直序扩频通信 matlab仿真DIRECT SEQUENCE SPREAD SPECTRUM_TECHNIQUES

Lab2 Direct Sequence Spread Frequency Techniques

直序扩频通信仿真

Content

Abstract-------------------------------------------------------------------------------------------3 Experiment Background----------------------------------------------------------------------3 Experiment Procedure------------------------------------------------------------------------5 Analysis and Conclusion---------------------------------------------------------------------10 Reference --------------------------------------------------------------------------------------10 Appendix----------------------------------------------------------------------------------------12

1. Abstract

The objective of this lab experiment is to learn the fundamentals of the direct sequence spread spectrum and code division multiple address techniques. To get familiar with the direct sequence spread spectrum modulator and demodulator.

And the direct sequence spread spectrum system can be shown as:

Figure 1. Direct sequence spread spectrum system

2. Experiment Background

2.1 Introduction of Direct Sequence Spread Spectrum [1]

In telecommunications, direct-sequence spread spectrum (DSSS) is a modulation technique. As with other spread spectrum technologies, the transmitted signal takes up more bandwidth than the information signal that is being modulated. The name 'spread spectrum' comes from the fact that the carrier signals occur over the full bandwidth (spectrum) of a device's transmitting frequency.

Figure 2.1 Procedure to generate a DSSS signal

2.2 Generation of Direct Sequence Spread Spectrum

To generate a spread spectrum signal one requires:

1. A modulated signal somewhere in the RF spectrum

2. A PN sequence to spread it

2.3 Features of Direct Sequence Spread Spectrum

DSSS has some features as following:

1. DSSS phase-modulates a sine wave pseudorandomly with a continuous string of pseudonoise (PN) code symbols called "chips", each of which has a much shorter duration than an information bit. That is, each information bit is modulated by a sequence of much faster chips. Therefore, the chip rate is much higher than the information signal bit rate.

2. DSSS uses a signal structure in which the sequence of chips produced by the transmitter is known a priori by the receiver. The receiver can then use the same PN sequence to counteract the effect of the PN sequence on the received signal in order to reconstruct the information signal.

2.4 Transmission of Direct Sequence Spread Spectrum

Direct-sequence spread-spectrum transmissions multiply the data being transmitted by a "noise" signal. This noise signal is a pseudorandom sequence of 1 and ?1 values, at a frequency much higher than that of the original signal, thereby spreading the energy of the original signal into a much wider band.

The resulting signal resembles white noise, like an audio recording of "static". However, this noise-like signal can be used to exactly reconstruct the original data at the receiving end, by multiplying it by the same pseudorandom sequence (because 1 × 1 = 1, and ?1 × ?1 = 1). This process, known as "de-spreading", mathematically constitutes a correlation of the transmitted PN sequence with the PN sequence that the receiver believes the transmitter is using.

For de-spreading to work correctly, the transmit and receive sequences must be synchronized. This requires the receiver to synchronize its sequence with the transmitter's sequence via some sort of timing search process. However, this apparent drawback can be a significant benefit: if the sequences of multiple transmitters are synchronized with each other, the relative synchronizations the receiver must make between them can be used to determine relative timing, which, in turn, can be used to calculate the receiver's position if the transmitters' positions are known. This is the basis for many satellite navigation systems.

The resulting effect of enhancing signal to noise ratio on the channel is called process gain. This effect can be made larger by employing a longer PN sequence and more chips per bit, but physical devices used to generate the PN sequence impose practical limits on attainable processing gain.

If an undesired transmitter transmits on the same channel but with a different PN sequence (or no sequence at all), the de-spreading process results in no processing gain for that signal. This effect is the basis for the code division multiple access (CDMA) property of DSSS, which allows

multiple transmitters to share the same channel within the limits of the cross-correlation properties of their PN sequences.

As this description suggests, a plot of the transmitted waveform has a roughly bell-shaped envelope centered on the carrier frequency, just like a normal AM transmission, except that the added noise causes the distribution to be much wider than that of an AM transmission.

In contrast, frequency-hopping spread spectrum pseudo-randomly re-tunes the carrier, instead of adding pseudo-random noise to the data, which results in a uniform frequency distribution whose width is determined by the output range of the pseudo-random number generator.

3. Experiment Procedure

3.1. Generate the pseudo random numbers sequences (m sequence) with a polynomial as following

151398751)(x x x x x x x p ++++++=

The polynomial ∑

==

n

k k k x c x p 0

)(is corresponding to the LFSR of the Figure 3.1, where 1=k c denotes a connection.

Figure 3.1 Linear feedback shift register

As the polynomial )(x p shows, we can get the LFSR in this experiment with 14 orders (n=14).

Figure 3.2 n=15 LFSR

As Figure 3.2 shows, the feedback output 15a has a relationship with the registers.

01521369788710515a c a c a c a c a c a c a ⊕⊕⊕⊕⊕=

Hence, we can get the longest m sequence as 3276712

15

=-. In this experiment, I take the

message data rate as 1bit/s, which means Tb=1. Here, the input sequence is initialized as (1 0 1 1 0 1 1 1 0 1 1 0 0). I take the PN sequence data rate as Tc=1/64bit/s, because the spreading gain is 64, in another word, Tb/Tc=64. And I can get the waveform of M sequences and message (input data) as follows:

Figure 3.3 Input message data waveform

Figure 3.4 M sequences waveform

In this experiment, in fact, both message data and m sequences are single polar codes. In Matlab we use a simple function to change them into double polar codes, which are easy to produce the BPSK signal (phase reversing).

3.2. Generate a spreading signal d(t), and the producing formula as following:

c

d

t

t

)(t

)(

*)(

b

Here we can get the waveform of d(t) comparing to b(t) and c(t).

Figure 3.5 c(t) (red) and d(t) (green)

Because b(t) equals 1 at the interval (0,1) and -1 at the interval (1,2), the d(t) is reversed at the interval (1,2) as Figure 3.5 shows. Now, I have get the spreading sequences d(t) with the data rate as 64bits/s.

3.3. Modulate the spreading sequences d(t) to be the BPSK signal

By using the formula of BPSK, I can get the BPSK signal of spreading sequences d(t).

)2sin(*)()(t f t d t s c π=

In this experiment, I take the carrier frequency as 128Hz. I can get the BPSK waveform as Figure 3.6.

Figure 3.6 BPSK of d(t)

At the same time, I should keep a PN sequence signal that has the same length as the spreading signal d(t) to keep the synchronization between the transmitter and receiver.

3.4. In an AWGN channel to transmit the BPSK signal.

First of all, I get the AWGN signal as follow

Figure 3.7 AWGN signal

We can find that the AWGN signal has large number of harmonics and it’s power spectral density is uniform and it’s amplitude distribution obeys the Gauss distribution. In our transmitting channel, I add the noise to the BPSK signal and I take the SNR equals 10. Then I get the signal as shown in Figure 3.8.

Figure 3.8 BPSK signal adding AWGN

3.4. Recover our message data b(t)

Firstly, I use two synchronized circuit to despread and demodulate the receiving signal.

)(*)2sin(*)()(t s t f t c t r c π=

Then I use a matching filter to take the value at the time Tb.

Figure 3.9 Matching filter (1)

Figure 3.10 Matching filter (2)

As we can see, because of the effect of AWGN, in each Tb time interval, the matching filter output has some differences. However, I can still get the nearly maximum and minimum value at the time points Tb+n*Tb (N=1,2,3,..,N and N equals the length of the message data).

Secondly, I do the judgment for maximum and minimum value. Obviously, the y(Tb) get the maximum value, the recovery bit will be 1 and the last time will be Tb, to be inverse, the recovery bit will be -1.

Here I can find that the output signal in our receiver is the same as that in transmitter.

Figure 3.11 Output signal on the receiver

4. Analysis and Conclusion

4.1. Spectrum Spread

Digital communication has played a more important role than analog communication. In digital communication, the fastest speed of data transmission is seen to be the bandwidth of digital channel, which is also called the capacity of the channel. We can know that the larger the capacity, the stronger the ability of anti-interference, because of the Shannon theorem:

)/1(log 2N S B C +=

B is the bandwidth of frequency spectrum. Obviously, when I enlarge the capacity, the bandwidth will be wider. This is also the reason I use the high baud rate m sequence to spread the message data bandwidth.

4.2. Matching Filter

In this experiment, the matching filter is achieved by using a simple function in Matlab which is ‘xcorr ’. This is a function used to calculate the cross-correlation of two sequences. As we know, in fact, matching filter is just like an autocorrelation calculating function.

4.3. The advantages of m sequence (double polar)

The characteristic of autocorrelation of m sequence is very good. I can know it from the following result.

??

?-==otherwise N

N N when R /12,,01

)(ττ I can find that when the N is very large which is just like that in this experiment, 0)(≈τR . This is very good for the multichannel processing.

In CDMA system, I take orthogonal code to encode different users ’ message data. However, the characteristics of cross-correlation and autocorrelation of orthogonal code is bad for the multichannel systems. In order to improve this phenomenon, I should multiple m sequences to the orthogonal codes.

APPENDIX

Some Parts of Matlab Codes

I. DSSS (main function)

clear;

%the PAM input digital sequence and the first input of PN producer p=[1 0 1 1 0 1 1 1 0 1 1 0 0];%get 0 1 0 0 1

pn_in=[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0];%get 0 0 0 0 0 0 0 0 0 0 0 %the period of input signal Tb=1;

%the period of PN sequence signal Tc=1/256;

%produce the PN sequence pn_sq=PN_Producer(pn_in); pn_dou=zero_double(pn_sq); p_dou=zero_double(p); %square wave

%[x1,y1]=square_wave(p_dou,Tb); %[a2,b2]=size(x1);

%[x2,y2]=square_wave(pn_dou,Tc); %plot(x1,y1);

%get the signal after spreading frequcecy operation b_dou=PN_Signal(p_dou,pn_dou,Tb,Tc); %the synchronization of PN p_syn=PN_Syn(p_dou,pn_dou,Tb,Tc); %the carry signal period T_carry=1/512;

%get the carry signal by PSK

wc=2*pi*1/T_carry;

[psks,tpsk]=PSK_Producer(b_dou,wc,Tc);

[a1,b1]=size(tpsk);

fs=b1-1;

N=400;

FSpectrum(psks,fs,N);

%plot(tpsk,psks);

%axis([0 1.6 -2 2]);

%grid on;

%add the noise to the PSK signal by AWGN

in_signal=awgn(psks,10);%the SNR is 20

%fs=b1-1;

%N=400;

%FSpectrum(in_signal,fs,N);

%plot(tpsk,in_signal);

%the recovery signal

signal_corr=Signal_Recover(in_signal,tpsk,p_syn,wc,Tc,Tb); II. PN_Producer (produce the m-sequence)

function y=PN_Producer(x)

m_sq(1).a=x;

m_sq(2).a=x;

m_sq(1).c=[1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 ];

%get1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 get1 1 0 0 1

[l_min,l_max]=size(m_sq(1).c);

n=2;

%the first digit of m-sequence

pn_out(1)=m_sq(2).a(1);

%the m-sequence producer for shifting first time

m_sq(2).a(l_max)=m_sq(1).c(2)*m_sq(1).a(l_max-1);

for i=1:1:(l_max-2)

if m_sq(2).a(l_max)==(m_sq(1).c(2+i)*m_sq(1).a(l_max-i-1)) m_sq(2).a(l_max)=0;

else

m_sq(2).a(l_max)=1;

end

end

for j=0:1:(l_max-2)

m_sq(2).a(1+j)=m_sq(2).a(2+j);

end

for j1=1:1:(l_max-1)

m_sq(3).a(j1)=m_sq(2).a(j1);

end

pn_out(n)=m_sq(2).a(1);

n=n+1;

%to check whether the m-sequence becomes back to the original sequence if isequal(m_sq(3).a,m_sq(1).a)

pn_check=1;

else pn_check=0;

end

%the whole shifting operation and produce the PN

while pn_check==0

m_sq(2).a(l_max)=m_sq(1).c(2)*m_sq(2).a(l_max-1);

for i=1:1:(l_max-2)

if m_sq(2).a(l_max)==(m_sq(1).c(2+i)*m_sq(2).a(l_max-i-1))

m_sq(2).a(l_max)=0;

else

m_sq(2).a(l_max)=1;

end

end

for j=0:1:(l_max-2)

m_sq(2).a(1+j)=m_sq(2).a(2+j);

end

for j1=1:1:(l_max-1)

m_sq(3).a(j1)=m_sq(2).a(j1);

end

pn_out(n)=m_sq(3).a(1);

if isequal(m_sq(3).a,m_sq(1).a)

pn_check=1;

else pn_check=0;

end

n=n+1;

end

%return the PN code

for i4=1:1:(n-2)

y(i4)=pn_out(i4);

end

III. PN_Signal (generate the signal after spreading spectrum) function y=PN_Signal(p,pn_in,Tb,Tc)

N=fix(Tb/Tc);

[a,b]=size(p);

[a1,b1]=size(pn_in);

c=fix(b*N/b1)

pn_original=pn_in;

if c>0

for j=0:1:c

pn_in=horzcat(pn_in,pn_original);

end

else

pn_in=pn_in;

end

s1=1;

e1=N;

for i=1:1:b

if p(i)==1

for m=s1:1:e1

y(m)=pn_in(m);

s1=1+N*i;

e1=N+N*i;

end

else

for m=s1:1:e1

y(m)=p(i)*pn_in(m);

s1=1+N*i;

e1=N+N*i;

end

end

end

end

IV. PSK_Producer (generate the BPSK signal)

function [y,z]=PSK_Producer(x,wc,Tb)

[a,b]=size(x);

%sampling the PSK signal and produce them the N is 1:2 for i=1:1:b

start1=(i-1)*Tb;

end1=i*Tb;%Tb is the period of PN sequence

Tcs(i).s=linspace(start1,end1,50);

if x(i)==1

c_sq(i).s=sin(wc*Tcs(i).s);

else

c_sq(i).s=(-1)*sin(wc*Tcs(i).s);

end

end

y=c_sq(1).s;

z=Tcs(1).s;

for j=1:1:(b-1)

y=horzcat(y,c_sq(j+1).s);

z=horzcat(z,Tcs(j+1).s);

end

end

V. PN_Syn (generate the synchronized PN sequence)

function y=PN_Syn(p,pn_in,Tb,Tc)

N=fix(Tb/Tc);

[a,b]=size(p);

[a1,b1]=size(pn_in);

c=fix(b*N/b1);

pn_original=pn_in;

if c>0

for j=0:1:c

pn_in=horzcat(pn_in,pn_original);

end

else

pn_in=pn_in;

end

s1=1;

e1=N;

for i=1:1:b

for m=s1:1:e1

y(m)=pn_in(m);

s1=1+N*i;

e1=N+N*i;

end

end

end

VI. Signal_Recover (receiver)

function y=Signal_Recover(x,tpsk,pn_syn,wc,Tb,Tc)

m_signal=sin(wc*tpsk);

[t_sqr,pn_syn_sqr]=square_wave(pn_syn,Tb);

c_psk=x.*pn_syn_sqr;

N=fix(Tc/Tb);

[a2,b2]=size(tpsk);

t_gap=b2/50/N;

mid=50*N;

for i2=1:1:mid

t_corr_mid(i2)=tpsk(i2);

end

[t_corr,t_corr_mid]=corr_x(t_corr_mid,Tb,N);

for k=1:1:t_gap

for k2=1:1:(50*N)

k3=k2+(k-1)*50*N;

in_psk(k).s(k2)=c_psk(k3);

in_sin(k).s(k2)=m_signal(k3);

end

ym=xcorr(in_psk(k).s,in_sin(k).s);

%[t_corr,t_corr_mid]=corr_x(t_corr_mid,Tb,N);

if ym(mid)>0

y(k)=1;

else

y(k)=0;

end

if k==2

plot(t_corr,ym,'g*:');

axis([0 2 -2000 2000]);

hold on;

grid on;

%elseif k==3

%plot(t_corr,ym,'mx:');

%axis([0 12.8 -2000 2000]);

%hold on;

%grid on;

else

disp('nice');

end

end

end

VII. square_wave (generate the square wave signal)

function [fss,sqrs]=square_wave(p,g)

%square wave sampling frequency

fs(1).s=linspace(0,g,50);

[a,b]=size(p);

%discrete ones in different time point

for i=1:1:(b-1)

if p(i)==1

sqr_p(i).s=ones(1,50);

else

sqr_p(i).s=(-1)*ones(1,50);

end

fs(i+1).s=linspace(0+g*i,g+g*i,50);

end

%the last time interval

if p(b)==1

sqr_p(b).s=ones(1,50);

else

sqr_p(b).s=(-1)*ones(1,50);

end

fss=fs(1).s;

sqrs=sqr_p(1).s;

for i2=1:1:(b-1)

fss=horzcat(fss,fs(i2+1).s);

sqrs=horzcat(sqrs,sqr_p(i2+1).s);

end

end

VIII. zero_double (cover the single polar signal to the double polar signal) function y=zero_double(x)

[a,b]=size(x);

for i=1:1:b

if x(i)==0

y(i)=-1;

else

y(i)=x(i);

end

end

end