The performance of faster-than-Nyquist intensity modulation and direct detection (IM/DD) systems can be severely degraded by the inter-symbol interference (ISI) due to the component bandwidth limitation and the faster-than-Nyquist filtering. In addition, nonlinearities caused mainly by optical modulation and square-law detection can further deteriorate signal quality. Here, we propose to incorporate transmitter-side Tomlinson-Harashima precoding to mitigate the ISI and a Volterra nonlinear equalizer (VNLE) to mitigate the nonlinear distortions for PAM4 faster-than-Nyquist systems. We experimentally demonstrate a single wavelength 145 Gb/s PAM4 IM/DD transmission with bandwidth limited commercial components and sub-Nyquist sampling at 70 GSa/s. The optimal VNLE filter length is also investigated to balance the implementation complexity and system performance. In addition, compared with the scheme using transmitter-side duobinary precoding (DuoBP), receiver-side VNLE and maximum likelihood sequence estimation (MLSE), both performance improvement and implementation complexity reduction are achieved.

The performance of high-speed intensity modulation direct detection (IM-DD) transmissions is severely degraded by the linear inter-symbol interference (ISI), due to both bandwidth-constrained optoelectrical components and the chromatic dispersion (CD). Meanwhile, nonlinear ISI due to intensity modulation and square-law detection can further deteriorate the IM-DD system performance significantly. Here, we first propose three metrics to quantify those impairments in IM-DD transmissions. Then, we compare both the BER performance and computational complexity of different DSP schemes to enable short-reach high-speed IM-DD transmissions with severe bandwidth constraint, using a C-band PAM-4 experimental test-bed with an end-to-end 10-dB bandwidth of 17 GHz. Those DSP schemes include receiver-side feedforward equalization (FFE), receiver-side Volterra filter equalization (VFE), transmitter-side Tomlinson-Harashima precoding (THP) together with receiver-side FFE, transmitter-side THP together with receiver-side VFE, channel-shortening filter (CSF) together with maximum likelihood sequence estimation implemented with linear branch metrics (MLSE-LI-BM), and CSF together with MLSE implemented with nonlinear branch metrics (MLSE-NL-BM). Our experimental results indicate that, only the combination of CSF and MLSE-NL-BM enables a 112 Gbit/s transmission over 5 km fiber at the KP4-FEC threshold, but with an increased computational complexity.

The key idea of this work is to treat the symbol- pattern-dependent inter-symbol-interference (ISI) that is avoided in conventional single-symbol modulation systems as useful symbol correlation, incorporate the feature of the symbol correlation into both adaptive equalization and sequence detection and thus, upgrade the system to a multi-symbol-oriented pattern-dependent equalization and detection regime. Specifically, we propose an adaptive equalization scheme sharing a pattern-dependent look- up-table with a maximum likelihood sequence estimation process to facilitate tolerance and mitigation on symbol-pattern-dependent ISI. The proposed scheme can be applied to various transmission systems with linear or nonlinear pattern-dependent ISI, such as bandwidth constrained systems with severe linear ISI, or high-power long-distance transmission systems with fiber nonlinearity induced self-phase modulation. In exemplary coherent transmission systems with digital narrow filtering before digital to analog conversion at transmitter, we experimentally demonstrate effective demodulation and detection of a polarization-division-multiplexing quaternary- phase-shift-keying signal with a constrained 3-dB transmitter bandwidth down to 1/8 of the signal baud rate.

We recently reported for the first time 200 Gbit/s/ $\lambda$ net rate data transmission with a single silicon photonic modula- tor in an intensity modulation direct detection link. Our demon- stration relied on an in-house designed, O-band segmented- electrode MZM. In this paper, we detail the optimization of the modulator driving scheme, bandwidth/efficiency trade-off and modulation format enabling this result. We use two single-ended RF signals, each having 2.3-Vpp amplitude only, to drive two 1.5- mm modulator segments and transmit data at 80 Gbaud PAM-8 (240 Gbit/s) across 2 km under the 20% soft-decision forward error correction BER threshold of 2E-02. We further decrease the BER using maximum likelihood sequence detection (MLSD), and discuss the related implications. Additionally, we present the system margins regarding modulator drive voltage, received optical power and equalizer taps. At 240 Gbit/s line rate, the modulator energy consumption is only 73 fJ/bit at the SD-FEC threshold. We finally discuss practical implementation considerations for our system.

For the digital subcarriermultiplexing (DSM) transmission, it is compulsory to realize the frequency offset estimation (FOE) and compensation (FOC) before the subcarrier de-multiplexing and the chromatic dispersion (CD) compensation (CDC). Here, we demonstrate a blind FOE method for the spectral-efficient DSM signals with a sharper root raised cosine (RRC) spectral shaping, with the capabilities of the transparent modulation format operation, a wide FOE range, and a high FOE accuracy. By reusing the spectral information for the CDC, the proposed FOE method is hardware efficient. Moreover, the proposed FOE method is numerically identified robust to transmission impairments, including the amplified spontaneous emission (ASE) noise, the optical filtering effect, and the accumulated CD, with an estimation error of less than 35 MHz under a FFT size of 2048. The correct function of the proposed FOE method is finally experimentally verified for 25 Gbaud 16QAM DSM signals under scenarios of both back-to-back (B2B) and standard single-mode fiber (SSMF) transmissions.

Short-time Fourier transform (STFT) is a vital tool to observe spectral dynamics of non-stationary signals. Conventional STFT based on digital signal processing (DSP) usually suffers from a limited acquisition frame rate within 10 ⁶ Fourier transforms per second (FTs/s). Thus, it is unable to fully intercept transient information in time and frequency shorter than a few microseconds. Further extending the acquisition frame rate can be achieved by employing the dispersion-based all-optical spectral analysis approach, while the optical dispersion usually introduces a large latency. Here, we experimentally report a low-latency STFT of microwave photonic processing, where a passive fiber loop is used to provide high value equivalent dispersion. Consequently, the latency of the STFT processing can be greatly reduced. The spectrograms of microwave signals, including instantaneous information in both time and frequency, are acquired in a real-time manner, with an acquisition frame rate of about 5×10 ⁸ FTs/s and a processing latency of less than 0.2 μs. High temporal resolution within tens of nanosecond range can be achieved, allowing us to capture 30-ns duration frequency transients in real time with a instantaneous bandwidth of about 530 MHz. Our proposed STFT processing scheme is promising for real-time and high-speed spectral dynamic analysis for non-stational signals.