To reduce peak-to-average power ratio is a significant task for Orthogonal Frequency Multicarrier Systems. In this paper, we propose a method to choose a suitable vector for a partial transmit sequence technique. Our method is to generate random vectors from the Gaussian distribution whose covariance matrix is a solution of a relaxed problem and to choose a vector from the random vectors. With our method, peak-to-average power ratio is lower than one with a conventional method in the same number of random vectors.

Signal to interference plus noise ratio (SINR) is an important index for wireless communications. This paper shows a method to derive spreading sequences utilized in code division multiple access systems as the solutions of the non-linear programming: maximize SINR. To this end, we consider a frequency-selective wide-sense-stationary uncorrelated-scattering channel and obtain the worst case of SINR. In the course of the evaluation, we derive an expression of SINR, whose main terms consist of periodic correlation terms and odd periodic correlation terms. Also, we show a relation between SINR and mean square correlations. With our expression, we obtain the problem: maximize SINR. Since this problem is not convex, we obtain the relaxed problem with a semidefinite relaxation technique. From this relaxed problem, we obtain the approximated solutions and evaluate the bit error rate for the solutions.

In this paper, we study the problems in the discrete fourier transform (DFT) test included in the National Institute of Standards and Technology (NIST) SP 800-22 released by the NIST, which is a collection of tests for evaluating both physical and pseudo-random number generators for cryptographic applications. The most crucial problem in the DFT test is that its reference distribution of the test statistic is not derived mathematically but rather numerically estimated; the DFT test for randomness is based on a pseudo-random number generator (PRNG). Therefore, the present DFT test should not be used unless the reference distribution is mathematically derived. Here, we prove that a power spectrum, which is a component of the test statistic, follows a chi-squared distribution with two degrees of freedom. Based on this fact, we propose a test, whose reference distribution of the test statistic is mathematically derived. Furthermore, the results of testing non-random sequences and several PRNGs showed that the proposed test is more reliable and definitely more sensitive than the present DFT test.

This study proposes a pseudorandom number generator of$q$-Gaussian random variables for a range of$q$values,$-\infty < q < 3$, based on deterministic chaotic map dynamics. Our method consists of chaotic maps on the unit circle and map dynamics based on the piecewise linear map. We perform the$q$-Gaussian random number generator for several values of$q$and conduct both Kolmogorov–Smirnov (KS) and Anderson–Darling (AD) tests. The$q$-Gaussian samples generated by our proposed method pass the KS test at more than 5% significance level for values of$q$ranging from$-{1.0}$to 2.7, while they pass the AD test at more than 5% significance level for$q$ranging from$-{1}$to 2.4.