Most of the existing spherical array modal beamformers are implemented in the frequency domain, where a block of snapshots is required to perform the discrete Fourier transform. In this paper, an approach to real-valued time-domain implementation of the modal beamformer for broadband spherical microphone arrays is presented. The microphone array data are converted to the spherical harmonics domain by using the discrete spherical Fourier transform, and then steered to the look direction followed by the pattern generation unit implemented using the filter-and-sum structure. We derive the expression for the array response, the beamformer output power against both isotropic noise and spatially white noise, and the mainlobe spatial response variation in terms of the finite impulse response (FIR) filters' tap weights. A multiple-constraint problem is then formulated to find the filters' tap weights with the aim of providing a suitable tradeoff among multiple conflicting performance measures such as directivity index, robustness, sidelobe level, and mainlobe response variation. Simulation and experimental results show good performance of the proposed time-domain broadband modal beamforming approach.

An approach to optimal design of circular harmonics based modal beamformers for circular arrays is presented. Theoretical analysis shows the equivalence between the element-space and circular-harmonics-domain beamformers. By deriving the expression for the signal and noise covariance matrices, array manifold, and the array response in terms of the circular-harmonics-domain beamforming weights, the weights design problem is formulated as one of minimum variance distortionless response beamforming in the circular harmonics domain. It is found that the well-known phase-mode beamformer for circular arrays can be viewed as an ideal minimum variance distortionless response beamformer against the planarly isotropic noise in the circular harmonics domain. This interesting result is useful for analyzing and evaluating the performance of the phase-mode circular arrays. In this circular-harmonics-domain beamformer, additional constraints can be imposed to improve its robustness and control the sidelobes, which is important in practical applications. The developed approach can include both the delay-and-sum and phase-mode beamformers as special cases, which leads to very flexible designs. Simulation and experimental results show excellent performance of the proposed beamforming approach.

The direct-adaptation based turbo equalizer (DA-TEQ) has been widely studied for underwater acoustic communications due to its decent performance and simple implementation. However, there are still some inherent problems that limit its practical application, such as slow convergence rate and error propagation effect. In this paper, a direct-adaptation based bidirectional turbo equalizer (DA-BTEQ) is proposed for underwater acoustic communications. The proposed scheme incorporates a forward DA-TEQ with a backward DA-TEQ to exploit bidirectional diversity gain and combat error propagation, thereby enabling faster convergence rate and better symbol detection performance. A general symbol combining scheme, which is suitable for turbo equalizers with high-order modulations, is derived by using the minimum mean square error criterion. The proposed scheme has been tested by the undersea trial data collected in an experiment conducted at the coast of Jiaozhou Bay in March 2017. The results demonstrate that the DA-BTEQ is effective against error propagation and clearly outperforms the traditional single-direction DA-TEQ for both single-input multiple-output and single-input single-output systems.

Hybrid turbo equalization is a novel and effective approach for communication systems as it can benefit from two turbo equalizers at different stages of iterative process. Despite its notable potential for performance improvement, hybrid turbo equalization has rarely been validated experimentally and its feasibility in underwater acoustic communications is presently not well understood. In this paper, a hybrid frequency-time domain turbo equalizer (FTD-TEQ) is proposed for underwater acoustic communications with comprehensive experimental investigations. In contrast to the traditional direct-adaptation-based turbo equalizers (DA-TEQs), which use one type of turbo equalizer for all iterations and may suffer from slow-convergence problem, the FTD-TEQ employs the frequency-domain channel-estimation-based turbo equalizer in the first iteration to provide a good initialization and utilizes the time-domain DA-TEQ in the subsequent iterations to maintain low-complexity implementation, aiming at benefiting from both turbo equalizers without incurring high computational burden. In the meantime, the high-quality soft-decision symbols and the relatively optimal initialization of the filter coefficients derived from the first iteration can be delivered to the next iteration, so as to improve symbol detection performance in the bottleneck region and achieve faster convergence rate. The effectiveness of this hybrid equalization mechanism has been well interpreted by numerical simulations, and also has been verified through an undersea communication experiment with high-order 8-phase shift keying modulation and 16-quadrature amplitude modulation. The results demonstrate that the FTD-TEQ not only shows more excellent performance, but also has lower computational complexity than the traditional DA-TEQ for the experimental data configuration.

Modal beamformer for circular arrays, which is based on a circular harmonics decomposition of the sound field, is flexible for use because it is decoupled from the sensor positions. A time-domain implementation of broadband modal beamformer for circular arrays is presented in this paper. This beamforming structure consists of a real-valued circular harmonics transform and steering unit, followed by a pattern generation unit implemented by a set of real-valued finite impulse response (FIR) filters. The beam pattern is controlled through the FIR filters' tap weights, whose design is decoupled from beam pattern steering and can be formulated as a constrained optimization problem that can be solved efficiently. Multiple array performance measures such as array gain, sensitivity, mainlobe, and sidelobes can be taken into consideration in beamformer design, which is very important in practical applications. Simulation and experimental results are presented to illustrate the effectiveness of the proposed time-domain broadband modal beamforming approach. Performance comparisons between the proposed and the classical methods in weight coefficients, beam patterns, and quality of audio output are also provided. The results show that the proposed approach possesses high robustness and can achieve good frequency invariance.