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View File - University of Engineering and Technology, Taxila

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A frequently used function is the Q function, which is related to the erfcfunction byQðuÞ ffi1 ð 1pffiffiffiffiffi2p ue x2 =x dxð3:17aÞComparing (3.17a) with (3.13), we write the relationship between Q <strong>and</strong> erfcasQðuÞ ¼ 1 2 erfc u ð3:17bÞ2For computational purposes, (3.16) in (3.12) enables the M-PSK systems errorrates to be evaluated, as demonstrated by Fig. 3.10.Fig. 3.10 shows the error performance P e for data bits b ¼ 1; 2; 3, <strong>and</strong> 4.P e decreases monotonically with increasing E b =N 0 . Theoretically, there is amarginal difference between the error performance <strong>of</strong> the BPSK <strong>and</strong> QPSKschemes. In practice, however, the error performance <strong>of</strong> both schemes is takento be similar because the 3-dB reduction in error distance for QPSK isconsidered to be <strong>of</strong>fset by the decrease in its b<strong>and</strong>width.FIGURE 3.10Bit error rates <strong>of</strong> M-PSK modulation systems.Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

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