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On the Probability Density Function of the Squared Envelope of a Sum of Random Phase Vectors

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1 Author(s)
Simon, Marvin K. ; California Inst. of Tech., Pasadena, CA

A recursive solution is presented for the probability density function of the sum of N independent, random phase vectors. The recursion parameter is N , the number of vectors in the sum. This approach allows one to rapidly compute a complete set of these density functions for values of N = 2, 3, ..., N_{\max } , where Nmaxtypically corresponds to the total number of system users in a multiuser FHMA/MFSK application, or one plus the total number of jamming tones in an FH/MFSK spread-spectrum application. Such evaluations are necessary for exact calculation of the average error probability performance of such systems.

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Communications, IEEE Transactions on  (Volume:33 ,  Issue: 9 )