Iterative-Detection-Aided Tomlinson-Harashima Precoding for Faster-Than-Nyquist Signaling

Abstract

Faster-than-Nyquist(FTN) is a promising technique due to higher spectral efficiency, but at a cost of introducing the inter-symbol interference (ISI) which usually requires the computationally demanding detection algorithms. In order to reduce the detection complexity at the receiver, in this paper, a novel Tomlinson-Harashima precoding (THP) scheme is proposed for FTN system. In the conventional THP (CTHP) scheme, the ISI introduced by time-packing can only be diminished from several preceding information symbols, which results in large residual ISI and an unattractive bit-error-rate (BER) performance. Moreover, due to the suboptimal receiver-a simple modulo operation which ignores the correlation between received symbols, CTHP faces obvious capacity loss and is ineffective to execute interference cancellation for FTNS. In this paper, residual ISI of FTNS in CTHP is formulated in detail and modeled mathematically. Further more, an improved THP method with an optimized receiver based on the soft interference cancelation (SIC) algorithm and iterative turbo process is proposed to combat residual ISI for FTNS. Computational complexity analysis and numerical simulation results show that the proposed scheme not only has inexpensive computational cost but also greatly outperforms CTHP and other cited schemes. Moreover, for moderate time-packing, it can approach the ISI-free BER performance boundary and is also competitive to the MAP equalization technique. INDEX TERMS Faster-than-Nyquist (FTN), precoding, inter-symbol interference (ISI), Tomlinson-Harashima precoding (THP), iterative detection. AIJUN LIU received the B.S. degree in microwave communications, the M.S. and Ph.D. degrees in communications engineering and information systems from the College of Communications Engineering, Nanjing, China,

The Evolution of Faster-Than-Nyquist Signaling

“…In contrast to the linear-precoding-aided FTN signaling of [13-15, 44, 45, 134], non-linear Tomlinson-Harashima precoding (THP) was exploited for FTN signaling in [47,48,133,[137][138][139][140][141]. The first THP-aided FTN signaling scheme was proposed in [47], based on the spectral factorization formulated as G(z) = D(z)D * (1/z * ), where G(z) represents the z-transform of the τ T 0 -spaced samples of g(t) [47].…”

“…in [47,130]. Moreover, it was revealed in [48] that significant residual ISI is encountered in THP-FTN signaling, albeit its detrimental effects may be mitigated by SIC at the receiver. In [133], THP-based FTN signaling was proposed for a singlemode fiber optical communication channel.…”

Joint Precoding and Pre-Equalization for Faster-Than-Nyquist Transmission Over Multipath Fading Channels

“…the specific precoding and the LPE-FTNS as well. Throughout this paper, ϕ (t) with Fourier transform ψ (f ) = F {ϕ (t)}, is fixed as a T -orthogonal root raised cosine (RRC) pulse with roll-off factor β and time support interval [0, 40T ], similar to prior FTN research [8]- [15], [19]- [22]. The signal s (t) traverses an L c -tap frequency-selective Rayleigh fading channel, which is assumed to be invariant within one block but varies from one block to another.…”

“…As a result, the FTN-ISI density in the received samples is reduced, and the post-equalization eliminates any residual FTN-ISI. The third category achieves better complexity-performance tradeoffs than the first two [20], [22], [24]. The papers cited above mainly assume additive white Gaussian noise (AWGN) channels, which can be impractical in real environments.…”

Multicarrier Faster-Than-Nyquist Based on Efficient Implementation and Probabilistic Shaping

“…DC leads to serious ISI and ICI. To eliminate ISI and ICI, the traditional MFTN with the DC usually requires the global iteration and complex equalization algorithm such as the BCJR [7], [15], [31], M-BCJR [8], CS-BCJR [11] [29], SIC [32], GASDRSE [9], MMSE equalization [12], GMP [33], FDE [34], deep learning (DL) technology [13], symbol-bysymbol receiver with SIC [16]- [22]. The LPE converts FTN transmission into orthogonal signaling.…”