To solve the problem of the high peak-to-average power ratio (PAPR) in Orthogonal Frequency Division Multiplexing (OFDM) for the underwater acoustic communication system, the paper offers a method of reducing PAPR which combines the amplitude limiting and the improved nonlinear transformation. Traditional amplitude limiting technique can reduce PAPR in OFDM system effectively, at the cost of reducing the bit error rate (BER). However the companding transformation has far less computation complexity than SLM or PTS technologies and can improve the BER performance compared to the amplitude limiting technique simultaneously. The paper combines these two kinds of techniques, takes full use of advantages of the two method, and puts forward a low-complexity scheme choosing parameters that are more appropriate to the underwater acoustic field, with the result of improved BER performance even in lower SNR. Both simulation and experiment results show that the new method which combines clipping and companding transformation can effectively reduce the PAPR in the underwater acoustic OFDM communication system and improve the BER performance simultaneously.
Recently, the main research direction of underwater acoustic communication includes high-speed underwater acoustic communication at near distance and low-speed acoustic communication at remote distance [
International and domestic research on reducing PAPR mainly divides into following several classes [
The discrete OFDM signal can be expressed as
Companding transformation technique belongs to amplitude limiting technique, whose core idea is to process the signal which has a higher peak power nonlinearly, so that the power will not run out of the dynamic range of the amplifier and avoid the large PAPR [
Companding technique will process the signal nonlinearly before it comes into the amplifier, amplifying small signal and keeping large signal invariant; therefore the decrease of PAPR is at the cost of increasing the system’s average power [
The traditional companding arithmetic function is as follows:
What is presented in Figure
Characteristic curve of companding technology.
The parameters of traditional radio communication companding function utilize the peak value of signal. However, the heavy multipath fading of the underwater acoustic channel, which is influenced by the burst noise coming from marine organisms and ships, leads to the unreliability of the peak value detection at the receiving terminal; therefore the traditional parameter selecting method is not suitable anymore.
The improved companding function can be expressed as follows:
The receiving signal is expressed as
Framework of improved companding technology in PAPR reducing for OFDM system.
Researches on the influences of the system’s BER performance caused by companding transformation are presented in this segment. Because the arithmetic that this paper adopted is the processing of a part of signal, when using QPSK to modulate signals, the BER of signals which have not been companding satisfies the equation
Companding signal
The communication frequent band is 6–12 kHz, the length of FFT is 8192, sample frequent is 48 kHz, adopting QPSK modulation, and amount of subcarriers is 1025. The shallow sea channel is generated by channel simulation software, the depth is 50 meters, the depth of the transducer and hydrophone, respectively, is 22 meters and 10 meters, and the horizontal distance is 2 km.
Figure
Simulation of channel impulse response.
Eigenray of the multipath channel.
Figure
Comparison of CCDF.
Figure
Amplitude of OFDM signals before and after processing.
Original
Clipping
C transformation
SLM
Proposed method
The influence of different decreasing PAPR method on system BER performance is presented in Figure
Influence of different method on OFDM system.
In 2015, at Harbin Engineering University, the experiment was done in the channel water tank. There are sands at the bottom of the water tank, valid depth is about 4 meters, the length is 45 meters, and width is 6 meters, with the silence wedge around. Transducer is at 1 meter underneath the surface, hydrophone is at 1.5 meters underneath the surface, and the horizontal distance is about 14 meters.
At first, we produce a transmission signal using MATLAB software and translate it into a WAV file, transmitting the signal from computer’s sound card. The signal goes through the power amplifier, transmitted by a transducer, passing the underwater acoustic channel, received by the hydrophone. The signal is collected and stored by a computer for distant processing.
Figure
Impulses response of tank channel.
Figure
Send and receive figure: (a) original, (b) clipping, (c) C companding, (d) SLM, and (e) the improved method.
At present, the technique to decrease PAPR is at the cost of increasing power, increasing BER, decreasing the data rate, and adding computational complexity. In practical, we need to choose a suitable method according to each influence factor of an OFDM system. In an underwater acoustic OFDM system, the transmitting of data is in severe surroundings. The band-width is limited in the acoustic channel, so it enlarges the influence of delay spread and frequency selective fading compared to wireless channels. This requires the method which decreases the PAPR to be of low complexity and to keep the signal recovered exactly with less influence in the meantime. The paper takes advantage of amplitude limiting arithmetic and C transformation, combining them to apply underwater acoustic OFDM communication system. After the simulation comparison of amplitude limiting arithmetic, C transformation, and improved arithmetic, we get the result that the improved arithmetic can both decrease PAPR and improve the performance of the system, with the advantage of low computation complexity and being easy to realize. The computation complexity will not be influenced by the amount of subcarriers, so it is suitable to apply in underwater acoustic communication system with a limited band-width.
The authors declare that they have no competing interests.
The authors thank the project of the National Natural Science Foundation of China no. 61431004, no. 6140114, and no. 11274079 and the Teaching and Research Project of Qiqihar University no. 2014087.