Signals and Systems - Electrical Engineering

740 CHAPTER 12: Applications of Discrete-Time Signals and Systems

plot(f,M);grid; axis([min(f) max(f) 0 1.1∗max(M)]); ylabel(‘—M(f)—’)

subplot(212)

plot(f,S); grid; axis([min(f) max(f) 0 1.1∗max(S)]);ylabel(‘—S(f)—’); xlabel(‘f (Hz)’)

% analog modulation and demodulation

s = s.∗cos(200∗pi∗t);

r = s.∗cos(200∗pi∗t);

% despreading

mm = r.∗c;

for k = 1:length(mm);

if mm(k)> 0

m2(k) = 1;

else

m2(k) = -1;

end

end

figure(3)

subplot(411)

plot(t,s); axis([0 max(t) 1.1∗min(s) 1.1∗max(s)]);grid; ylabel(‘sa(t)’)

subplot(412)

plot(t,r); axis([0 max(t) 1.1∗min(r) 1.1∗max(r)]);grid; ylabel(‘r(t)’)

subplot(413)

plot(t,mm); axis([0 max(t) 1.1∗min(mm) 1.1∗max(mm)]);grid; ylabel(‘ma(t)’)

subplot(414)

bar(t,m2); axis([0 max(t) -1.2 1.2]);axis([0 max(t) 1.1∗min(mm) 1.1∗max(mm)])

grid;ylabel(‘\m(t)’); xlabel(‘t (sec)’)

Orthogonal Frequency-Division Multiplexing

OFDM is a multicarrier modulation technique where the available bandwidth is divided into nar-

rowband subchannels. It is used for high data-rate transmission over mobile wireless channels

[27, 60, 4].

If{dk,k=0,...,N− 1 }are symbols to be transmitted, the OFDM-modulated signal is

s(t)=

∑∞

m=−∞

N∑− 1

k= 0

dkej^2 πfktp(t−mT) (12.27)

whereTis the symbol duration,fk=f 0 +k 1 ffor a subchannel bandwidth 1 f= 1 /Twith initial

frequencyf 0 , andp(t)=u(t)−u(t−T). Thus, the carriers are conventional complex exponentials.

Considering a baseband transmission, at the receiver the orthogonality of these exponentials in

[0,T] allows us to recover the symbols. Indeed, assuming that no interference is introduced by the

transmission channel (i.e., the received signalr(t)=s(t)), multiplyingr(t)by the conjugate of the

exponential carrier and smoothing the result we obtain fork=0,...,N−1, andm≤t≤(m+ 1 )T