Question

Consider a DS-BPSK spread spectrum transmitter in Figure 2. Let d(t) be a binary sequence 1101 arriving at a rate of 100 bps, where left most bit is the earliest bit. Let c(t) be the pseudorandom binary sequence 100110111000 with a clock rate of 300 Hz. Assuming a bipolar signaling scheme with binary 'O' and binary 'l' represented by a signal levels -l' and '+1', respectively: d(t) Binary-to-bipolar mapping Binary-to-bipolar mapping 2Pcos(211) (1) BPSK modulator P(t) VZPpt) cos(ft) (b) (c) Figure 2 Compute the final transmitted binary sequence corresponding to the bipolar signal sequence, plt). What is the bandwidth of the transmitted spread signal? Calculate the processing gain in dB. Assuming that the spread signal is not corrupted by noise, suppose the estimated delay at a spread spectrum receiver is too large by one chip time, compute the despread and decoded signal sequence (assuming majority logic decoding) What is the number of bit errors due to the estimation delay is? [CLO3, PLO2, C4) (20 marks) (d) e)

Answer 1

Answer -

   (a) Given,

   d(t) : 1101

x(t) : +1 +1 -1 +1

c(t) : 100110111000

   g(t) : +1 -1 -1 +1 +1 -1 +1 +1 +1 -1 -1 -1

Spread Sequence, p(t) = x(t)g(t)

x(t) : +1 +1 +1 +1 +1 +1 -1 -1 -1 +1 +1 +1

g(t) : +1 -1 -1 +1 +1 -1 +1 +1 +1 -1 -1 -1

p(t) : +1 -1 -1 +1 +1 -1 -1 -1 -1 -1 -1 -1

The Binary sequence corresponding to p(t) : 100110000000

(b) Bandwidth of the transmitted spread signal (DSSS-BPSK) is same as clock rate of the pseudorandom binary sequence = 300 Hz.

(c) The processing gain is,

Processing gain = (Pseudorandom chip rate) / (data rate)

   Processing gain = 300 / 100

   Processing gain = 3

Processing gain in dB = 10 log₁₀3 = 4.77 dB.

(d) Despread sequence, ((p(t)) (delayed g(t)) =

p(t) : +1 -1 -1 +1 +1 -1 -1 -1 -1 -1 -1 -1

g^'(t) : -1 +1 -1 -1 +1 +1 -1 +1 +1 +1 -1 -1

r(t) : -1 -1 +1 -1 +1 -1 +1 -1 -1 -1 +1 +1

Majority logic decoding ( taking 3 bits at a time ) yields : 0001

(e) In comparison with d(t), we see that the decoded bit sequence differs in bit positions 1 and 2. Thus, the number of bit errors in the decoded sequence is 2 .