Without redundant channel estimations, direct-adaptation-based turbo equalization (DA-TEQ) commonly implements suboptimal performance by disposing of adaptive filtering and gradually converges equalizer taps. Recently, a soft DA-TEQ (SDA-TEQ) has been proposed, and the significant innovation is that the data source of the feedback filter (FBF) is the a priori soft decisions of the MAP decoder instead of hard-decision symbols, which accelerates the convergence rate of iterations and eliminates the error propagation of hard detections [15; 16]. In recent research works, the SISO equalizer adaptive algorithms of UWA TEQs concentrated on the least mean square (LMS) category. In [15], a DA-TEQ with an improved proportional normalized LMS (IPNLMS) algorithm used in a multi-input multi-output (MIMO) system shows BER and MMSE performance improvements compared to NLMS. In [27], the researchers developed sparsity-aware IPNLMS adapted in DA-TEQ for a sparse UWA channel. In [16], the fast self-optimized LMS (FOLMS) algorithm embedded in Soft-DA-TEQ is proposed, and experiments show a faster convergence rate than Hard DA-TEQ. Recursive least-squares (RLS) adaptive algorithms have exhibited tremendously faster convergence in situations of longer channel taps in comparison with LMS category algorithms [28; 29; 30]. In [31], a CE-TEQ scheme for MIMO system with a low-complexity homotopy RLS algorithm is proposed, and lake trial results demonstrate the superiority of the RLS-type algorithm could achieve promising detection performance, while the IPNLMS-based scheme cannot obtain a satisfactory manifestation. Recently, the proportional RLS (PRLS) algorithm [32] has been proposed and exhibits superior performance over conventional RLS for both UWA channel estimation and equalization problems [28; 33]. In this paper, motivated by the work in [15; 16; 34], we propose a bidirectional soft direct-adaptation-based turbo equalization for SISO UWA communication systems. In comparison to existing works, the improvements of the proposed scheme are summarized as follows. First, the proposed scheme, namely virtual space-time diversity turbo equalization (VSTD-TEQ), integrates a fractionally spaced soft interference cancellation equalizer (FS-SE) and a time-reversed FS-SE. Attributed to the low correlation between the soft outputs of the bidirectional equalizer, the virtual time diversity gain would alleviate error propagation. Furthermore, a fractionally spaced structure can exploit the virtual space diversity gain in SISO systems and mitigate wrong decision symbols effectively. Second, an interpolator is inserted into VSTD-TEQ, which accomplishes the Doppler effect dislodgement together with a DPLL, especially in the circumstance that evolves a higher residual Doppler frequency shift due to low-resolution Doppler search gap or dynamic Doppler phenomenon. The main function of the interpolator is to mitigate the accumulated sampling timing error of the baseband caused by Doppler motion in a harsh ISI channel. Third, the PRLS algorithm is modified using mixed-norm regularization to satisfy the cluster sparse UWA channel. For the sake of clarity, all of the abbreviations used in this paper are summarized in the Abbreviation section.