Via Dei Berio, No 91,00155 Rome, Italy. Abstract - A Fourier-Bessel series based analysis that allows real-time symbol-by symbol error performance evaluation ...
ISIT 97, Ulm, Germany, June29-July4
Bit Error Performance Evaluation for Double Differential QPSK using Gaussian plus Impulsive Noise Model in Heavily Disturbed Aeronautic Channel R. Albano, C. Cornacchini, S. A. Kosmopoulos ( Member IEEE) Space Engineering S.p.A. Via Dei Berio, No 91,00155 Rome, Italy
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Abstract A Fourier-Bessel series based analysis that allows real-time symbol-by symbol error performance evaluation for mobile radio direct sequence code division multiple access (DS-CDMA) systems, is described. This technique analyses radio communication aeronautic links, and generates average bit error rate (BER) vs. E O , estimation. Using the proposed theoretical analysis, a double differential QPSK (DDQPSK) modulation scheme, operating in a realist flat fading channel, accompanied by the presence of additive white Gaussian and impulsive E-mixture noise, Doppler shift and Multi-access-Interference(MAI), is studied. I. INTRODUCTION
In the aeronautic radio channel numerous parameters are usually present (e.g., signal-to-noise ratio, data rate, modulation type, MAI, impulsive noise, mobile speed), affecting the BER performance of the incorporated modulation scheme. Indeed, it is extremely difficult to evaluate such performances of mobile communication systems using “traditional” analysis techniques alone. On the other hand, computer simulations, being viable tools in performance prediction of mobile communication schemes for many years, become almost impractical when symbolby-symbol real-time analysis in multi-access environments is required. Hence other type of analysis, based on series or polynomial expansion concepts, have to Se applied. A theoretical semi-analytical performance evaluation approach, based on the fast converging Fourier-Bessel series [ 11, analysing asynchronous and quasi synchronous DSCDMA configurations without considering Gaussian approximation for MAI, has been used here. This analysis approach can accommodate very high data rates, E O , from 0 to 100 dB, MA1 caused by the various families of spreading sequences (e.g., maximal length), degradation caused by the simultaneous presence of AWGN and Impulsive E-mixture type of noise and flat fading accompanied by Doppler shift when the receiver moves with speed up to 900 Km/h (typical aeronautical environment).
faster timing acquisition (the carrier recovery is obviously not required), and due to its Doppler shift cancellation effect [ 2 ] . It is this latest features, that makes DDQPSK an attractive and most efficient modulation scheme to be incorporated in future planned aeronautic links using DSCDMA in order to improve the channel capacity vs. MA1 and other heavily disturbing phenomena (e.g., fading, impulsive noise).
III. THE FOURIER-BESSEL ANALYSISINAERONAUTICAL LINKS The use of the Fourier-Bessel series expansion is mostly based on the application of the concept of spherical symmetry, in modelling the instantaneous compound random vector of additive disturbance (AWGN+impulsive noise+fading+MAI) [ 11. Indeed, it is the spherical symmetry that permits the substitution of the Fourier-Bessel coefficient by the characteristic function of the random disturbing vector and, hence, truncating efficiently infinitetype of Fourier-Bessel series. Therefore the numerical efficiency imposed by the method (e.g. calculation time versus numerical accuracy) is partly dependent on the number of the considered series terms L, representing the grade in which the series is arrested (truncated). The truncation error associated to the value of the parameter L, obviously, depends on the p.d.f. asymptotic trend of the disturbing random vector statistics. On the other hand, a second as important parameter on which computational efficiency is strongly dependent, is the outmost radius R of a spherical statistical locus, within which the random disturbing vector may be allocated. It is clear [l] that out of :his statistical locus the integral expressing the Fourier transform, which defines the characteristic function of the disturbing random vector, takes negligible small values. Indeed, in the case of a typical aeronautical channel [3], the adopted approach converges rapidly and accurately in the presence of an elevated numbers of channel users (K=50), under severe environmental conditions (both Rician or Rayleigh multipath plus man-made or atmospheric noise plus MAI).
11. MODULATION SCHEME vs. DOPPLER
REFERENCES
It is well know that if differentially coherent detection is considered, phase offset induced by the Doppler shift becomes particularly significant when high carrier frequency values and slow band rates are combined (i.e., 1.6 GHz with 4800 b/s). These type of problems are severely enhanced if a burst-mode of operation is required and, hence, double differential demodulation schemes are generally preferred. This is mostly due to its simpler and
0-7803-3956-8/97/$10.00 0 1 9 9 7 IEEE
S. A. Kosmopoulos, P. T. Mathiopoulos and M. D. Goutha, “FourierBessel error performance analysis and evaluation of QAM schemes in an impulsive noise environment,” IEEE Truns. on Commun., vol. COM -39 pp.398-404, March 1991. [2] M. Pent, “Doubly Differential PSK Scheme in the Presence of Doppler Shift”, Digirul Communication in Avionics, AGARD Proc. # 239, pp 43-1 to 43-1 1, 1978. P. A. Bello, “Aeronautical channel characterisation IEEE Trans. on [3] Commun., vol. COM-21, pp. 548-563, May. 1973.
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