Wavelet-Based Demodulation Design for Vehicular Communication Network

Abstract

Wavelet-based Software-defined radios (SDRs), have become very important in both commercial as well as military applications that demand high Quality of Service (QoS) in hostile physical and spectral conditions. It could also be utilized in the vehicle to vehicle communication networks. This WD-based SDR is compose of a AMR and a modulation. This paper focus on the development of the WD-based Demodulation, which enables of obtaining original signal information by demodulation in the wavelet-domain without an inverse transform of a signal to its time-domain form. The development is proven analytically herein. Extensive Monte Carlo simulations also show that the Bit Error Rates (BERs) obtained from wavelet-based demodulation are very comparable with the optimal case of matched filter-based demodulation. The results of this work show the ability of wavelet transforms to enable the demodulation of communications signals in a single processing sequence by solely using the computationally-friendly mathematics of the Discrete Wavelet Transform.

Appendices

Appendix A: Algorithm Computational Complexity Comparison

Comparing with the CWT, another improvement of using the DWT is reduction of the computational complexity as the different fundamental of the CWT [7, 8] and the DWT technologies. The overall WD-AMR method’s computational complexity consists of: Generation of WD templates; Transformation of received signals into the WD; Correlation of WD-templates and WD-received signals; and Decision procedure.

If the CWT was used in the instantaneous featured template AMR process, a test signal has a length of L bits, and there are N samples for each bit. The template size is set at M samples, M ≤ N. So the size of the CWT domain based template would be a M * M matrix and the computation cost of a CWT-template generation is O(M²). The next computation is to continuously wavelet transform received signals, whose complexity could up to O(N²). The third step is correlation of the WD template matrix with the WD received signal matrix. In the instantaneous featured template method, the size of template is usually shorter than or equal to the signal bit size. So the WD signal matrix N * N will be fragmented to M * M. Hence the complexity of their correlation is O(M²). Thus, the summation this three term lead the overall complexity to O(N²).

For the CWT statistical featured template AMR process, a test signal has a length of L symbols, and there are N samples for each symbol. The template size is N samples per symbol as well. Hence, followed by similar analysis as above, the overall complexity is O(N²).

For the DWT Instantaneous featured template AMR process, by defining the same signal size as in the CWT case, a test signal has a length of L bits, and there are N samples for each bit. The template size is set at M samples. So the size of one WD template would be a M * (log₂M) matrix and the computation cost of a DWT-template generation is O(Mlog₂M). The next computation is to discretely wavelet transform received signals, which complexity could up to O(Nlog₂N). The third step is correlation of the WD template matrix with the WD received signal matrix. In the instantaneous featured template method, the size of template is usually shorter than the signal bit size. So the WD signal matrix N * log₂N will be fragmented to M * log₂M. Hence the complexity of their correlation is O(Mlog₂M).

For the DWT Statistical featured template AMR process, a test signal has a length of L bits, and there are N samples for each bit. The template size is set at N samples as well. Similarly, the overall complexity is O(Nlog₂N).

In CWT-based Demodulation algorithm [9], because it basically adheres from two CWT-AMR methodology. Hence it also contains the same complexity as the AMR. In DWT-based Demodulation system developed in this dissertation, it has proved that the DWT-based correlation and the regular correlation deliver the same output. Hence, in the DWT-based demodulation system, the DWT-based correlator replaced the regular correlation was used in the contemporary correlation based receiver. So the overall complexity is the same as the DWT-based correlation complexity, which is O(Nlog₂N).

In summary, there are two points could be pointed through the comparisons:

• 1. The DWT-based AMR algorithm cost less computation effort than the AMR CWT-based algorithm;

• 2. Although the statistical featured templates AMR algorithm costs higher computational complexity than the instantaneous featured templates AMR algorithm, the statistical feature-based algorithm is able to process more multiple modulation signal types than the instantaneous feature based algorithm.

• 3. Although the instantaneous feature-based AMR algorithm remains higher efficiency, but it can only work with binary modulation signals (Table 25.1).

  Table 25.1 CWT-based and DWT-based algorithm complexity comparison

Appendix B: WD-Demodulator and TD-Demodulator Performances Comparison

Under the same experimental environment as setup in the Chap. 6, another set of comparison tests were implemented in MATALAB. Each received, noisy signal has been demodulated using the WD demodulator, and the same each received, noisy signal has been also demodulated using the TD (correlation-based) demodulator. Correspondingly, their two performance curves of two demodulators performance results were presented in Figs. 25.15, 25.16, 25.17, 25.18, 25.19, 25.20, 25.21 and 25.22. One curve corresponds to the simulated performances of the TD (correlation-based) Demodulation introduced in Chap. 6. The other curve is the simulation results for the WD Demodulators developed in this dissertation.

Fig. 25.15

BPSK BER curve comparison

Fig. 25.16

QPSK BER curve comparison

Fig. 25.17

8-PSK BER curve comparison

Fig. 25.18

4-QAM SER curve comparison

Fig. 25.19

4-PAM SER curve comparison

Fig. 25.20

16-QAM BER curve comparison

Fig. 25.21

BFSK BER curve comparison

Fig. 25.22

64-QAM SER curve comparison