IMPLEMENTATION OF GMSK MODULATION SCHEME WITH CHANNEL EQUALIZATION

IMPLEMENTATION OF GMSK MODULATION SCHEME WITH CHANNEL EQUALIZATION

References MX589 GMSK MODEM Application Modem Techniques in Satellite Communication Practical GMSK Data Transmission GMSK MODEM Application A Real Time DSP GMSK Modem with all Digital Symbol Synchronization by Richard Paul Lambert MATLAB CODE: clear all; close all; %********************************* % Variable Definition %********************************* DRate = 1; % data rate or 1 bit in one second M = 18; % no. of sample per bit N = 36; % no. of bits for simulation [-18:18] BT = 0.5; % Bandwidth*Period (cannot change ) T = 1/DRate; % data period, i.e 1 bit in one second Ts = T/M; k=[-18:18]; % Chen's values. More than needed; % only introduces a little more delay %****************************************************************** ********************** % CONSTRUCTION OF GAUSSIAN FILTER FOLLOWED BY SHAPING OF DATA BITS USING GAUSSIAN FILTER % %****************************************************************** ********************** alpha = sqrt(log(2))/(2*pi*bt); % alpha calculated for the gaussian filter response

h = exp(-(k*ts).^2/(2*alpha^2*t^2))/(sqrt(2*pi)*alpha*t); % Gaussian Filter Response in time domain figure; plot(h,'*r') title('response of Gaussian Filter'); xlabel( 'Sample at Ts'); ylabel( 'Normalized Magnitude'); grid; bits = [zeros(1,36) 1 zeros(1,36) 1 zeros(1,36) -1 zeros(1,36) -1 zeros(1,36) 1 zeros(1,36) 1 zeros(1,36) 1 zeros(1,36)]; % here the data is randomly selected to be transmitted and, here 1 indicates 1 and -1 indicates % zero %************** % MODULATION % %************** m = filter(h,1,bits);% bits are passed through the all pole filter described by h, i.e bits are % shaped by gaussian filter t0=.35; % signal duration ts=0.00135; % sampling interval fc=200; % carrier frequency kf=100; % Modulation index fs=1/ts; % sampling frequency t=[0:ts:t0]; % time vector df=0.25; % required frequency resolution int_m(1)=0; for i=1:length(t)-1 % Integral of m int_m(i+1)=int_m(i)+m(i)*ts; end tx_signal=cos(2*pi*fc*t+2*pi*kf*int_m); % Frequency Modulation (FM) is a form of angle modulation in which the instantaneous frequency % of the carrier signal is varied linearly with the baseband message signal m(t),

x = cos(2*pi*fc*t); y = sin(2*pi*fc*t); figure; subplot(2,1,1) stem(bits(1:250)) title('random DATA BITS,+1 FOR ONE AND -1 FOR ZERO '); grid; subplot(2,1,2) plot(m(1:250),'r') title('gaussian SHAPED TRAIN'); xlim([0 260]); figure; plot(tx_signal) title('modulated SIGNAL'); xlim([0 225]); % Channel Equalization % First, a channel simulator is designed to introduce effects common to wireless signals such as % Doppler shifts, Rayleigh fading, phase offsets, and multipath interference. These channel % conditions are used to test the performance of the system in a simulated mobile radio environment. % Second, AWGN is added in the signal. The variance of the Gaussian noise may be changed to test % the performance for different signal to noise ratios, while signal amplitude is held constant. % load 'C:\CASE\Digital_Communication\project\channel.mat' load 'channel.mat' h = channel; N1 = 700; x1 = randn(n1,1); d = filter(h,1,x1); Ord = 256; Lambda = 0.98; delta = 0.001;

P = delta*eye(ord);% Create output pulse: rectangular pulse convolved with first-order % low-pass filter impulse response. w = zeros(ord,1); % adaptive equalization technique is used to cancel the effects of channel % induced effects, underneath is the code for the technique for n = Ord:N1 u = x1(n:-1:n-ord+1); pi = P*u; k = Lambda + u'*pi; K = pi/k; e(n) = d(n) - w'*u; w = w + K *e(n); PPrime = K*pi'; P = (P-PPrime)/Lambda; w_err(n) = norm(h-w); end figure; subplot(2,1,1); plot(h,'g'); title('channel RESPONSE'); subplot(2,1,2); plot(w,'r'); title('adaptive CHANNEL RESPONSE'); % now the channel effects are added to our transmitted signal rcvd_signal = conv(h,tx_signal); figure; plot(rcvd_signal); title('received SIGNAL, AFTER INDUCING CHANNEL EFFECTS'); axis([50 400-0.8 0.8]) eq_signal = conv(1/w,rcvd_signal); figure; %subplot(3,1,1); plot(eq_signal,'r');

axis([150 550-2.5 2.5]) title('received SIGNAL AFTER CANCELLING EFFECTS OF CHANNEL (EQUALIZATION DONE)'); figure; subplot(2,1,1); plot(eq_signal,'g'); title('received SIGNAL AFTER CANCELLING EFFECTS OF CHANNEL (AXIS CORRECTED)'); axis([208 500-2 2]);% here the scale for the received signal is corrected subplot(2,1,2); plot(tx_signal,'r'); title('modulated SIGNAL'); %The following is the source code for a Matlab function that does one-bit diffren- %tial detection. This detection function also simulates synchronization using Gardner's %timing recovery algorithm for the case of over-sampling.it was creating %the problem thats why it has been left % num = 1; % time = 2*N+1; % T =N; % mu = 0.02; % error(1) = 0; % shift = 0; % timing_error =0; % totsteps = 0;.44 %B = fir1(32,0.18); % Demodulation eq_signal2 = eq_signal(215:460-1); eq_signal1 = eq_signal(200:460-1); EQ_SIG=awgn(eq_signal2,20); % here directly matlab function is made use of for the demodulation of the % received signal z_dir=demod(eq_sig,fc,fs,'fm',1);

%figure;plot(z_dir);title('signal OBTAINED FREQUENCY DEMODULATION)'); In = x.*eq_signal1; Qn = y.*eq_signal1; noisei = awgn(in,20); noiseq = awgn(qn,20); I = In + noisei; Q = Qn + noiseq; LP = fir1(32,0.18); yi = filter(lp,1,i); yq = filter(lp,1,q); figure; subplot(2,1,1); plot(yi); title('inphase COMPONENT'); xlim([0 256]); subplot(2,1,2); plot(yq,'r'); title('quadrature COMPONENT'); xlim([0 256]); Z = yi + yq*j; % OQPSK (Offset QPSK) is used to detect the signal. Giving an offset makes the phase shift of 90 % instead of 180. Therefore signal transition ( at every Tb sec) does not pass through a zero and % so no phase change occurs. demod(1:n) = imag(z(1:n)); demod(n+1:length(z)) = imag(z(n+1:length(z)).*conj(z(1:length(z)-n))); xt = -10*demod(1:N/2:length(demod)); xd = xt(4:2:length(xt)); figure; stem(xd)

title('demodulated SIGNAL USING OQPSK'); %m2 = conv(1/h,z_dir);figure;plot(m2)% here signal is convolved back with the inverse gaussian filter % to recover the bits figure; subplot(2,1,1);stem(z_dir,'r');title('recovered SIGNAL AFTER FREQUENCY DEMODULATION'); subplot(2,1,2);stem(bits(1:250));title('bits WHICH WERE TRANSMITTED'); %figure; %plot(demod); % while(time <=length(z)-t) % num = num+1; % samples(num) = (demod(time) >0)*2-1 % error(num) = (sign(demod(fix(time)))-sign(demod(fix(time- T))))*(demod(time-T/2)); % shift = error(num)*n*mu; % steps = fix(shift); % time = time + T-steps; % end Results:

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IMPLEMENTATION OF GMSK RADIO MODULATION Gaussian Minimum Shift Keying (GMSK) is a digital modulation scheme commonly used in wireless, mobile communications. Advantages of using GMSK are its relatively narrow BW, constant envelope modulation, and its suitability for both coherent and non-coherent detection. GMSK is derived from MSK. MSK is a continuous phase modulation scheme where the modulated carrier contains no phase discontinuities and frequency changes occur at the carrier zero crossings. The fundamental problem with MSK is its side lobes extending well above the data rate as shown in the figure. To reduce the transmission BW required input data may be prefiltered prior to modulation using a specific form of low pass filtering. The pre-modulation low pass filter must have a narrow BW with a sharp cutoff frequency and very little offshoot in its impulse response which is characterized by a classical Gaussian distribution.

The amount of ISI introduced depends on the BW-time product, BT, of the Gaussian transmit filter. The premodulation Gaussian filtering introduces ISI in the transmitted signal, but it can be shown that the degradation is not severe if the 3 db-bandwidth-bit duration product (BT) of the filter is greater than 0.5. The GMSK premodulation filter has an impulse response given by h G 2 π π ( t) = exp t 2 α α 2 Where the value of alpha is calculated using the equation α = ln 2 2B 0.5887 = B The premodulation Gaussian filtering introduces ISI in the transmitted signal, but it can be shown that the degradation is not severe if the 3 db-bandwidth-bit duration product (BT) of the filter is greater than 0.5.

Gaussian Filtering: The GMSK modulation is done with the help of Gaussian shaped filter. The signal is made by convolving the bit sequence with the Gaussian Filter. The message signal is integrated to get the phase of it. Then this phase is modulated which results ultimately in a FM signal. The single output is the GMSK signal. Shaped Impulse Input "Gaussian" Gaussian Lowpass Filter Output

Frequency Modulation Frequency Modulation (FM) is a form of angle modulation in which the instantaneous frequency of the carrier signal is varied linearly with the baseband message signal m(t), t f s = A cos[ 2πfct + θ ( t)] = A cos[2πf t + 2πk m( η) dη] FM c c c Where kf is the frequency deviation constant (measured in units of Hz/V) The Channel: First, a channel simulator is designed to introduce effects common to wireless signals such as Doppler shifts, Rayleigh fading, phase offsets, and multipath interference. These channel conditions are used to test the performance of the system in a simulated mobile radio environment. Second, AWGN is added in the signal. The variance of the Gaussian noise may be changed to test the performance for different signal to noise ratios, while signal amplitude is held constant. Demodulation: is done by multiplying the signal with the carrier. After filtering out the carrier signal with a pair of low pass filters, only the baseband I and Q components remain.

Detection: OQPSK (Offset QPSK) is used to detect the signal. Giving an offset makes the phase shift of 90 instead of 180. Therefore signal transition ( at every Tb sec) does not pass through a zero and so no phase change occurs.

Channel Equalization Channel Equalization is to cancel the effect of the channel distortion. It removes Inter symbol interference and assist in the decision of detecting the bits. Several advanced techniques are used in the equalization of channel and most of the methods are adaptive e.g: Minimum Mean Square Method Least Square Method Recursive Least Square Least Mean Square Basic Idea

All the equalization filters are basically adaptive transversal filter, they are basically based on minimum mean square error i.e. J = E(e 2 ) This is basically cost function for over scenario and we have to minimize it with respect to our weights of transversal filter which are basically adapting with the help of error. J = E[(y d) 2 ] J = E[ue] And finally we get The desired Weinner Hopf equation W = R -1 r All the algorithms are basically are the version of this equation.