Research On Application Of Fracional Fourier Transform In Underwater Acoustic Communication

The underwater acoustic channel has spatial-temporal-frequency dependent characteristic,severe channel fading effect and complex ambient noise, which makes it become the mostcomplex wireless channel. Therefore, the pursuit of a reliable and effective high speedunderwater acoustic modulation and demodulation method is becoming the main content ofunderwater acoustic communication. The fractional Fourier transform (FRFT) is a recentdevelopment algorithm for chirp signal, which can be interpreted as chirp basisdecomposition or time-frequency plane rotation and chirp signal energy accumulation peakformation in the appropriate fractional domain. Hence, there is positive significance inintroduction of FRFT to underwater acoustic communication and developing a novelcommunication method based on FRFT to deal with complex underwater ambient noise andsuppression fading channel effects.The traditional orthogonal frequency division multiplexing (OFDM) technology has highspeed communication rate and bandwidth efficiency, by means of FFT technique OFDM caneasily achieve fast modulation and becomes foundation of the4G wireless communicationtechnology. However, when OFDM was introduced to underwater acoustic field, the narrowbandwidth, comb frequency-amplitude response and frequency selective fading of underwaterchannel makes its performance degradation. For these problems, this paper presented a novelorthogonal multi-carrier modulation based on FRFT, which used orthogonal LFM signals assub-carriers and used FRFT as modulation and demodulation method. Comparing tosinusoidal sub-carrier, the LFM sub-carrier can not be faded by null steering of underwaterchannel, thus this method can reliably transmit information. And comparing to OFDM system,the FRFT-OFDM system has a better anti-Doppler effect because of the large Dopplertolerance of LFM signal.The chirp decomposition characteristic of FRFT shows that the LFM signal’s energy willfocus and form an impulse function in corresponding fractional domain but will not in theother order fractional domain. Interference signal only has the time-frequency distributionapproximately like LFM signal will produce interfering effect and the ambient noise can beseem as evenly spread in the whole time-frequency plane, any order FRFT of ambient noisewill not produce interference. Therefore, in this paper, the pulse position modulation based onFRFT (FRFT-PPM) was presented, and the transmitted information was modulated in thepeak position in fractional domain, which can have a strong ability of anti-noise andanti-interference. On this basis, according to the positive and negative slope LFM signalenergy focused on corresponding order of fractional domain without mutual interference, this paper presented the positive and negative slope LFM signal FRFT-PPM communicationsystem, doubled FRFT-PPM communication rate without doubled the system bandwidth,which enhanced the robustness and performance of the system.Severe multi-path spread of underwater acoustic channel causes inter-symbolinterference (ISI), thus the equalizer at receiving end can effectively suppress multi-patheffect and reduce error. Actually the multi-path effect is to increase the signal time delay, andaccording to time delay shift of FRFT, the shift of signal in time domain causes transformedsignal shift in fractional domain. In order to reduce interference, this paper presented time andfractional domain guard interval (GI) to reduce ISI. However, this method reduced systemefficiency, and because of the underwater channel severe multi-path spread, completelyreducing ISI with GI will be unacceptable. In this paper, the Rake receiver and the timereverse mirror (TRM) technique was presented to suppression the impact of multi-pathchannel. Rake receiver is a special path diversity technique, and time delay shift of FRFT cancompletely isolate independent fading channel path in fractional domain, thus the Rakereceiver used in FRFT communication system has theoretical basis, and the combiningmethods were discussed in this paper. Comparing to Rake receiver, the TRM dose not needthe exact channel information and suppresses the channel effect, enhances main path energyand signal to interference and noise ratio (SINR) and reduces error by the probe signal’sapproximate reverse channel impulse function convolution with receiving signal.Relative motion of communication platform generates Doppler effect, which makesreceiving signal compression and expansion in time domain, and frequency dispersion infrequency domain. According to scale transformation of FRFT, the change of signal time scalemakes its FRFT fractional domain scale change. So the Doppler effect just causes unifiedoffset and scale of fractional domain change rather than change the LFM signal orthogonalproperty, in this paper, the novel fractional domain Doppler effect compensation method waspresented to suppress Doppler effect by estimating Doppler factor and change the scale andresample in fractional domain.By a large number of simulation and lake experiment to verify the effectiveness andfeasibility of the underwater acoustic communication scheme based on the fractional Fouriertransform, which has broad application prospects.