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Encoding QR-Code in Software Spectrum spreading and despreading

14.10.4 Spectrum spreading and despreading
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In Sec. 10.6.3 the idea of bandwidth for PSK modulation was introduced. In general, for a BPSK signal at a bit rate Rb, the main lobe of the powerdensity spectrum occupies a bandwidth extending from fc Rb to fc Rb. This is sketched in Fig. 14.38a. A similar result applies when the
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(b) (a) The delay lock loop; (b) the waveform at the adder.
W/Hz
fc Rb
fc (a)
fc+Rb
W/Hz
fc Rch
fc (b)
fc+Rch
Spectrum for a BPSK signal: (a) without spreading, (b) with spreading.
Fourteen
modulation signal is c(t), the power-density spectrum being as sketched in Fig. 14.38b. It should be mentioned here that because c(t) exhibits periodicity, the spectrum density will be a line function, and Fig. 14.38b shows the envelope of the spectrum. The spectrum shows the power density (watts per hertz) in the signal. For constant carrier power, it follows that if a signal is forced to occupy a wider bandwidth, its spectrum density will be reduced. This is a key result in CDMA systems. In all direct-sequence spread-spectrum systems, the chip rate is very much greater than the information bit rate, or Rch Rb. The bandwidth is determined mainly by Rch so that the power density of the signal described by Eq. (14.34) is spread over the bandwidth determined by Rch. The power density will be reduced approximately in the ratio of Rch to Rb. Assuming then that acquisition and tracking have been accomplished, c(t) in the receiver (Fig. 14.33) performs in effect a despreading function that it restores the spectrum of the wanted signal to what it was before the spreading operation in the transmitter. This is also how the spreadspectrum technique can reduce interference. Figure 14.39a shows the spectra of two signals, an interfering signal that is not part of the CDMA system and that has not been spread, and the desired DS/SS received signal. Following the despreading operation for the desired signal, its spectrum is restored as described previously. The interfering signal, however, is simply multiplied by the c(t) signal, which results in it being spread.
W/Hz
Interfering signal DS/SS desired signal
fc Rch
fc+Rch
W/Hz De-spread desired signal Spread interfering signal
fc Rch
fc+Rch
(b) (a) Spectrum of an interfering, nonspread signal along with the spread desired signal; (b) the effect of the despreading operation on the desired signal resulting in spread of the interferer.
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14.10.5 CDMA throughput
The maximum number of channels in a CDMA system can be estimated as follows: It is assumed that the thermal noise is negligible compared with the noise resulting from the overlapping channels, and also for comparison purposes, it will be assumed that each channel introduces equal power PR into the receiver. For a total of K channels, K 1 of these will produce noise, and assuming that this is evenly spread over the noise bandwidth BN of the receiver, the noise density, in W/Hz, is N0 (K 1)PR BN (14.46)
Let the information rate of the wanted channel be Rb; then, from Eq. (10.22), Eb PR Rb (14.47)
Hence the bit energy to noise density ratio is Eb N0 (K BN 1)Rb (14.48)
The noise bandwidth at the BPSK detector will be approximately equal to the IF bandwidth as given by Eq. (10.15), but using the chip rate BN > BIF (1 )Rch (14.49)
where is the rolloff factor of the filter. Hence the bit energy to noise density ratio becomes Eb N0 (1 (K )Rch 1)Rb (14.50)
As pointed out in Chap. 10, the probability of bit error is usually a specified objective, and this determines the Eb/N0 ratio, for example, through Fig. 10.17. The number of channels is therefore K 1 (1 ) Rch N0 R b Eb (14.51)
Fourteen
The processing gain Gp is basically the ratio of power density in the unspread signal to that in the spread signal. Since the power density is inversely proportional to bandwidth, an approximate expression for the processing gain is Gp Hence K
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