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    National Institute of Technology: Communication Engineering Lab II

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    retgertreter
    The document describes a simulation of a digital communication system using PCM and DPCM modulation techniques. It involves sampling an analog input signal, quantizing it, modulating it using BPSK, transmitting over an AWGN channel, demodulating and reconstructing the signal. The mean squared error between the original and reconstructed signals is calculated for different sampling frequencies and quantization levels. Plots of MSE vs sampling frequency and quantization levels are generated for both PCM and DPCM. Observations show that MSE decreases with increasing sampling frequency and quantization levels for PCM, while DPCM has higher MSE but requires less bandwidth.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    National Institute of Technology: Communication Engineering Lab II

    Uploaded by

    retgertreter
    48 views11 pages
    The document describes a simulation of a digital communication system using PCM and DPCM modulation techniques. It involves sampling an analog input signal, quantizing it, modulating it using BPSK, transmitting over an AWGN channel, demodulating and reconstructing the signal. The mean squared error between the original and reconstructed signals is calculated for different sampling frequencies and quantization levels. Plots of MSE vs sampling frequency and quantization levels are generated for both PCM and DPCM. Observations show that MSE decreases with increasing sampling frequency and quantization levels for PCM, while DPCM has higher MSE but requires less bandwidth.

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    B6_Exp1Report

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    The document describes a simulation of a digital communication system using PCM and DPCM modulation techniques. It involves sampling an analog input signal, quantizing it, modulating it using BPSK, transmitting over an AWGN channel, demodulating and reconstructing the signal. The mean squared error between the original and reconstructed signals is calculated for different sampling frequencies and quantization levels. Plots of MSE vs sampling frequency and quantization levels are generated for both PCM and DPCM. Observations show that MSE decreases with increasing sampling frequency and quantization levels for PCM, while DPCM has higher MSE but requires less bandwidth.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    48 views11 pages

    National Institute of Technology: Communication Engineering Lab II

    Uploaded by

    retgertreter
    The document describes a simulation of a digital communication system using PCM and DPCM modulation techniques. It involves sampling an analog input signal, quantizing it, modulating it using BPSK, transmitting over an AWGN channel, demodulating and reconstructing the signal. The mean squared error between the original and reconstructed signals is calculated for different sampling frequencies and quantization levels. Plots of MSE vs sampling frequency and quantization levels are generated for both PCM and DPCM. Observations show that MSE decreases with increasing sampling frequency and quantization levels for PCM, while DPCM has higher MSE but requires less bandwidth.

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    of 11

    National Institute of Technology

    CALICUT

    Communication Engineering Lab II


    Experiment - 1

    PCM AND DPCM (BPSK)

    SUBMITTED BY : GROUP B6
    1 MIRIYALA KISHAN B181030EC miriyala_b181030ec@nitc.ac.in

    2 POLISETTY SAI ROHITH B180482EC sairohith_b180482ec@nitc.ac.in

    3 PYLA KOUSTHUB B180669EC pyla_b180669ec@nitc.ac.in

    1
    Problem Statement :
    Simulate using MATLAB a digital communication system that employs
    PCM to convert an analog n signal to a bit stream and subsequently uses
    BPSK modulation to transmit it over an Additive White Gaussian Noise
    Channel.
    Input the analog signal 5+5.cos(2πf0 t), t ϵ [0,30/f 0 ]
    Sample the signal at rate fs .Denote the number of quantization levels as l.
    Assume that f 0 =1 KHz. At the receiver, reconstruct the analog signal from
    the demodulated bit
    stream.
    (i) Calculate the Mean Squared Error (MSE) between the original analog
    signal and the reconstructed signal.

    (ii) Plot the MSE v/s f for f s = f0, 2f0 , 4f0 , 8f0 , 16f0 , 32f0 for all l (values
    s
    given below)
    (iii) Plot the MSE v/s l, l= 4, 8, 16,…, 32 for all fs .
    Repeat the experiment using DPCM. Compare the performance of PCM and
    DPCM.

    Theory
    Pulse coded modulation (PCM)

    Pulse Code Modulation Pulse-code modulation (PCM) is a method used


    to digitally represent sampled analog signals.

    In a PCM stream, the amplitude of the analog signal is sampled


    regularly at uniform intervals, and each sample is quantized to the
    nearest value within a range of digital steps.

    A PCM stream has two basic properties that determine the stream's
    fidelity to the original analog signal: the sampling rate, which is the
    number of times per second that samples are taken; and the bit depth,
    which determines the number of possible digital values that can be used
    to represent each sample.
    Differential Pulse Code Modulation (DPCM)

    Differential pulse-code modulation (DPCM) is a signal encoder that


    uses the baseline of pulse-code modulation (PCM) but adds some
    functionalities based on the prediction of the samples of the signal.

    The DPCM Transmitter consists of Quantizer and Predictor with two


    summer circuits. Following is the block diagram of DPCM transmitter.

    The predictor assumes a value, based on the previous outputs at both


    the transmitter and receiver.

    The input given to the decoder is processed and that output is summed
    up with the output of the predictor, to obtain a better output.

    Transmitter
    Receiver

    Algorithm and Outputs


    ● A input wave 5 + 5sin(x) is taken with a frequency of 1 kHz and is
    sampled at a frequency higher than the nyquist rate frequency
    ● The resultant signal is quantized and is converted into binary
    equivalent i.e. a PCM signal. (Encoded)
    ● The binary wave is then modulated using BPSK scheme with NRZ
    modification.
    ● Then this modulated wave is sent through a AWGN channel and is
    received at the receiver.
    ● BPSK demodulation is performed and then, Decoding is performed
    and reconstructed signal is hence plotted.
    ● Similarly for DPCM an extra parameter Predictor is introduced to
    predict the upcoming output sampled value.
    ● Corresponding Mean Square error vs quantization levels and
    sampling frequency is plotted

    Mean Square error


    ● The MSE can be written as the sum of the variance of the estimator
    and the squared bias of the estimator, providing a useful way to
    calculate the MSE and implying that in the case of unbiased
    estimators, the MSE and variance are equivalent
    Code :
    clear;
    close all;
    global ct
    ct=1;
    A=zeros(5,5);
    B=zeros(5,5);
    Fs=[1,2,4,8,16];
    N=[2,3,4,5,6];
    for i =1:1:5
    for u =1:1:5
    A(i,u)=MSE(Fs(u),N(i));
    end
    end

    for i=1:1:5
    for u=1:1:5
    B(i,u)=MSE(Fs(i),N(u));
    end
    end

    figure(4)
    for i =1:1:4
    hold on
    la=num2str(2^N(i));
    lab=strcat("L=",la);
    plot(Fs,A(i,:),'DisplayName',lab)
    title('MSE vs fs')
    legend

    end

    figure(5)
    for i =1:1:5
    hold on
    la2=num2str(Fs(i));
    lab2=strcat("fs=",la2);
    plot(N,B(i,:),'DisplayName',lab2)
    title('MSE vs number of Quantization Levels')
    legend
    end

    function out=MSE(fs_,l)
    f=1000;
    fs=fs_*f;
    n=l;
    t=[0:1/(fs*10) :2];
    x=5*cos(2*pi*f*t);
    x1=x+5;
    %quantisation
    %q=round(x1);
    maxsig=max(x1); %signal max
    interv=maxsig/(2^n-1);
    u=maxsig+interv/2;
    partition = [0:interv:maxsig];
    codebook = [0-interv/2:interv:u];
    [q,quants] = quantiz(x1,partition,codebook);
    enc=de2bi(q,'left-msb');

    h=length(enc);
    bpsk_=reshape(enc,1,h*n);
    bpsk(bpsk_==1)=1;
    bpsk(bpsk_ ==0)=-1;

    SNR=10.^(14/10);
    No=1/SNR;
    N=sqrt(No/2)*randn(1,h*n);
    BPSK_AWGN=bpsk+N;
    detected=zeros(1,h*n);
    for i = 1:1:length(BPSK_AWGN)
    if(BPSK_AWGN(i)>0)
    detected(i) = 1;
    else
    detected(i) = -1;
    end
    end

    detected_(detected==1)=1;
    detected_(detected==-1)=0;
    rec=reshape(detected_,h,n);
    dec=bi2de(rec,'left-msb');
    x_re=dec*interv;

    y=lowpass(x_re,1000.001,30000);
    y=reshape(y,1,length(y));

    out=immse(y,x1);
    global ct
    if fs_== 2 && ct==1
    ct=0;
    figure(1);
    subplot(3,1,1);
    plot(t,x1,'r');
    title('Original Signal')
    xlim([0.001 0.003])
    subplot(3,1,2);
    stem(t,x1);
    title('Sampled Signal')
    xlim([0.001 0.003])
    subplot(3,1,3);
    plot(t,q);
    title('Quantized Signal')
    xlim([0.001 0.003])
    figure(2);
    subplot(3,1,1);
    stem(bpsk)
    title('BPSK modulated')
    xlim([0 90])
    subplot(3,1,2);
    stem(BPSK_AWGN)
    title('BPSK in AWGN')
    xlim([0 90])
    subplot(3,1,3);
    plot(t,x_re,t,y);
    title('Recovered Signal')
    xlim([0.001 0.003])
    figure(3);
    plot(t,y)
    xlim([0.001 0.003])
    title('Reconstructed Signal')
    end
    end
    Plots And Waveforms:
    Plots And Waveforms:
    Observations and Inferences

    ● The Mean Square error decreases as quantization levels are increased


    ● The Mean Square error decreases as sampling frequency is increased
    ● DPCM takes less bandwidth to transmit the same signal than PCM.
    ● DPCM has more Mean square error than PCM for the same
    quantization levels and sampling frequency
    ● Mean Square error in DPCM is higher than PCM and hence is not
    advised to use. DPCM only helps us in saving the bandwidth as we are
    only transmitting the difference and not the whole signal.

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