On the Capacity of Faster Than Nyquist Signaling

Abstract

This letter considers the capacity computations of faster-than-Nyquist (FTN) signaling. It calculates the theoretical capacity of FTN signaling which is obtained by a correlated input. The capacity-achieving power spectral density (PSD) is derived and its superiority over the independent input is shown. The practical issue imposed by the capacity-achieving PSD, i.e., outof-band (OOB) emission, is shown. To solve this issue, an upperbound is introduced for the input PSD to limit the OOB emission. The new optimization problem is solved and the constrained PSD is obtained. The introduced PSD captures the trade-off between the obtained capacity and the OOB emission.

The Evolution of Faster-Than-Nyquist Signaling

“…The capacity of FTN signaling was derived for several scenarios, revealing the achievable gain of FTN signaling over its Nyquist signaling counterpart. Here, we consider three FTN signaling scenarios, namely, unprecoded FTN signaling [5, 6, 8-11, 135, 136], FTN signaling relying on FD filtering [12,131,143,144], and precoded FTN signaling [13][14][15]17]. The related literature is summarized in Tables 8, 9, and 10, respectively.…”

“…Ganji et al [12] Presented the design guideline of an FD filter to increase the information rate of FTN signaling both for the AWGN and frequency-selective fading scenarios, based on the Lagrange multiplier method.…”

“…To further increase the information rate, an FD filter was invoked in unprecoded FTN signaling [12,143,144].…”

“…Most of the studies of FTN signaling can be classified into four categories: information-theoretic analysis [5][6][7][8][9][10][11][12][13][14][15][16][17][18], reduced-complexity receiver , channel estimation (CE) issues [35,39,[41][42][43], and transmit preprocessing/precoding [13-15, 18, 21, 44-51]. In the informationtheoretic studies, the achievable performance gains of FTN signaling over Nyquist signaling were investigated in terms of several metrics, such as the minimum Euclidean distance (MED), the mutual information, the capacity and the bit error ratio (BER).…”

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

“…1/ (1 + β) ≤ τ < 1, the excess bandwidth is exploited by FTN. However, as τ < 1/ (1 + β), further compression provides no extra gain for the Gaussian FTN [40]. The traditional FTN significantly benefits from the excess bandwidth [39], i.e., compression gain.…”