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This explanation covers how to modulate an input binary bit stream using DPSK signaling, along with the non-coherent demodulation process at the receiver. It also addresses the bit error probability of DPSK signaling in both AWGN and Rayleigh fading channels. By examining the encoding and modulation process, as well as demodulation techniques and performance comparisons, this text provides insights into how DPSK performs in different channel conditions.
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Question 1 Modulate an input stream of binary bits: m = 0 0 1 1 1 0 1 1 0,with DPSK signaling. Assume that encoder at the transmitter is dk = mk dk – 1, where mk is the input bit and dk is the encoded bit at time k, (d0 = 0). The modulator maps dk = 0 to ‘cos (0) = +1’ and dk = 1 to ‘cos(p) = –1’. Explain how the receiver can demodulate the received signal non-coherently. What is the bit error probability of DPSK signaling in AWGN channel? What is the bit error probability of DPSK signaling in Rayleigh fading channel?
DPSK modulation and encoding dk = mk dk – 1 k 0 1 2 3 4 5 6 7 8 9 Information bit mk 0 0 1 1 1 0 1 1 0 Encoded bit dk-1 0 0 0 1 0 1 1 0 1 1 Encoded bit dk 0 0 1 0 1 1 0 1 1 DPSK Symbol +1 +1 +1 -1 +1 -1 -1 +1 -1 -1
DPSK demodulation (1) • We send cos(qk = 0) or cos(qk = p): • But we will receive: qk-g
DPSK demodulation (2) • We form the following variable at the receiver side to determine the information bit that was sent
DPSK demodulation (3) From dk = mk dk – 1we conclude that mk = dk dk – 1.
Demodulation of m in question 1 If qk - qk-1= 0, we decide mk = 0. If qk - qk-1= p, then mk = 1.
DPSK performance in AWGN • The BER performance of DPSK in AWGN is given by:
Rayleigh fading channels (1) • The received signal model in Rayleigh flat fading channels:
Rayleigh fading channels (2) • We assume that phase distortion has been compensated or is not a deciding factor in the demodulation (as in DPSK):
Rayleigh fading channels (3) • The instantaneous signal to noise ratio in fading channels is affected by a and is given by: • Therefore the instantaneous BER performance of DPSK signaling is also affected by a and is given by: • Therefore the average error • probability is the given by:
