(solution) ( Simulation of a binary communication system using antipodal signaling ) The prob- ability of bit

(solution) ( Simulation of a binary communication system using antipodal signaling ) The prob- ability of bit

( Simulation of a binary communication system using antipodal signaling ) The prob- ability of bit error, or bit error rate (BER), is an important performance parameter for any digital communication system. However, obtaining such a performance parame- ter in a closed-form expression is sometimes very difficult, if not impossible. This is especially true for complex systems that employ error control coding, multiple access techniques, wireless transmission, etc. It is common in the study and design of digi- tal communication systems that the BER is evaluated through computer simulation. In this problem you will use Matlab to write a simple simulation program to test the BER performance of a binary communication system using antipodal signaling. The specific steps in your program are as follows: Information source Generate a random vector b that contains L information bits “0” and “1.” The two bits should be equally likely. For this step, the functions rand and round in Matlab might be useful. Modulator The binary information bits contained in vector b are transmitted using antipodal signaling, where a voltage V is used for bit “1” and − V for bit “0.” Thus the transmitted signal is simply y=V * (2 * b-1); Channel The channel noise is AWGN with two-sided power spectral density N 0 / 2 = 1 (watts/hertz). The effect of this AWGN can be simulated in Matlab by adding a noise vector w to the transmitted signal y. The vector of independent Gaussian noise samples with variance of 1 can be generated in Matlab as follows: w=randn(1,length(y)); The received signal r is simply r=y+w; Remark In essence, the above implements a discrete (and equivalent) model of an antipodal signaling system. In particular, the simulated vector r is the output of the correlator or matched filter. Also for simplicity, it is assumed that T b = 1 second. Demodulator (or receiver) With antipodal signaling, the demodulator is very simple. It simply compares the received signal with zero to make the decision. Determine the minimum values of V to achieve the bit error probability levels of 10 − 1 , 10 − 2 , 10 − 3 , 10 − 4 , and 10 − 5 . Use each value of V you found to run your Matlab program and record the actual BER. Plot (on a logarithmic scale) both the theoretical and experimental BER versus V 2 (decibels) on the same graph and compare. Remark If you expect a BER of 10 − K for K = 1, … , 5, then the length L of the infor- mation bit vector b should be at least L = 100 × 10 K . This is to ensure that at least about 100 erroneous bits are recorded in each simulation run and the experimental BER value is reasonably reliable.