Application of wavelet in spread spectrum communication

Figure 1 SDMA's multi-rate modulation model

Figure 2 SDMA multi-rate demodulation (best receiver) model

In actual systems, there are always , So the system capacity is M = -M, And M are the upper and lower limits of the system resolution, respectively. If multi-level PAM modulation is used on a channel of scale m, the transmission rate of the channel is Bm = 2mlog2Lm bits / second, where Lm is the number of modulation levels. When the data is in Transmission on the frequency band. For this modulation method, the bit error rate in the additive Gaussian fractal noise channel [2] can be obtained without coding. In fact, it is similar to the additive white Gaussian noise (AWGN) channel.

(13)

Where Em is the average energy per symbol, and σ2 is the variance of AWGN. From equation (13), it can be seen that the bit error rate of each channel will be inconsistent.

4. The performance and characteristics of SDMA The previous analysis shows that the SDMA system has good anti-narrowband noise performance. At the same time, it can also make the transmitted signal similar to the background noise spectral characteristics by selecting the appropriate base wavelet w, making it very strong. The confidentiality of [2]. Similar to CDMA, only the receiver who knows w can get the information, and it is difficult for others to steal it; and it can also allow the sender to send information with different wavelets according to a certain rule (called wavelet hopping spread spectrum) to enhance system security, which is similar to frequency hopping spread spectrum (FH / SS). SDMA system distributes signal energy to different frequency subbands for transmission, which also makes the system highly resistant to narrowband noise Performance. In Figures 1 and 2, the transfer functions p (n), q (n) and p (-n), q (-n) are the realization of this allocation and its inverse process. These transfer functions can be used Cross-mirror filter (PR-QMF) group implementation.
On the other hand, it is also possible to use the SDMA synthesis / analysis filter bank instead of the Gold sequence M sequence in the traditional CDMA system to spread the information [3, 4], so that the same user ’s message location can be allocated to different subbands Transmission. Figure 3 shows the structure of this spread spectrum system. The integrated filter bank and analysis filter bank are implemented with PR-QMF, and subband selection / extraction can be used to control the transmission of information bits on different subbands. Figures 4 and 5 show the computer simulation results of the single-user and two-user performance of this system under the AWGN channel, respectively.

Figure 3 SDMA spread spectrum system model

Figure 4 Single-user performance of SDMA system under AWGN channel

Figure 5 Performance of two-user asynchronous CDMA system based on different spreading codes under AWGN channel (PR-QMF spreading factor is 32, and length of Gold sequence and M sequence is 31)

In the previous analysis, it was mentioned that each channel of the SDMA system has different bit error rate and transmission rate. For the former, the bit error rate of each channel can be made close by power control; for the latter, the unfairness of this channel But it is inherent in the SDMA system. For users of the same service, let them use the same channel in a time-sharing manner to narrow the gap between the average transmission rates of each user. For example, in an odd time slot, user A uses sub-channel C1. B uses sub-channel C2; while even time slots, user A uses C2 and user B uses C1. For users with different services, this unfairness may be one of the advantages of SDMA systems: using high-rate channels to transmit broadband services ( Such as images), use low-rate channels to transmit narrow-band services (such as voice), and the system naturally combines these services together, so this will be suitable for transmitting multimedia signals.
In fact, the number of sequences in the spreading sequence family close to orthogonal (or quasi-orthogonal) is relatively small, so when the channel capacity is fixed, the capacity of the CDMA system using this spreading sequence is correspondingly small [ 9]. In the actual CDMA system, in order to increase the system capacity, a large number of non-orthogonal spreading sequences are usually used, but this will directly lead to the existence of near-far problem, which seriously affects the system performance. In the SDMA system, when the fundamental wavelet w is determined, the wavelet function family formed by it is theoretically orthogonal, and there are more spreading functions available (because it can be guaranteed from the frequency or time domain Its orthogonality), so it can better suppress the near-far effect, thereby reducing the complexity of the receiver.
The performance of the SDMA spread spectrum system is closely related to the selected fundamental wavelet w, which can be measured by analyzing the coding gain Gs of the filter bank. Here

(14)

Where σ2i is the variance of the output of the i-th analysis filter, and K is the number of layers of wavelet decomposition. The length of the synthesis / analysis filter is L (that is, the support length of the orthogonal wavelet, and it is even) and the given signal spectral density In the case of P (ω), the choice of the optimal wavelet that guarantees the best system performance comes down to In the closed concentration of the dimensional space, look for the best advantage to make Gs reach the maximum value. Figure 6 (a) and (b) respectively give some numerical calculation results of the signal spectral density with uniform distribution and truncated Laplace distribution.

(a) Evenly distributed,
(b) Truncated Laplace distribution, p (ω) = ec | ω | cos (ω / 2)
Figure 6 Local optimal results of Gs under different information spectral densities (L = 6)

In the numerical analysis in Figure 6, the local optimal search results are used instead of the global optimal values, because there is currently no perfect algorithm for solving the global optimal results. In addition, when the spectral density of the signal is more complicated, the search is the most The complexity of the optimal results also increases accordingly.

5. Conclusion Wavelet analysis theory has been widely used in image processing, signal detection and other communication fields. Here, the principle of spread spectrum communication based on wavelet is discussed, a multi-rate modulation and demodulation model is proposed, and the AWGN is given. The performance simulation results of the system in the channel. Through analysis, it shows that the SDMA system has better anti-narrowband noise performance and confidentiality, and can be better suited for multimedia services. In order to make the system have stronger confidentiality, the power of the transmitted signal is required There is no obvious peak in the spectrum (even if the energy is distributed as evenly as possible in the frequency band), and the spectral structure of the fundamental wavelet w determines the spectral structure of the transmitted signal, so how to choose w to meet the above requirements needs further research; how to design orthogonal mirror filtering (PR-QMF) is also an important subject; the performance of SDMA systems with more than two users needs to be further explored.