Communications, Radar & Electronic Warfare (201.. - Index of

74 Communications, Radar and Electronic Warfare4.4 Radio Link Budgets in the Presence of NoiseLink performance in terms of Bit Error Rate (BER) can be estimated for differentmodulation schemes based on the signal energy to noise over the duration of a bit. This isreferred to as EblNo; the energy of the signal per bit over noise in the same time interval.For mUltiple state systems such as 4QAM and higher order QAM systems, the factor isE,lNo; energy per symbol over noise over the duration of the transmission of the symbol.Assuming that one bit is transmitted in the same time as one symbol, the two become thesame. If transmitted power does not vary but noise is increased, this clearly has an effecton this parameter. In simple terms, if the noise increases, so does the BER.The BER for digital systems can be determined by considering the probability oferror. In this analysis, the Gaussian complimentary error function is important:For even numbered QAM modulation schemes, the probability of a bit or symbolerror (depending on the relationship between bits and symbols) can be approximatedby the following for EblNo» 1 and for even k:wherek is the number of bits per symbol.M is the order of modulation.For 16QAM, for example, k = 4 and M = 16. Note that this is a linear equation, andthe EblNo ratio must be converted from dB to its linear equivalent.For odd-k QAM it is more difficult to determine the exact BER, but it is possible todetermine the upper bound by:3kEb(M- l)NoFigure 4.7 shows a graph of BER curves for a number of digital modulation schemes,including Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK),8-, 16- and 64-Quadrature Amplitude Modulation (QAM). Note that the more complexmodulation schemes require a higher value of EblNo to achieve the same BER as lowermodulation schemes. However, they offer the capability to transmit information at ahigher rate.One other factor is important in this analysis; noise jammers increase noise, andhigher digital modulations are more vulnerable to this as well as noise increases.)