One of the main disadvantage of multi-carrier CDMA (MC-CDMA) signals is the high peak power of the transmitted signals which limits their applications. To account for this issue, we provide a simple signal processing for reducing the high crest factor (CF) of MC-CDMA signals. Using this modified MC-CDMA signal, the high CF due to Walsh spreading sequences can be mitigated without explicit side information and degradation in the detection performance.

In this study, we construct balanced Boolean functions with a high nonlinearity and an optimum algebraic degree for both odd and even dimensions. Our approach is based on modifying functions from the Maiorana-McFarland's superclass, which has been introduced by Carlet. A drawback of Maiorana-McFarland's function is that their restrictions obtained by fixing some variables in their input are affine. Affine functions are cryptographically weak functions, so there is a risk that this property will be exploited in attacks. Due to the contribution of Carlet, our constructions do not have the potential weakness that is shared by the Maiorana-McFarland construction or its modifications.

In this paper, we show a method to locate a single stuck-at fault of a random access memory (RAM). From the fail-bitmaps of the RAM, we obtain their Walsh spectrum. For a single stuck-at fault, we show that the fault can be identified and located by using only the 0-th and 1-st coefficients of the spectrum. We also show a circuit to compute these coefficients. The computation time is O(2n), where n is the number of bits in the address of the RAM. The computation time is much shorter than one that uses a logic minimization method.

Simple genetic algorithm (SGA) is a population-based optimization method based on the Darwinian natural selection. The theoretical foundations of SGA are the Schema Theorem and the Building Block Hypothesis. Although SGA does well in many applications as an optimization method, it still does not guarantee the convergence of a global optimum in GA-hard problems and deceptive problems. As an alternative schema, therefore, there is a growing interest in a co-evolutionary system where two populations constantly interact and cooperate each other. In this paper we propose a schema co-evolutionary algorithm (SCEA) and show why the SCEA works better than SGA in terms of an extended schema theorem. The experimental analyses using the Walsh-Schema Transform show that the SCEA works well in GA-hard problems including deceptive problems.

This report describes face image recognition by 2-dimensional discrete Walsh transform and multi-layer neural networks. Neural network (NN) is one of the powerful tools for pattern recognition. In the previous researches of face image recognition by NN, the gray levels on each pixel of the face image have been used for input data to NN. However, because the face image has usually too many pixels, a variety of approaches have been required to reduce the number of the input data. In this research, 2-dimensional discrete Walsh transform is used for reduction of input data and the recognition is done by multi-layer neural networks. Finally, the validity of our method is varified.

In this paper, we propose a simple method to find the optimal rational function, with a fixed denominator, which minimizes an integral of polynomially weighted squared error to given analytic function. Firstly, we present a generalization of the Walsh's theorem. By using the knowledge on the zeros of the fixed denominator, this theorem characterizes the optimal rational function with a system of linear equations on the coefficients of its numerator polynomial. Moreover when the analytic function is specially given as a polynomial, we show that the optimal numerator can be derived without using any numerical integration or any root finding technique. Numerical examples demonstrate the practical applicability of the proposed method.

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.

In this paper, a novel adaptive beamforming scheme is described. This scheme basically employs the GSC algorithm which is one of the famous adaptive interference suppression schemes. The implementation of the GSC algorithm requires complex computations due to the adaptive filtering. Therefore, we propose an efficient GSC algorithm based on the split RLS algorithm. In order to reduce the estimation error caused by the correlation between the splitted blocks, the modified GSC is employed with Walsh blocking matrix instead of Bi-diagonal one. In conclusion, the SINR of the proposed method is very close to the SINR obtained by the full tap solution, e.g. when the system complexity decreases nearly half, the SINR of the proposed method becomes 1 dB worse than that of full tap solution.

The conventional synthesis procedure of discrete time sparsely interconnected neural networks (DTSINNs) for associative memories may generate the cells with only self-feedback due to the sparsely interconnected structure. Although this problem is solved by increasing the number of interconnections, hardware implementation becomes very difficult. In this letter, we propose the DTSINN system which stores the 2-dimensional discrete Walsh transforms (DWTs) of memory patterns. As each element of DWT involves the information of whole sample data, our system can associate the desired memory patterns, which the conventional DTSINN fails to do.

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.

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.

An adaptive LMS filtering system is proposed for computing the Discrete Walsh Transform (DWT). The signal to be transformed serves as the 'desired signal' for the adaptive filter, while a set of periodic Walsh sequences serve as the input signal vector for the adaptive filter. The weights of the adaptive filter provide the DWT. The given approach is more efficient in terms of the required computations and memory locations compared with the direct approach. In contract with existing Fast DWT algorithm, the proposed solution provides more flexibility as far as the signal block length is concerned. In other words, the proposed approach is not restricted to a block length N to be of power 2.