MODIFIED GOLD PSEUDORANDOM SEQUENCES IN TELECOMMUNICATION SYSTEMS WITH CODE DIVISION OF CHANNELS Dr. Hab, prof. А. Semenko Dr. Phil. N.Bokla

Currently, considerable attention is paid to the broadband system with channels code division, which uses direct spread spectrum technique with the use of carrier wave modulation by the pseudo- random sequence

Wideband signal forming by direct spread spectrum

Advantages of systems using channels code division: increased subscriber capacity compared with using the methods of frequency and time division multiple access; increased confidentiality; increased noise immunity when exposed to narrow-band and wide-band interference; improved electromagnetic compatibility with neighboring radio-electronic systems;. improved energy efficiency

modulation type Δ F γ for р пом =10 -7 S=Δ Fγ 1АМ- 2 2 С 26,3 52,6 С 2FM- 2 2С 12,0 24 С 3FM- 4 С 13,5 13,5 С 4FM- 8 2,33 С 31,6 73,63 С 5ЧМ- 2 4 С 26,3 105,2 С 6ЧМ- 4 4 С 13,2 52,8 С 7ЧМ- 8 5,31 С 10,5 55,76 С To increase the efficiency of telecommunication systems multiposition FM signals are sued, which allow reducing the required bandwidth of the radio channel in K times (K-number of bits of binary signal) Moreover, from the energy point of view, preference should be given to FM = 4

m-sequence PR sequence Walsh Gold Kasami

Type of sequenceAdvantagesShortages m- sequence 1.Simple generation rule; 2.Good values of the side lobes levels ACF CCF Small number of realizations Kasami 1.Simple generation rule; 2.Two times better values of then the Gold PR-sequence The size of the codes set is N times less that the Gold codes Walsh 1.Simple generation rule; 2.Orthogonal 3.Number Big levels of autocorrelation and cross-correlation functions side lobes Gold 1.Simple generation rule; 2.Good value of the side lobes levels ACF CCF Large number of realizations Unpaired number of impulses PR sequences comparison analysis

A feature of m-sequence is a limited number of signals in the ensemble of sequences suitable for the creation of coded channels determined by the Eulers formula [2] where N- number of elements of the sequence (maximum sequence length).

The number of various M- sequences of Gold PRS The most suitable for the formation of the coded channels is to use the Golds sequence, which allows creating a number of quasi-orthogonal signals, many times more than the M-sequences. This formation is based on using M-sequence k N Q Gold

Number of PR sequences with N=1023 PR sequence length, N m-sequence, Q Kasami, L Classic Gold Codes, М gold Modified Gold Codes, 4PSK Number of different PR sequences

To create the wideband signal it is proposed to use a method developed by the authors using the modified Gold pseudo-random sequence (PRS), which gives the ability to create a multi- position using the phase modulation (FM) signals, enabling the system to increase throughput capacity for a given radio channel bandwidth. Classical Gold pseudorandom sequence has an odd number of pulses and can not be used directly to create the multi- position signal.

To form the authors developed modified Gold PRS, one pulse at the beginning or in the end of the sequence is added or subtracted to the classical Gold PRS.. With the help of the graphic user interface the analysis of the correlation characteristics of the modified Gold PRS is carried out and realization of acceptable low level of petals cross-correlation function [4] are determined

Analysis of correlation properties Comparative analysis and selection of the effective PR sequences Impacts on communication system

polynomial polynomial polynomial 1[520]3[54320]5[54310] 2[530]4[53210]6[54210] Forming polynomials Shift register LFSR, containing k separate memory cells

[520] 2[530] 3 [54320] 4[53210] 5[54310] Thus we have 15 pairs of sequences which form the Gold codes. Each group has 33 codes with the length N= 31. In total, there is 495 codes[2].

For classical Gold sequences, three-level periodic ACF and CCF [2] are inherent:

123…n … n Calculation of the cross-correlation function pairs total number ACF CCF

Graphic user interface for the comparison analysis of the classic and modified PR- sequences

ACF Periodic ACF of the Gold PR-sequences with the length of N=31

CCF Periodic CCF of the Gold PR-sequences with the length N=31

N kM 2FM-4 +1( +1,- 1),- 1 +1(+1,-1) +1(+1,-1) 3FM-8-*) *) *) *) 4FM (+1,- 1) 5FM &) *) &) 6FM &) &) 7FM &) 8FM (+1,-1) 9FM &) 1010 FM Примечания: *)-модификация не требуется; &)- модификация невозможна; М=2 k ; N= 2 n -1. Добавлять и отнимать больше 1 импульса нецелесообразно. Модификация целесообразна при М 2N. Принципы образования модифицированных ПСП Голда

Conclusions: 1.All the classic Gold PRS can form a modified Gold PRS with the addition of 1 (+1, -1) or subtraction 1 to create systems with FM-4, FM 16 and FM Classic Gold PRS with the length of 15, 63, 255 and 1023 does not require modification for system creation with FM-8. 3.When creating a system with FM-32, classical Gold PRS with the length of 255 does not require modification. Moreover, classical Gold PRS with the length of 63, 127 and 1024 can not be modified. 4.Modification for FM-64 system is only possible with classic Gold PRS with the length of 511. Modification of the classic Gold PRS with the length of 255 and 1023 is not possible. 5.Modification for FM-128 system is only possible with classic Gold PRS with the length of Modification of the classic Gold PRS with the length of 255 and 511 is not possible. 6.Modification for FM-256 system is only possible with classic Gold PRS with the length of 511 and Modification for FM-512 and FM-1024 systems is impractical with classic Gold PRS. Modification with the length of 1024 for FM-512 is impossible.

Modified Gold PR-sequence selection method

Block-diagram of the modified Gold sequences study

Practical spectral width of the radio signal is determined by the duration of the elementary pulse τ Virtually, the number of coded channels will be determined by: where T- duration of the data pulse; B – wideband base

An effective way of increasing coded channels number with the specified bandwidth Δf к = Δf is the using of the multiposition signal N= Δf к Т log M, Where M – number of the signal positions М=2 k

Usage of the modified Gold PR-sequences can reduce required radio channel bandwidth t transmit a signal with the given number of channels

System implementation of data transmission from 10 CCTV cameras for the project "Smart House", application of the modified Gold PRS with the length N= pulses and 4-position FM-4 signal allowed achieving efficiency in 16.3 dB compared with the method of time-division multiplexing.

Parameters Values Operating frequency, GHz 2,4 Bit rate, kbit / s 1500 Bandwidth with channels time division, MHz 132 Bandwidth with channels code division using modified Gold PRS with the length N= 15+1 and 4 multi-position FM-4 signal (K = 2), MHz 12 Bandwidth reducing factor in system with channels code division using modified Gold PRS with the length N= 15+1 compared to time division. 11 Energy improvement factor of radiolink with the use of FM-4 instead of AM-2 3,9 Integral efficiency factor with channels code division compared to time division channels 42,9 (16,3 dB)

1 - transmitter; 2 - signal source; 3 - signal divider; 4 - the intermediate frequency signal generator; 5, 13- modulators; 6, 14- FM-4 signal formers; 7, 15 - PN signal generators; 8, 16 - modified Golds pseudo-random sequence generators; 9, 17 - generators of the PN FM-4 signal; 10, 18 - frequency converters; 11, 19 - power amplifiers; 12, 20, 22, 39 - antennas; 21 - receiver; 23, 40 -filters; 24, 41 - low noise amplifiers; 25, 42 - frequency converters; 26, 33, 43, 48 - demodulators of FM-4 pseudo noise signal; 27, 34, 44, 49 – correlators; 28, 35, 45, 50 - generators of referenced modified Golds pseudo-random sequence; 29 - synchronizers; 30, 36, 46, 51 - demodulators of FM-4 signal; 31, 37, 46, 51 – detectors;, 32, 38, 48, 54 – solvers; 55, 56, 57 - signal combiners, 1 / and 1 // - transmitter subsystems, 21 / - 1, 21 / - 2, 21 // - 1, 21 // receiver subsystems.

1.Proposed telecommunication system with channel code division of two spaced antennas (2x2 MІMO system) allows the separate processing of signals from 2 channels at the receiver and gain the signal / noise ratio, i.e. improve the noise immunity of the system. 2.Application of realizations 2 and 4 of modified Golds pseudorandom sequences with the number of pulses N = 6 reduces in 2 times required bandwidth of a radio channel with a minimum bandwidth of the PN signal. 3.When there is a frequency resource it would be appropriate to use modified Gold PRS with plenty of pulses and to create a pseudo- noise signal with greater basis. It will implement enhanced immunity system with the use of a pseudo wideband signal with larger basis.

PRS max. side petals ВКФ max. side petals АКФ , , , ,7 0, ,3 PRS N=7-1(substracted at the beginning)

Conclusions 1.broadband telecommunication system with channels code division has advantages such as subscribers increased capacity, noise immunity when broadband and narrowband interference affect the system, privacy, electromagnetic compatibility, energy efficiency. 2.To increase the efficiency of telecommunication system multiposition FM signals are used, that allow reducing of required channel bandwidth in K times (K-number of bits of binary signal) for a given number of coded channels. Mostly, it is impossible to create a multiposition FM signal implementing classic Gold PRS. 3.The proposed modified sequence allows an implementation of multiposition FM signal, particularly, the most efficient FM-4 to reduce required bandwidth for a given number of coded channels.

4.The use of modified Gold pseudo-random sequence with the length of 15 and FM-4 allows to create a video surveillance system of 10 cameras gaining 16,3 dB (10.4 dB- bandwidth reduction, 5.9-dB improvement in signal / noise ratio). 5.The use of modified Gold pseudo-random sequence of length 7 Gold and FM-4 allows to create a system employing MIMO (2x2) with separate signal processing from 2 channels at the receiver (modified Gold pseudo-random sequence has 2 implementations with petals level of CCF the same level as it has the classic sequence).