Design of One-Coincidence Frequency Hopping Sequence Sets for FHMA Systems

Department of Electrical EngineeringIn the thesis, we discuss frequency hopping multiple access (FHMA) systems and construction of optimal frequency hopping sequence and applications. Moreover, FHMA is widely used in modern communication systems such as Bluetooth, ultrawideband (UWB), military, etc. For these systems, it is desirable to employ frequency-hopping sequences (FHSs) having low Hamming correlation in order to reduce the multiple-access interference. In general, optimal FHSs with respect to the Lempel-Greenberger bound do not always exist for all lengths and frequency set sizes. Therefore, it is an important problem to verify whether an optimal FHS with respect to the Lempel-Greenberger bound exists or not for a given length and a given frequency set size. I constructed FHS satisfying optimal with respect to the Lempel-Greenberger bound and Peng-Fan bound for efficiency of available frequency. Parameters of a new OC-FHS set are length p^2-p over Z_(p^2 ) by using a primitive element of Z_p. The new OC-FHS set with H_a (X)=0 and H_c (X)=1 can be applied to several recent applications using ISM band (e.g. IoT) based on BLE and Zigbee. In the construction and theorem, I used these mathematical back grounds in preliminaries (i.e., finite field, primitive element, primitive polynomial, frequency hopping sequence, multiple frequency shift keying, DS/CDMA) in order to prove mathematically. The outline of thesis is as follows. In preliminaries, we explain algorithm for minimal polynomial for sequence, linear complexities, Hamming correlation and bounds for FHSs and some applications are presented. In section ???, algorithm for complexity, correlation and bound for FHSs and some applications are presented. In section ???, using information in section ??? and ???, a new construction of OC-FHS is presented. In order to prove the optimality of FHSs, all cases of Hamming autocorrelation and Hamming cross-correlation are mathematically calculated. Moreover, in order to raise data rate or the number of users, a new method is presented. Using this method, sequences are divided into two times of length and satisfies Lempel-Greenberger bound and Peng-Fan bound.clos

Enhanced 3-D OCDMA code family using asymmetric run length constraints

Abstract : This paper suggests an enhanced performance of the 3-D optical code division multiple access (OCDMA) codes, a space/wavelength/time spreading family of codes. The initial codes are in the format wavelength hopping/time sequence (WH/TS), selected according to their performance requirements and the TS sequence is constructed to achieve a linear space- time complexity. The asymmetric run length constraints are introduced in that regard, such that the positive bit positions align with the encoder/decoder frequency spacing pattern, yielding a 3-D WH/WS/TS. The selected 2-D OCDMA codes are one- coincidence frequency hopping codes (OCFHC) and optical orthogonal codes (OOC). As a time sequence code, the OOC code length is extended with a code rate of 0.04. The complexity and the bit error rate (BER) are herein given and compared with previous work. The results of the performance show not only an improvement in the number of simultaneous users due to the code length extension, but better correlation properties and hence a better signal-to-noise ratio