Consider highly compressed (using a suitable vocoder) voice transmission using B

Question

Consider highly compressed (using a suitable vocoder) voice transmission using BPSK signaling at a transmission rate (bit rate) of 8 kb/s and a bandwidth efficiency of 1 b/s/Hz. This corresponds to the symbol rate of 8 kBaud (or 8 ksymbols/s), since each BPSK symbol carries only one bit. Lightly compressed (using the standard PCM with logarithmic quantization) voice requires 64 kb/s. We want to transmit the latter voice signal at the same symbol rate of 8 kBaud (and hence the same bandwidth) using a modulation with a higher number of points in its constellation (larger constellation size). The constellation size (number of points in the constellation); the bandwidth efficiency (also known as the spectral efficiency) of the modulation scheme used.

Explanation / Answer

given BPSK signaling

some points to remember let call following quantity as

a) bitrate=Rb

bandwidth is given by following formula

BW=[bitrate(Rb) / log2(M)]

part (1)

(i) from the question given Rb=64 kb/s

but as we know that bitrate =baud rate x N (no of bits per symbol )

so we get 64kb/s= 8kbaud xN

therefore N=8 (but N gives us the quantity of how many bits per symbol)

so constellation point let call (M)

so we know that N= log2(M)

by solving above we get M=(2 ^8) = 256

so the answer of part b) is there are 256 points in the constellation

(c) actually  bandwidth efficiency is the indication of No of bits transmitted through a channel in 1 hz bandwidth per second

and it can be given by formula below

bandwidth efficiency= (bit rate / bandwidth)

as bandwith is calculated by above formula like

(Rb/log2(M))= (64kbps/ log2(256))= (64kbps/8)=8kbps

so bandwidth efficiency= 64kbps/ 8kbps=8=800%

bandwidth efficiency always consider in percentage only

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