In recent years, underwater acoustic communications have developed rapidly due to the needs for marine observation and exploration. However, underwater acoustic communications still face various challenges, such as limited bandwidth, large-scale fading, and fast time-variation.
Although several optimal equalizers, such as the maximum a posteriori probability equalizer and the maximum likelihood sequence estimation equalizer, can fulfill the detection demands, they still suffer from the high computational complexity. Consequently, their practical uses are inevitably limited and gradually replaced by some suboptimal equalizers, such as the decision feedback equalizer.
Motivated by the turbo-decoding principle, a new advance has been made by turbo equalization in improving the detection performance via the soft information exchange between the equalizer and the decoder. Recently, the soft interference cancellation based turbo equalizer and soft decision feedback turbo equalizer have been proposed to achieve a satisfactory performance with a low-complexity implementation.
However, most of the existing turbo equalization schemes are based on channel estimation. The detection performance largely depends on the accuracy of the channel estimation which becomes less robust in the time-varying channel.
Most recently, researchers XI Junyi, YAN Shefeng, XU Lijun and TIAN Jing from the Institute of Acoustics of the Chinese Academy of Sciences propose a direct-adaptation based bidirectional turbo equalizer for underwater acoustic communications. Simulated and experimental results demonstrate that the bidirectional turbo equalizer outperforms the single directional one.
It can be seen from the experimental results that, compared with the channel estimation based algorithm, the direct-adaptation based algorithm is less sensitive to the time-varying channel and has a lower bit error rate.
Abandoning the channel estimation process, the direct-adaptation based turbo equalizer embedded with digital phase-locked loop is adopted to track time-varying channel. The fast self-optimized algorithm is used to adjust the step size, thus a good tradeoff between the convergence speed and performance has been made.
Meanwhile, by minimizing the mean squared error, an optimal weighting factor is derived to exploit bidirectional diversity gain. The forward turbo equalizer is combined with the backward turbo equalizer to eliminate error propagation effect.
In order to verify the efficiency of the algorithm, an underwater acoustic communication experiment has been conducted in May 2016 in the Qiandao Lake. The original data bits come from a black-and-white picture. The experiments are conducted for three conditions: 1200 m communication range with arrays relatively static, 500 m communication range with 5.4 m/s relative velocity, and 800 m communication range with 4.3 m/s relative velocity.
(a) direct-adaptation based turbo equalizer (bit error rate =0.00019) (b) direct-adaptation based bidirectional turbo equalizer (bit error rate =0)
Fig. 1 Results of the 1200 m transmission (Image by XI Junyi et al.)
(a) direct-adaptation based turbo equalizer (bit error rate =0.0087) (b) direct-adaptation based bidirectional turbo equalizer (bit error rate =0.0016)
Fig. 2 Results of the 500 m transmission (Image by XI Junyi et al.)
(a) direct-adaptation based turbo equalizer (bit error rate =0.032) (b) direct-adaptation based bidirectional turbo equalizer (bit error rate =0.0090)
Fig. 3 Results of the 800 m transmission (Image by XI Junyi et al.)
For the 1200 m transmission, the performance comparison between the direct-adaptation based turbo equalizer and the direct-adaptation based bidirectional turbo equalizer after 3 turbo iterations is shown in Fig.1.
Since the arrays are relatively static, both of the algorithms can achieve desirable performance. For the direct-adaptation based turbo equalizer, there are only a few blocks having error bits and the bit error rate of the whole picture is 0.00019, while the direct-adaptation based turbo equalizer can achieve error-free detection.
The performance discrepancy of the algorithms still can be seen from the detailed comparisons. The performance comparisons of the 500 m and 800 m transmissions are illustrated in Fig. 2 and Fig.3, respectively. For the 500 m transmission, the 23th block is corrupted by the impulse noise and the direct-adaptation based turbo equalizer suffers from the error propagation effect, thus resulting in an unsatisfactory bit error rate=0.2976.
In the contrast, by using the direct-adaptation based bidirectional turbo equalizer, this block can achieve bit error rate=0.0031 and the bit error rate of the whole picture is reduced to 0.0016 from 0.0087. For the 800 m transmission, several blocks (from the 57th block to the 61th block) are also corrupted by strong interferences, the direct-adaptation based bidirectional turbo equalizer can exploit the bidirectional diversity and correct the most of the error bits caused by the error propagation.
XI Junyi, YAN Shefeng, XU Lijun, and TIAN Jing. Bidirectional Turbo Equalization for Underwater Acoustic Communications. Chinese Journal of Acoustics (Vol.35, No. 4, pp.440-451, 2016).
Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China