence construction than is possible by a sequence construction that generates sequence sets from a single arbitrary Hadamard matrix.

The channel noise in OFDM systems affects the accuracy of channel estimation, deteriorating the performance of equalization. We present a novel algorithm with MMSE (Minimum Mean Square Error) channel estimation based on Hadamard Transform, to mitigate the effects of noise. The performance of the proposed algorithm is proved to be better than that with LS (Least Square) estimation, and very close to that with the MMSE estimation based on Fourier Transform, while the computation required is pretty small due to the use of Hadamard Transform.

In this paper, we present a polynomial construction based on Jacket and Hadamard matrices over the Galois Field. The construction has two modes, one only includes matrices extension, and the other includes a center-weighted scheme for polynomial representations. Here, an "addition" scheme is used to represent matrices, which can lead to simple operations and convenient implementation of hardware.

This paper proposes a high-resolution CMOS image sensor, which has Hadamard transform function. This Hadamard transform circuit consists of two base generators, an array of pixel circuits, and analog-to-digital converters. In spite of simple composition, a base generator outputs a variety of bases, a pixel circuit calculates a two-dimensional base from one-dimensional bases and outputs values to common line for current addition, and analog-to-digital converter converts current value to digital value and stabilize a common line voltage for elimination of parasitic capacitance. We simulated these circuit elements and optimized using SPICE. Basic operations of this Hadamard transform circuit are also confirmed by simulation. A 256 256 pixel test chip was designed in 4.73 mm 4.73 mm area with 0.35 µm CMOS technology. A fill factor of this chip is 42% and dynamic range is 55.6 [dB]. Functions of this chip are Hadamard transform, Harr transform, projection, obtaining center of gravity, and so on.

This paper proposes an Orthogonal Frequency Division Multiplexing system with Grouping Adaptive Modulation method (GAM-OFDM). The salient feature of the proposed system is to enable the reduction of required transmission bits for adaptive modulation information (AMI) that is required in the demodulation process at the receiver. This paper also proposes an efficient AMI transmission method for the GAM-OFDM system to enable the efficient transmission of AMI bits by using only two preamble symbols, and the Multi-Carrier Spectrum Spreading (MC-SS) technique to achieve the excellent performance of AMI transmission even under severe multi-path fading environments. This paper presents the various computer simulation results to verify the performance of proposed GAM-OFDM system.

The UCHT (Unified Complex Hadamard Transform) has been proposed as a new family of spreading sequences for DS-SSMA systems recently. In this Letter, the periodic autocorrelation (PAC) properties of the Unified Complex Hadamard Transform (UCHT) sequences are analyzed. Upper bounds for the out-of-phase PAC are derived for two groups of the UCHT sequences, namely the HSP-UCHT and the NHSP-UCHT sequences (the later is a more general representation of the well-known Walsh-Hadamard (WH) sequences). A comparison of the two bounds is performed. It turns out that the HSP-UCHT sequences have a lower upper bound for the out-of-phase PAC. This makes the HSP-UCHT sequences more effective than the WH sequences in combating multipath effect for DS-SSMA systems.

A circuit that carries out an Hadamard transform of an input image using the pulse width modulation technique is proposed. The proposed circuit architecture realizes the function of an Hadamard transform with a full-size pixel image. A test chip that we designed and fabricated integrates 64 64 pixels in a 4.9 mm 4.9 mm area, with 0.35 µm CMOS technology. The functional operation and linearity of this chip are measured. An image processing application utilizing this chip is demonstrated.

In this paper we deal with Voronoi diagram in simply connected complete manifold with non positive curvature, called Hadamard manifold. We prove that a part of the Voronoi diagram can be characterized by hyperbolic Voronoi diagram. Voronoi diagram in simply connected complete manifold is also characterized for a given set of points satisfying a distance condition.

This paper discusses factorization of bent function type complex Hadamard matrices of order pn with a prime p. It is shown that any bent function type complex Hadamard matrix has symmetrical factorization, which can be expressed by the product of n matrices of order pn with pn+1 non-zero elements, a matrix of order pn with pn non-zero ones, and the n matrices, at most. As its application, a correlator for M-ary spread spectrum communications is successfully given, which can be simply constructed by the same circuits with reduced multiplicators, before and behind.

In this paper, comparison of various orthogonal transforms in Wiener filtering is discussed. The study involves the family of discrete orthogonal transforms called Complex Hadamard Transform, which has been recently introduced by the same authors. Basic definitions, properties and transformation kernel of Complex Hadamard Transform are also shown.

In this paper, we consider the selection of analysis filters used in the delayless subband adaptive digital filter (SBADF) and propose to use simple analysis filters to reduce the computational complexity. The coefficients of filters are determined using the components of the first order Hadamard matrix. Because coefficients of Hadamard matrix are either 1 or -1, we can analyze signals without multiplication. Moreover, the conditions for convergence of the proposed method is considered. It is shown by computer simulations that the proposed method can converge to the Wiener filter.

It is well known that M-ary/spread spectrum (M-ary/SS) system is superior to direct-sequence spread spectrum system under AWGN, and can achieve high spectral efficiency. On the other hand, however, the main drawback of this system is that the synchronization acquisition is difficult. In this paper, we propose a new synchronization acquisition method of M-ary/SS system. This method acquires the code synchronization by introducing a symmetrical property in spreading sequences, and detecting this property with the differential decoding technique. As spreading sequences, a set of orthogonal sequences and a set of non-orthogonal sequences are considered. The strong features of proposed systems are that the systems can acquire the code synchronization in carrier band and can reduce the complexity of calculation greatly. Among the comparison results of the systems with newly proposed orthogonal and some specific non-orthogonal spreading sequences, it is especially noted that the latter can reduce the mean acquisition time and calculation complexity much greater than the former.

In this paper, we present orthogonal multi-code CDMA systems with the constant amplitude transmission. In general, the dynamic range of the amplitude of the transmitting signal is very large in the case of orthogonal multi-code CDMA systems. In order to realize the constant amplitude transmission for orthogonal multi-code CDMA systems, we propose a constant amplitude coding. First, we show the basic concept of the constant amplitude coding. And then, we show that the constant amplitude transmission can be realized by the combination of the conventional orthogonal multi-code CDMA and the constant amplitude coding. Finally, the effectiveness of the proposed method is evaluated in terms of the bit error rate performance and it is shown that the proposed method is robust to the non-linear distortion caused by a high power amplifier (HPA).

In this paper, we examine a new initial symbol acquisition method for M-ary spread-spectrum (M-ary/SS) signals that are affected by large carrier frequency offset. By the effect of the carrier frequency offset, preamble signal energy is dispersed to the undersired outputs. The proposed method is based on the collection of such dispersed signal energies by using reference patterns. The reference patterns are constructed by using the characteristic of Hadamard code sequences. The effectiveness of the proposed method is evaluated in terms of mean acquisition time.

M-ary orthogonal keying (MOK) systems under carrier frequency offset (CFO) are investigated. It is shown that spurious signals are introduced by the offset frequency components of spectrum after multiplication in correlation detection process, and some conditions on robust orthogonal signal sets are derived. Walsh function sets are found to be very weak against CFO, since they produce large spurious signals. As robust orthogonal signal sets against CFO, the rows of circulant Hadamard matrices are proposed and their error performanses are evaluated. The results show that they are good M-ary orthogonal signal sets in the presence of CFO.

The performance of an M-ary spread-spectrum multiple-access (M-ary/SSMA) scheme in the presence of carrier frequency offset is discussed in this paper. The influence of carrier frequency offset on the non-coherent reception of M-ary/SSMA signals is examined and it is shown that the carrier frequency offset degrades the performance remarkably, yet. this influence has a distinctive property. Making use of this property, we propose a new M-ary/SSMA scheme that can mitigate the influence of the carrier frequency offset. The scheme is based on the assignment of two distinctive Hadamard codes to in-phase and quadrature components of the transmitted signal. The effect of simultaneous transmission is evaluated in terms of bit-error-rate performance with the carrier frequency offset. As the result, it is observed that the satisfactory bit-error-rate performance can be achieved in the presence of carrier frequendy offset.

This paper discusses the performance of non-coherent reception for M-ary spread-spectrum (M-ary/SS) signals in the presence of carrier frequency offset. In general, the M-ary/SS scheme is expected to be of higher spectral efficiency than the conventional DS/SS schemes, but its performance may be degraded by the carrier frequency offset. We, therefore, analyze the effect of carrier frequency offset on the performance of the non-coherent M-ary/SS system with orthogonal modulation using a set of sequences generated by the Hadamard matrix. As a result of the analysis, it has been found that the carrier frequency offset may cause a great deal of degradation in the performance, and that its effect has a distinctive property which is due to the characteristic of Hadamard matrix, at the same time. Making use of this property, we propose two schemes that can mitigate the effect of carrier frequency offset: one is based on choise of the code sequences, the other is on the error correcting code. The effectiveness of the schemes is evaluated in the terms of symbol-error-rates through analysis and computer simulation.

We propose an algorithm for image decomposition based on Hadamard functions, realized by answer-in-weights neural network, which has simple architecture and is explored with steepest decent method. This scheme saves memory consumption and it converges fast. Simulations with least mean square (LMS) and absolute mean (AM) errors on a 128128 image converge within 30 training epochs.

In this letter we present an electronic circuit based on a neural net to compute the discrete Walsh transform. We show both analytically and by simulation that the circuit is guaranteed to settle into the correct values.

Synchronization has been one of the problems in M–ary spread spectrum communication systems. In this letter, we propose the frame synchronization method using the Hadamard matrix and a frame synchronization method of PCM communication systems. Moreover, we analyze the probabilities of keeping synchronous state and frame renewal rates, and we evaluate the relationship between these probabilities and the number of stages of counters.