Analysis and design of binary pseudorandom sequences based on the Magma package

Due to the complexity and variability of the underwater acoustic channel, the communication signal is affected by multi-path, time delay, and Doppler frequency shift. Based on the advantageous characteristics of fractional Fourier transform on chirp signal processing, a fractional Fourier transform–based algorithm using combined linear frequency–modulated signal is proposed, which can estimate parameters of underwater acoustic channel and has a better performance than the existing methods. To distinguish multi-user in underwater acoustic communication system, a single-carrier direct sequence code division multiple access communication system combined with the fractional Fourier transform–based algorithm is proposed. Thus, a preliminary study on underwater multi-target identification is carried out. The simulation and experimental results show that the fractional Fourier transform–based algorithm is simple and effective, and the energy can be focused at the “best” fractional order, which can directly determine the multi-path number and complete the channel estimation. The proposed single-carrier direct sequence code division multiple access communication system has good performance on bit error rate when we use corresponding spreading code to distinguish multi-user.

Optical code division multiple access has been proposed as an alternative multiple access scheme for multiuser fiber-optic communication systems. Many previous works on the receivers for such systems have focused on the correlation receiver which is optimal in the single user case. However, it has been shown that the performance of the correlation receiver is unsatisfactory when there is a large number of interferers. Multiuser detection becomes an appealing method to improve the system performance. In this paper, a new multiuser detector for optical code division multiple access communication systems, referred to as the multistage decorrelating receiver, is proposed. Its structure is much simpler than the optimal multiuser detector at the expense of slight performance degradation. Both simulation and analysis of the receiver are carried out. Comparison of the proposed detector with several other receivers is also presented.

New results for a multiuser detector based on recurrent neural network structures (MU-RNN) for a direct sequence code division multiple access communication system with multipath propagation are given. Contrary to other neural network approaches the MU-RNN has the advantage, that the network size as well as the weight coefficients of the network can be derived from the parameters characterizing the communication system. The energy function of the MU-RNN matches the loglikelihood function of the maximum likelihood detector and thus has the potential for optimum performance. Different iteration algorithms for the MU-RNN with an emphasis on parallel processing are discussed. The performance and complexity of the MU-RNN are compared with other optimum and suboptimum detection algorithm, specifically the multistage detector.

The optical ZCZ code, which is a set of pairs of binary and biphase sequences with zero correlation zone, can provide code division multiple access (CDMA) communication system without co-channel interference. The M-ary amplitude shift keying spread spectrum (M-ary/ASK-SS) system using this code can detect a desired sequence without interference of undesired sequences. We have proposed the compact construction of a matched filter bank for this code, which is called the compact-type matched filter bank. However, M-ary/ASK-SS system using this filter bank might go down the bit error rate (BER) performance because input-output characteristics of this filter bank for this code with zero correlation zone 4n - 2 are nonlinear characteristics. In this paper, we clarify that BER performance in the M-ary/ASK-SS system over the additive white Gaussian noise (AWGN) channels is not influenced by nonlinear characteristics of this filter bank by the theoretical formula of BER characteristics and the computer simulation. The BER performance in the ASK-SS system using compact-type matched filter under the AWGN environment go down compared to that using direct-type matched filter as expected. But the BER performance in the M-ary/ASK-SS system using this compact-type matched filter bank under the AWGN environment is almost equal compared to that using parallel-type matched filter bank. In fact, this compact-type matched filter bank is effective in the M-ary/ASK-SS system.

We investigate the average information rates attained by adapting the transmit power and the information rate relative to channel variations in code division multiple access communication systems. Our results show that the rate adaptation provides a higher average information rate than the power adaptation for a given average transmit power, and the rate increase when using rate adaptation is more significant for channels with a faster decaying multipath intensity profile and weaker line-of-sight component.

A cyclically permutable code is a binary code whose codewords is cyclically distinct and has a full cyclic order. Important classes of these codes are the constant weight cyclically permutable codes. These codes have wide applications in optical code division multiple access communication systems. In this paper, we propose a tunable cyclic shifter based on the super-imposed holographic grating using photopolymer as the holographic medium, which can be used with a cyclically permutable code by applying appropriate strain to the photopolymer.

This paper shows simulations of an all-fiber fast optical code division multiple access communications system (OCDMA), using strong apodized fiber Bragg gratings (FBGs) arrays as passive encoding-decoding devices. Auto and cross-correlation functions of the user signals, and bit error rate (BER) were used as evaluation criteria. Through numerical analysis, we demonstrated that when strong Bragg gratings are used the performance of the system is increased. We obtain the BER performance for strong gratings and compare results in various cases.

Wavelet packets (WP) have been found a promising candidate for user signature waveforms in code division multiple access communication systems. They have better orthogonality properties, and are capable of effectively suppressing certain types of noise/interferences. In this paper we present a method to model wireless communication channels using wavelet packets as bases. Modeling of wireless communication channels using WP has the advantage of more efficiency in wideband modulation. In addition, time-varying channel modeling can also be relatively easily accommodated. To evaluate the effectiveness of the proposed modeling method, we have tested it on indoor multipath fading channels. The results show promising features of the proposed model.

In this paper, a new signal processing algorithm for ultrasonic sensory systems in airborne transmission is presented. The proposal is based on a phased array (PA) where the excitation signals are loosely synchronous (LS) sequences, often used in code division multiple access communication systems. Hence, by setting a different LS sequence for each steering angle, it is possible to simultaneously acquire all the information of the scanned area with a single fire, in order to detect possible reflectors in front of the sensory array. The use of these LS sequences combined with PA techniques allows to simultaneously steer the main beam in different directions with low interference. Simulation results reveal that this approach does not only provide longer distance inspection, but also noise robustness. Furthermore, this algorithm provides higher image rate than conventional PA techniques even for high-quality images, since the image rate does not depend on the number of steering angles to be explored.

In stream cipher systems, random key sequence generation is the primary task. The concept of chaotic systems can be considered in generating a random key sequence due to its inherent randomness property. Though the chaotic real sequences are random, the randomness will be lost after converting them to binary sequences. In this context, the authors propose a technique which uses a non‐linear feedback system to enhance the randomness of the binary sequences. In this work, three binary chaotic sequences using a logistic map are generated with three different initial conditions and each real value of the chaotic sequence is converted to ‘k’ bit binary value using a thresholding function. Some of the resulting sequences are not random. Hence, in this article a non‐linear structure is used to make the resulting sequence random. Here, a non‐linear function similar to the structure of the Simplified Data Encryption Standard is used to generate a sequence using two non‐random chaotic binary sequences. The resulting sequence is XORed with another non‐random chaotic binary sequence to get a random sequence. Sequences obtained from this nonlinear system are subjected to randomness tests and the results indicate that the sequences pass all the randomness tests. Hence, the sequences qualify as random key sequences, which can be used in a stream cipher based system to encrypt the data samples like audio, image, video, and so forth.

Binary sequence pairs as a class of mismatched filtering of binary sequences can be applied in radar, sonar, and spread spectrum communication system. Binary sequence pairs with two-level periodic autocorrelation function (BSPT) are considered as the extension of usual binary sequences with two-level periodic autocorrelation function. Each of BSPT consists of two binary sequences of which all out-phase periodic crosscorrelation functions, also called periodic autocorrelation functions of sequence pairs, are the same constant. BSPT have an equivalent relationship with difference set pairs (DSP), a new concept of combinatorial mathematics, which means that difference set pairs can be used to research BSPT as a kind of important tool. Based on the equivalent relationship between BSPT and DSP, several families of BSPT including perfect binary sequence pairs are constructed by recursively constructing DSP on the integer ring. The discrete Fourier transform spectrum property of BSPT reveals a necessary condition of BSPT. By interleaving perfect binary sequence pairs and Hadamard matrix, a new family of binary sequence pairs with zero correlation zone used in quasi-synchronous code multiple division address is constructed, which is close to the upper theoretical bound with sequence length increasing.

In recent years, the joint decoding of combined source and channel coding have shown the capability of delivering performances exceeding that of separately decoded schemes. In this paper, a well-known joint source/channel coding scheme is investigated for possible use in future 4th Generation (4G) direct sequence spread spectrum multiple access (DS/SSMA) code division multiple access (CDMA) communication systems. Due to the availability of potentially large sets of sequences with good correlation characteristics, the DS/SSMA CDMA system considered in this paper employs complex spreading sequences (CSS). A multiuser CSS-based DS/SSMA CDMA communication system was implemented as test platform for the joint source/channel coding scheme. Several families of CSSs, including Zadoff-Chu (ZC), double sideband constant envelope linearly interpolated root-of-unity filtered general chirp-like (DSB CE-LI-RU Filtered GCL), analytical bandlimited complex (ABC) and quadriphase (QPH) sequences are investigated on this platform. Simulated bit error rate (BER) performances are presented for uncoded, separate source and channel coded and joint source/channel coded systems under realistic multipath fading channel conditions.

In earlier papers finite pseudorandom binary sequences were studied, quantitative measures of pseudorandomness of them were introduced and studied, and large families of “good” pseudorandom sequences were constructed. In certain applications (cryptography) it is not enough to know that a family of “good” pseudorandom binary sequences is large, it is a more important property if it has a “rich”, “complex” structure. Correspondingly, the notion of “f-complexity” of a family of binary sequences is introduced. It is shown that the family of “good” pseudorandom binary sequences constructed earlier is also of high f-complexity. Finally, the cardinality of the smallest family achieving a prescibed f-complexity and multiplicity is estimated.

Computer Algebra and Algebraic. Geometry—Achievements and Perspectives

Macaulay is a system for computing in algebraic geometry and cummutative algebra; it is capable of a variety of computations which are tedious or impossible to perform by hand. The primitive types in the system are polynomials, matrices, ideals, polynomial rings, modules, maps between rings, and complexes of modules. The system performs algebraic manipulation on objects of these types. The possible manipulations include the computation of standard (Gröbner) bases, modules of syzygies, finite free resolutions, Hilbert polynomials and functions. Using these basic operations, a variety of derived operations are possible, such as projections, ideal intersections, and the computation of coherent sheaf cohomology groups. The algorithm used for constructing standard (Gröbner) bases and syzygies is described in ([Buc76], [Zac78], [Sch80], [Bay82], [BaSt86a]).