# DLI-Based DP-QPSK Reception Scheme for Short-Range Optical Communication
## 1 Introduction  
Digital coherent optical transmission is currently the mainstream scheme used for medium-to-long-distance optical communication, where it is optimal from the standpoint of spectral efficiency as it allows for the encoding of information in both quadrants and polarization of the electric field [1; 2]. However, the cost of a coherent receiver, which requires highly customized hardware and complex compensation algorithms, is unacceptably high for short-range links, such as intra-datacenter interconnections [3; 4; 5]. In recent years, the requirement for alternatives to digital coherent transmission in short-reach applications has spawned a series of studies on direct detection (DD) systems due to their low cost, high power efficiency, and easy implementation [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. Some schemes have been proposed in the published literature. The earliest is the on-off keying (OOK) scheme for low-speed communications [6], which is also the simplest but has high bandwidth and fiber dispersion matching requirements. To improve the spectral efficiency, high-order modulation formats are adopted. The most common is the pulse-amplitude modulation (PAM) scheme, which encodes information at multiple amplitude levels, such as PAM-4 [7] and PAM-8 [8]. However, the reception sensitivity will be significantly reduced as the level increases. Two other popular approaches are carrier-less amplitude and phase (CAP) modulation and discrete multi-tone (DMT) modulation [9; 10; 11]. CAP is relatively simple to implement in real time, while DMT offers lower computational complexity. However, both of them have a low tolerance for linear propagation effects. To this end, a self-coherent heterodyne scheme was proposedby [PERSON] and [PERSON] [12; 13], which requires transmitting a frequency offset local oscillator (LO), together with the signal, thereby allowing for a complete reconstruction of the complex-valued field. More recently, some other schemes that are capable of full-field reconstruction, including Stokes vector direct detection (SV-DD) [14; 15], single-sideband modulation/direct-detection (SSB-DD) [16; 17], and Kramers-Kronig (KK) receivers [18; 19], have been proposed. It is noteworthy that these schemes all require an auxiliary signal from the transmitter to enable full-field reconstruction at the receiver. In this study, a dual-polarization quadrature phase-shift keying modulation/direct detection (DP-QPSK-DD) scheme for short-range optical communications was investigated. Compared with traditional binary modulation formats (OOK, BPSK (Binary Phase Shift Keying), etc. ), DP-QPSK is modulated in multiple dimensions of polarization, phase, and amplitude at the same time, with greater degrees of freedom and lower complexity in each dimension, which gives it the advantage of a narrower spectral width, higher spectral efficiency, and higher tolerance to various fiber-based transmission impairments [20]. Hence, DP-QPSK is one of the mainstream modulation formats in the current 100 Gbps optical communication systems and is one of the solutions used for 400 Gbps optical transmission [21; 22]. The DP-DQPSK-DD scheme is implemented based on a delay-line interferometer (DLI), which has simple and low-cost hardware implementation and is an ideal alternative to digital coherent transmission for short-range, non-cooperative communication. We propose an algorithm for recovering the raw data from the transmitting end. Based on this, we also studied measures used to improve the performance of the DP-QPSK reception and it was found that appropriately decreasing the free spectral range (FSR) of the DLI could increase the tolerance to transmission impairments to a certain extent. The remainder of this paper is organized as follows. Section 2 briefly introduces the structure and basic principle of the DLI-based DP-QPSK-DD system. The data recovery algorithm is proposed in Section 3. In Section 4, the impact of FSR adjustment is analyzed theoretically.