Lets take up some bandwidth-efficient linear digital modulation techniques (BPSK,QPSK and QAM) and compare its performance based on their theoretical BER over AWGN. (Readers are encouraged to read previous article on Shannon’s theorem and channel capacity). Table 1 summarizes the theoretical BER (given SNR per bit ration – Eb/N0) for various linear modulations. Note that the Eb/N0 values used in that table are in linear scale [to convert Eb/N0 in dB to linear scale - use Eb/N0(linear) = 10^(Eb/N0(dB)/10) ]. A small script written in Matlab (given below) gives the following output. Table 1: Theoretical BER over AWGN for various bandwidth-efficient linear digital modulation techniques: The following table is obtained by extracting the values of Eb/N0 to achieve BER=10^-6 from Figure-1. (Table data sorted with increasing values of Eb/N0). Table 2: Extracted data from Figure 1 where, is the Bandwidth efficiency for linear modulation with M point constellation, meaning that ηB bits can be stuffed in one symbol with Rb bits/sec data rate for a given minimum bandwidth. is the minimum bandwidth needed for information rate of Rb bits/second. If a pulse shaping technique like raised cosine pulse [with roll off factor (a)] is used then Bmin becomes Next the data in table 2 is plotted with Eb/N0 on the x-axis and η on the y-axis (see figure 2) along with the well known Shannon’s Capacity equation over AWGN given by, which can be represented as (refer [1]) Matlab Code [crayon-54366d069a0be282473872/] Reference: [1] “Digital Communications” by John G.Proakis ,Chapter 7: Channel Capacity and Coding. See […]
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