Performance Analysis of Frequency HoppedCoherent MPSK in the Presence of Multitone Jamming

Fu(u) P(u 5 u)= P(g($('))5 u) =
and the density function Of can be Obtained
(4)
by differentiating
F.I.( U
009M778/96$05.00 0 1996 IEEE
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 44, NO. 2, FEBRUARY 1996
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A closer inspection of u = g(q5(i)) leads us to consider the problem for two cases. The first case occurs when the signal power is greater than the jamming tone power (i.e., 0 < y < 1). Then the inverse transformation of the function u = g(q5(')) is double-valued. In the second case, the jamming tone power is greater than the signal power (i.e., y 2 1);then the inverse transformation of u = g ( q ! ~ ( ~ ) )single-valued. is
I. INTRODUCTION
COHERENT frequency hopped spread spectrum system was proposed in [ l ] and 121 as a possible way to combat interference introduced by a jammer in a digital radio system. Simon and Polydoros examined the performance of sp= J2SeW + J21ejd". (1) quadrature modulations in the presence of jamming in [l]. Their analysis was based on the assumption that either a In the optimum receiver structure, in the presence of widecoherent frequency synthesizer can be realized or the phase band noise, the receiver compares the received signal phase continuity from one hop to another can be maintained by mg( s?)) with all possible M phases and decides on the phase other means. Recently, researchers studied the performance that provides the smallest absolute phase difference. Then the of several coherent frequency hopped systems in the presence probability of symbol error for symbol intervals which are of jamming [3]-[6]. The assumption of a coherent frequency jammed Pe,3 is given by synthesizer in which the phase of the signal can be tracked Pe,j = 1 - Prob = arg (sp)) - O ( 2 ) from the dehopped signal is used in [3] and [4]. The performance of binary signals in partial-band noise jamming and partial-band multitone jamming was obtained and the effect of (2) nonideal channel phase response was studied in [4]. In the previous works, the performance evaluation of coHence, to analyze the probability of error for a M-ary PSK herent frequency hopped PSK in the presence Of system, it is necessary to obtain the pdf of the random phase jamming has been limited to BPSK and QPSK systems. The difference p i (+) . main contribution of this paper is to derive the expression for the probability density function (pdf) of the received signal 111. PROBABILITY DENSITY phase in the presence of multitone jamming and then use this FUNCTION OF PHASE DIFFERENCE ?1, pdf to obtain the probability of error expressions for any M-ary PSK signal. For QPSK (i.e., M = 4) our probability of error The probability density function of the random phase is expressions are identical to the ones given in [7, VOl. 11, ch. completely known Once the pdf of u = arg(3 ) : is determined. 31, which were obtained using a different approach. Let us consider the pdf of u, where u can be expressed as
Ibrahim Ghareeb and Abbas YongaGoglu
Abstract- This paper studies the performance of frequency hoppedkoherent M-ary PSK signals in the presence of partialband multitone jamming. The probability density function for the jammed received signal phase is found and utilized in obtaining a probability of error expression. The analytical expressions to assess the performance under worst case multitone jamming are provided.
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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 44, NO. 2, FEBRUARY 1996
Performance Analysis of Frequency HoppedCoherent MPSK in the Presence of Multitone Jamming
Paper approved by G. L. Stuber, the Editor for Spread Spectrum of the IEEE Communications Society. Manuscript received June 28, 1994; revised March 4, 1995, and May 18, 1995. I. Ghareeb is with Jordan University of Science and Tecnology, Irbid, Jordan. A. YongaGoglu is with the Department of Electrical Engineering, University of Ottawa, Ontario, Canada, KIN 6N5 (e-mail: yongacog@elg.uottawa.ca). Publisher Item Identifier S 0090-6778(96)01615-7.
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PSK SYSTEM MODEL 11. FWM-ARY In a FWM-ary PSK system, the transmitted signal s(2) in the ith signaling interval can be represented in the complex ) form by s ( ~= d%?eje('), where S is the signal power and 15'(~) the phase of the signal taking one of the equally likely is and equally spaced 2 x / M values.