Contents
Theory Behind Working
Direct Sequence Spread Spectrum:
Direct Sequence is the best known Spread Spectrum Technique. The data signal is multiplied by a Pseudo Random Noise Code (PN code).Processes involved:
Input:
· Input data x(t) with symbol rate fs = 1/Ts (= bit rate fb)
· Pseudo – Noise code p(t) with chip rate fc = 1/Tc(an integer of fs)
Spreading:
In the transmitter, the input data x(t)is directly multiplied with the PN sequence code pt(t), which is independent of the input signal, to produce the transmitted baseband signal y(t)
y(t) = x(t) . pt(t)
The effect of multiplication of x(t) with a PN code is to spread the baseband bandwidth fs.
Despreading:
The spread spectrum signal cannot be detected by a conventional narrowband receiver. In the receiver, the received baseband signal rb is multiplied with pr(t).
· If pt = pr and synchronization to the PN sequence in the received data, than the recovered data is produced on output. The effect of multiplication of the spread spectrum signal rb with the PN sequence pt(t)used in the transmitter is to despread the bandwidth of rb to Rs.
· If pt ? pr, than there is no despreading action. The signal has a spread spectrum. A receiver not knowing the PN sequence of the transmitter cannot reproduce the transmitted data.
Modulation:
fs << fc The amplitude and the power in the SS signal tb is the same as in the original information signal dt. Due to the increased bandwidth of the SS signal the power spectral density must be lower. The bandwidth expansion factor, being the ratio of the chip rate fc and the data symbol rate fs, is usually selected to be an integer in practical SS systems:
Demodulation:
· pt = pr :
To demodulate the received signal is multiplied by pr, this is the same PN sequence as pt (the Pseudo – Noise code used in the transmitter), synchronized to the PN sequence in the received signal rb. This operation is called (spectrum) Despreading, since the effect is to undo the spreading operation at the transmitter
Since
pr = synchronized pt
The multiplier output in the receiver is then
dr = rb . pr = (dt . pr) . pt
Now pt . pt =1 for all t
Thus:
Autocorrelation Ra = avg. (pt . pt) = 1
The data signal is reproduced at the multiplier output:
dr = dt
If the PN sequence at the receiver is not synchronized properly to the received signal, the data cannot be recovered.
· pr ? pt :
If the received signal is multiplied by a PN sequence pr, difference from the one used in the modulator, the multiplier output becomes:
dr = rb . pr = (dt . pt) . pr
In the receiver, detection of the desired signal is achieved by correlation against a local reference PN sequence. For secure communications in a multi-user environment, the transmitted data dt, may not be recovered by a user that doesn’t know the PN sequence pt used at the transmitter.
Therefore: Cross correlation Rc = average (pt . pt) for all t is required. This orthogonal property of the allocated spreading codes. Means that the output of the correlator used in the rceiver is approximately zero for all the except the desired transmission.
Effect of Interference:
To simplify the influence of interference, the spread spectrum system is considered for baseband communication (without filtering).
The received signal rb consists of the transmitted signal tb plus an additive interference i (noise, other users, jammer…):
To recover the original data dt, the receiver signal rb is multiplied with a locally generated PN sequence pr that is an exact of that used in the transmitter (that is pr = pt and synchronized). The multiplier output is therefore given by:
dr = dt + i. pt
The data transmitted part is narrow band. However the noise signal on being multiplied with the pseudo noise sequence becomes a spread signal. This signal is diminished in power and therefore by using a low pass filter equal to bandwidth of the transmitted signal we can recover the original signal without any significant interference.
Frequency Hopped Spread Spectrum:
This is another technique of transmitting signals. In this the pseudo noise code is generated in such a way that the frequency of the carrier signals “hops” after regular intervals in time. The time period of these hops and their frequency is determined by the pseudo noise code sequence.
