Differential Phase Shift Keying 2.6 2001/06/28 2004/01/07 09:54:23.154 US/Central Behnaam Aazhang aaz@ece.rice.edu Dinesh Rajan dinesh@ece.rice.edu Mohammad Jaber Borran mohammad@ece.rice.edu Roy Ha rha@rice.edu Shawn Stewart mrshawn@alumni.rice.edu Behnaam Aazhang aaz@ece.rice.edu differential phase shift keying modulation DPSK phase lock loop A description of differential phase shift keying, which is a method of error correcting for the common pi phase ambiguity in phase lock loops. The phase lock loop provides estimates of the phase of the incoming modulated signal. A phase ambiguity of exactly is a common occurance in many phase lock loop (PLL) implementations. Therefore it is possible that, θ ^ θ without the knowledge of the receiver. Even if there is no noise, if b 1 then b ^ 0 and if b 0 then b ^ 1 . In the presence of noise, an incorrect decision due to noise may results in a correct final desicion (in binary case, when there is phase ambiguity with the probability: P e ¯ 1 Q 2 E s N 0 Consider a stream of bits a n 0 1 and BPSK modulated signal n n -1 a n A P T t n T 2 f c t θ In differential PSK, the transmitted bits are first encoded b n a n b n − 1 with initial symbol (e.g. b 0 ) chosen without loss of generality to be either 0 or 1. Transmitted DPSK signals n n -1 b n A P T t n T 2 f c t θ The decoder can be constructed as b n − 1 b n b n − 1 a n b n − 1 0 a n a n If two consecutive bits are detected correctly, if b ^ n b n and b ^ n − 1 b n − 1 then a ^ n b ^ n b ^ n − 1 b n b n − 1 a n b n − 1 b n − 1 a n if b ^ n b n 1 and b ^ n − 1 b n − 1 1 . That is, two consecutive bits are detected incorrectly. Then, a ^ n b ^ n b ^ n − 1 b n 1 b n − 1 1 b n b n − 1 1 1 b n b n − 1 0 b n b n − 1 a n If b ^ n b n 1 and b ^ n − 1 b n − 1 , that is, one of two consecutive bits is detected in error. In this case there will be an error and the probability of that error for DPSK is P ¯ e a ^ n a n b ^ n b n b ^ n − 1 b n − 1 b ^ n b n b ^ n − 1 b n − 1 2 Q 2 E s N 0 1 Q 2 E s N 0 2 Q 2 E s N 0 This approximation holds if Q is small.