Problem 3. Consider the direct-sequence CDMA system as de- scribed in Lecture 15. At the receiver suppose that instead of using the local code qi(t) we instead use q₁(t+A) where A is some ± fraction of a bit time, i.e., the local code may be shifted one direction or the other. Compute the degradation (in dB) to E₁/No due to a nonzero A at the output of the corre- lator for BPSK signaling. You may assume for the local code that adjacent chips are equally likely to match or differ. Receiver CDMA Operations (cont.) Now, d,(t), i = 1,2,..., N is a constant (±1) over T, seconds. Note that q(t) = 1. So, for User 1 we get (ideally) Ть r(t)q₁(t)dt = d₁ 0 Where d₁ just denotes the constant value of d₁(t) at any time in the bit interval which is either +1 or -1 in the given 7,-second interval. Each user repeats the above operations using their particular code. CDMA Receiver Block Diagram From satellite Address Code Sync Correlator Phase-coherent carrier Tb Jo Bit Decision 0 CDMA Receiver

Problem 3. Consider the direct-sequence CDMA system as de- scribed in Lecture 15. At the receiver suppose that instead of using the local code qi(t) we instead use q₁(t+A) where A is some ± fraction of a bit time, i.e., the local code may be shifted one direction or the other. Compute the degradation (in dB) to E₁/No due to a nonzero A at the output of the corre- lator for BPSK signaling. You may assume for the local code that adjacent chips are equally likely to match or differ. Receiver CDMA Operations (cont.) Now, d,(t), i = 1,2,..., N is a constant (±1) over T, seconds. Note that q(t) = 1. So, for User 1 we get (ideally) Ть r(t)q₁(t)dt = d₁ 0 Where d₁ just denotes the constant value of d₁(t) at any time in the bit interval which is either +1 or -1 in the given 7,-second interval. Each user repeats the above operations using their particular code. CDMA Receiver Block Diagram From satellite Address Code Sync Correlator Phase-coherent carrier Tb Jo Bit Decision 0 CDMA Receiver