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

Abstract

Faster-than-Nyquist signaling (FTNS) has emerged as a promising technique to increase communication capacity in bandwidth-limited channels. However, the presence of FTNinduced inter-symbol interference (FTN-ISI) in the received observations, is detrimental to channel estimation (CE) and data detection in terms of computational complexity and performance. This paper copes with these problems by incorporating linear pre-equalization (LPE) and composite precoding formed by linear spectral precoding and Tomlinson-Harashima precoding (THP), into the FTNS. Specifically, LPE completely pre-equalizes the FTN-ISI, while spectral precoding resolves the LPE-caused signal spectral broadening by introducing proper artificial ISI, which is pre-equalized by THP. Channel-induced ISI, as the only ISI component in the observations, is estimated and equalized using the classical frequency-domain low-complexity schemes. We show that there are four advantages of the LPE-aided CE over the CE designed for the FTN transmissions without FTN-ISI preequalization, namely lower pilot overhead, simpler yet optimal pilot sequence design, lower mean-squared error of CE, and more robust against the FTN-ISI. Simulation results show that our scheme improves the performance of CE and detection, compared to existing FTN frequency-domain CE and equalization schemes.

Performance Evaluation of MIMO-FTN Signaling Under Multipath Fading Channels

“…Since it has been proven that the RRC pulse-shaping filter induces (1 + α) times greater system bandwidth than that of the normal bandlimited communication systems [26], such the limitation of bandwidth should be included for fair and more practical comparisons. Different from some existing works that consider a given Nyquist bandwidth or even didn't highlight the bandwidth limit to transmit data [12], [13], [16], [17], [19]- [21], [28], [29], the total utilized bandwidth is fixed in our simulations. Precisely, the concept of the power spectrum can be illustrated in Fig.…”

“…Some related simulation parameters are summarized in Table 2. The constellation pattern for 16APSK is [4,12], of which 4 inner points are concentric with radius r 0 = 0.5, and inner/outer radius ratio = 2.57 [30]. Furthermore, we acquire the channel coefficients [h] l of the L-tap fading channel with the distribution CN (0, 1/L) and assume the channel estimation is ideal.…”

“…In [23], the Mazo limit on a MIMO channel was investigated. MIMO TX modulation scheme multipath colored noise detection method This paper ✓ SC, OFDM (MFTN) ✓ ✓ FDE [9] ✓(STMIM) coded-SC ✓ ✓ Gaussian MP [10] ✓ SC -✓ -(capacity analysis) [11] SC ✓ FDE/ML [12] SC ✓ ✓ FDE [13] ✓ SC -✓ -(capacity analysis) [18] ✓ SC ✓ iterative FDE [19] ✓ SC ✓ ✓ FDE [20] SC decision feedback [16] MFTN ✓ ✓ FDE [17] ✓(IM) MFTN ✓ ✓ VAMP [21] NOMA ✓ ✓ ML [22] ✓ NOFDM ML The authors in [10], [13] derived the capacity expressions and demonstrated the superiority of MIMO-FTN-SC systems.…”

“…Recently, numerous equalization and detection methods have been developed to eliminate the effects of ISI. We can briefly divide them into two main categories: (a) iterative algorithms [9], [11], [17], [18], [20]- [22], [24] and (b) one-tap equalizers [11], [12], [16], [19], [25]. For iterative methods, diversified algorithms are designed to decode the received signals.…”

“…On the other hand, one-tap equalizers based on classic zero-forcing (ZF) and minimum mean square error (MMSE) criteria are most commonly used. The equalizers in [11], [12] were developed based on the additive white Gaussian noise (AWGN) environment. However, especially for MMSE equalizers, which involves calculating the noise covariance matrix, the effect imposed by the colored noise from ISI should be introduced.…”