Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
The GSM System for Mobile Communications
The GSM System for Mobile Communications
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We show a new approach to analytically compute the error probability BERin mobile radio channels. The method is applicable to a variety ofdifferentially detected modulation formats; here we use minimum shift keying(MSK) as an example. We include the following effects: (i) fading and (ii)time dispersion of the mobile radio channel (iii) noise, and (iv) filteringboth of the data sequence and the received signal. Sampling is at a fixedbut arbitrary instant. We develop a new mathematical formalism, which wecall the two-path equivalent-matrix (TPEM) method. In this method, we reducethe general channel (including noise) exactly to a two-path fading channelwithout noise, whose BER can be easily computed. With this method, we canfind analytically the BER for both filtered and unfiltered (G)MSK if the BERis small; for large BER a single well-behaved integral must be solvednumerically. Asymptotic equations for unfiltered MSK and small BERs are alsogiven. To a first approximation, the BER is 0.5· [(S/T)²+1/SNR] for pure MSK, where S/T is the delayspread normalized to the bit duration and SNR is the signal-to-noise ratio.The BER is increased by less than 50% for Gaussian filtering of thedata sequence and receiver filtering with a time-bandwidth product largerthan 0.3.