Efficient Direct Detection of Twin Single-Sideband Quadrature-Phase Shift Keying Using a Single Detector with Hierarchical Blind-Phase Search

: We propose a novel reception scheme for twin single-sideband (twin-SSB) signals using just a single photodetector (PD), significantly reducing the system complexity and cost. To detect a twin-SSB with power-unbalanced quadrature-phase shift keying (QPSK) sidebands upon detection via a single PD at the receiver side, two QPSKs carried in two sidebands are coherently superposed and detected in a 16-ary quadrature amplitude modulation (16-QAM) format. This technique notably diminishes the linearity and effective number of bits required for the transmitter components in high-speed optical transmission systems. Moreover, a hierarchical blind-phase search (HBPS) algorithm is proposed to compensate for the imperfect phase rotation of QPSK signals during transmission. To demonstrate the effectiveness of our proposed method, we successfully conducted simulations of 112 Gb/s 16-QAM signal transmission over a 10 km standard single-mode fiber (SSMF), achieving bit error ratios (BERs) of 7.84 × 10 − 4 , well below the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10 − 3 . In addition, the synthetic transmission scheme proposed in this paper is compared with the traditional 16-QAM signal transmission scheme, and the results show that the proposed scheme does not introduce a performance cost with the same received optical power (ROP) and transmission distance.


Introduction
Recently, high-speed, short-distance optical interconnections have attracted extensive attention [1][2][3][4][5].Emerging services such as cloud computing and video streaming have put higher requirements on optical transmission systems [6,7].Twin single-sideband (twin-SSB) features high spectral efficiency, robust interference resilience, and energy efficiency.This makes twin-SSB suitable for diverse communication scenarios, particularly those demanding superior signal quality and spectral utilization efficiency.Several twin singlesideband (twin-SSB) schemes have been proposed [8][9][10][11][12][13].However, the receiver's resource demands are significant due to the requirement for two photodetectors (PDs), two optical bandpass filters, two analog-to-digital converters (ADCs), and two signal processing units.Some efforts have been made to simplify the twin-SSB receiver architecture.Zhou et al. [14] and Zhao et al. [15] have proposed a twin-SSB detection scheme through coherent superposition at the receiver side.However, the substandard modulation formats deployed in the scheme are incompatible with conventional optical communication systems.
Here, we propose a simple reception scheme for twin-SSB quadrature-phase shift keying (twin-SSB-QPSK) signals using a single PD through coherent superposition.In addition, a phase compensation algorithm, namely hierarchical blind-phase search (HBPS), is employed to compensate for the phase distortion in the reception.We demonstrate the transmission of 52,72,92,112,132,152,172,192, and 212 Gbps twin-SSB-QPSK vector signals when the transmission length varies from 5 km to 20 km.The simulation results show that the bit error ratio (BER) can reach values lower than the hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10 −3 .The proposed scheme in this paper provides an efficient data transmission idea for the open-network operating system architecture and fronthaul networks that transport radio information between antennas and distributed/central units [16,17].
The remainder of the paper is structured as follows: The second section introduces the principle of the proposed twin-SSB-QPSK reception and the deployed HBPS compensation digital signal processing (DSP) process.The third section presents the experimental verification, followed by a conclusion in the fourth part.

Twin-SSB-QPSK Transmitter
Figure 1 illustrates the transmitter configuration of a twin-SSB-QPSK signal with a Hilbert filter and an in-phase quadrature-phase Mach-Zehnder modulator (IQMZM).Two pseudo-random bit sequence (PRBS) data streams undergo QPSK mapping, root-raised cosine (RRC) filtering, up-conversion, and Hilbert transformation, finally facilitating the generation of two independent SSBs.Note that an unbalanced power ratio of 1:4 is set between the two SSBs.The SSB signal with less power is named QPSK S , and the other SSB signal with higher power is named QPSK L , and they are where S S and S L represent the QPSK signals, while a 1 and a 2 correspond to the real parts of QPSK S and QPSK L , respectively.Similarly, b 1 and b 2 denote the imaginary parts of QPSK S and QPSK L , respectively.Figure 1b illustrates the optical synthesis of the twin-SSB-QPSK signal using an external cavity laser as a laser source and an IQMZM for modulation.A continuous wave is combined with the unbalanced SSBs generated using an IQMZM to form the resultant twin-SSB signal.The optical spectrum of the twin-SSB-QPSK signal in the optical domain is illustrated in Figure 1(iv) and can be represented as follows: where A represents the amplitude of the laser signal, f c corresponds to the frequency associated with the laser wavelength, and S S and S L denote QPSK S and QPSK L , respectively.

Proposed Twin-SSB Reception by Coherent Superposition
As an example, the operation principle of the proposed twin-SSB-QPSK reception scheme is discussed in this section.In the proposed twin-SSB reception scheme, a single PD is employed to implement the coherent combination and simultaneous detection of both SSBs modulated in QPSKs.Upon direct detection with a single PD, two SSBs are coherently superposed at a frequency of f r f .Owing to the unbalanced power between two QPSKs in the SSBs, the coherent superposition results in the generation of a 16-QAM at f r f .The DSP flow at the receiver side is illustrated in Figure 2.After the PD, the detected electrical signal can be represented as follows: The signal is then filtered out to remove the DC component and interference.In the time domain, a linear channel equalizer based on the least mean square is employed for channel equalization.Unlike conventional M-QAM channel equalization, it is imperative to avoid employing the modified constant modulus algorithm in the equalizer and refrain from using it for the initialization of equalizer taps.Otherwise, it is difficult to ensure the convergence of the equalizer in the presence of imperfect phase rotation.After the processing through the DSP shown in Figure 2, a baseband signal is obtained and given by the following equation: where S S * is the conjugation of S S , and n f r f denotes the in-band noise.As depicted in Figure 3, if two SSBs are modulated in QPSK (QPSK S and QPSK L ) and have a power ratio of 1:4 or an amplitude ratio of 1:2, the coherent superposition combines QPSK S and QPSK L through vector addition, finally obtaining a standard 16-QAM constellation.In this superposition process, the constellation point of QPSK S is shifted to the position centered on the constellation of QPSK L .The synthesized 16-QAM is compatible with conventional modulation formats deployed in optical communications.This compatibility allows for the seamless integration of our method into existing communication systems without requiring significant modifications or upgrades.

Phase Compensation Algorithm: HBPS
In our proposed direct detection of twin-SSB-QPSK using a single PD scheme, since the 16-QAM is obtained by coherently superimposing two SSBs in the twin-SSB-QPSK, the imperfect phase rotation in QPSK S and QPSK L may cause symbol deviation from the desired positions, thus resulting in distortions in the composite high-order 16-QAM constellation.
To address imperfect phase rotation, we propose the HBPS algorithm, which is based on the conventional blind-phase search (BPS) algorithm.The HBPS algorithm corrects the phase rotation of the synthesized 16-QAM signal in two stages, as shown in Figure 4a,c.The schematic of this process is illustrated in Figure 4.In the first stage, the constellation points in each quadrant of the received 16-QAM signal are centralized.The points in each quadrant are considered a single converging point.Consequently, the 16-QAM signal can be treated similarly to a QPSK signal, as illustrated in Figure 4b, with points labeled in four different colors.As shown in Figure 5a, the constellation points indicated by the red dashed lines are the center points in each quadrant of the standard 16-QAM signal.The standard 16-QAM constellation is then rotated N times with N phases ( φ 1 , • • • , φ N ).After each rotation, the minimum Euclidean distance between the center point in each quadrant of the received 16-QAM signal (solid red circles in Figure 5a) and the center point in each quadrant of the standard 16-QAM signal is calculated separately.The minimum Euclidean distance is given by the following equation: where S standard is the standard QPSK constellation diagram, and r k is the rotational phase.
The phase rotation corresponding to the minimum Euclidean distance value could be considered the overall offset (φ L ) for the "large" QPSK.The corrected constellation diagram after the first stage is shown in Figure 5b.It can be seen that the phase at the center of each quadrant has been corrected properly.
In the second stage, phase corrections are applied to each "small" QPSK constellation in each quadrant.The implementation process is similar to that of the first stage.The minimum Euclidean distance is calculated between the four small constellation points in each quadrant (solid black circles in Figure 5b) of the recovered 16-QAM and those points of the standard 16-QAM signal in the corresponding quadrant (dashed gray circles in Figure 5b).The corrected constellation diagram after the second stage is shown in Figure 5c.It can be seen that the phase at the center of each quadrant has been recovered.After that, the phase compensation of the entire received signal is realized.We aimed to better quantitatively illustrate the computational complexity of a BPS and an HBPS.Compared with the conventional BPS, the proposed HBPS algorithm takes advantage of the Manhattan distance and eliminates the actual multiplication operations.The numbers of operations required by the two methods when considering N test phase angles in M-QAM notation are as follows: 2N real multiplications and 3N real additions are required for a conventional BPS, and [4(log 4 M − 1) + 1] × N operations are required for the HBPS algorithm.

Experimental Verification
Figure 6 illustrates the experimental setup for the proposed reception scheme of twin-SSB-QPSK using a single PD.The detailed DSP procedures for the transmitter and receiver are provided in Section 2. At the transmitter side, a laser source operating at a wavelength of 1552.52 nm is generated from an ECL.The IQMZM is biased at the null point, suppressing the optical carrier, and finally synthesizing a twin-SSB-QPSK signal.The inserts in Figure 6 show the spectra of the two SSBs (LSB and USB) and twin-SSB-QPSK at a symbol rate of 28GBaud.Incorporating an optical carrier at the transmitter side enables the receiver to directly detect the optical signal using a single photodetector (PD).
. After the PD at the receiver side, a 16-QAM signal is synthesized through coherent superposition.Its spectrum is shown in Figure 6d.DSP processing, including the proposed HBPS algorithm, is deployed for phase distortion compensation and constellation reconstruction.Figure 7 illustrates the received constellation diagrams of a 112Gb/s 16-QAM signal at an ROP of −12 dBm after the 10 km fiber transmission.These diagrams show the experimentally measured constellation diagrams when around 0 • and 20 • imperfect phase rotations are intentionally introduced in the LSB and USB, respectively.The constellation after linear equalization is depicted in Figure 7a. Figure 7b and Figure 7c show the equalized constellation diagrams after the processing using the conventional BPS and our proposed HBPS, respectively.It is clear that compared with the BPS, the measured Q factor of the 16-QAM is improved by 3.36 dB, and the corresponding BER is decreased from 1.54 × 10 −2 to 7.33 × 10 −4 successfully.Figure 9 shows the measured BER at an ROP of −13 dBm versus different bit rates from 52 Gb/s to 212 Gb/s when the SSMF transmission length varies from 5 km to 20 km.As expected, the measured BERs increase with the bit rate but can still reach below the HD-FEC threshold of 3.8 × 10 −3 for all the different transmission distances.To further verify the reliability of the proposed 16-QAM synthesis scheme, we compare the Q factors of our synthesized 16-QAM signal against those of the 16-QAM signal generated by a conventional 16-QAM transmitter at different ROPs.The comparison is made under identical conditions of transmission distance and spectral efficiency.Figure 10 presents the measured Q factors and electrical spectra of the signals produced by these two approaches.The simulation results demonstrate that both approaches yield comparable performance across various ROPs.

Conclusions
In this paper, we propose a simple and effective reception scheme for twin-SSB signals using a single PD.The simultaneous detection of two SSBs is implemented by synthesizing 16-QAM signals through the coherent superposition of two SSBs modulated in QPSKs.We have experimentally demonstrated the synthesis of a 112 Gb/s 16-QAM signal by combining two independent 56 Gb/s QPSK SSBs.Our method presents a cost-effective approach for detecting twin-SSB QPSKs while ensuring compatibility with standard modulation formats.In the future, the LSB and RSB signals could also be extended to signals with 4-QAM, 16-QAM, or higher-order modulation, and researchers could also try to extend the two sideband signals to four independent SSB signals to adapt to the needs of higherspeed communication.Additionally, phase distortion algorithm (HBPS) was implemented to correct imperfect constellation phase rotation at the receiver.The proposed HBPS algorithm could also be used in other communication systems to improve communication reliability.

Figure 1 .
Figure 1.Schematic of the twin-SSB-QPSK transmitter with (a) DSP at the transmitter side; (b) transmitter setup; electrical spectra of (i) lower sideband, QPSK S , and (ii) upper sideband, QPSK L ; (iii) the electric spectrum of twin-SSB-QPSK; and (iv) the optical spectrum of twin-SSB-SSB.

Figure 2 .
Figure 2. Receiver side DSP: (i) the twin-SSB-QPSK signal spectrum before the PD and (ii) the received signal spectrum after the PD and filtering.

Figure 3 .
Figure 3.A synthesis diagram for the 16-QAM signal.

Figure 4 .
Figure 4. Architecture of the proposed HBPS algorithm for correcting the possible imperfect phase rotation in the synthesized 16-QAM: (a) illustration of the 1st stage processing, (b) experiment data processing in the 1st stage, and (b) illustration of the 2nd stage processing.abs: absolute value; slc: selector.

Figure 5 .
Figure 5. Constellation diagram for compensating phase rotation using the HBPS algorithm.(a) Constellation diagram before HBPS algorithm.(b) Constellation diagram after the first HBPS stage.(c) Constellation diagram after the second HBPS stage.

Figure 6 .
Figure 6.Experimental setup.(a) The LSB signal spectrum.(b) The USB signal spectrum.(c) The twin−SSB−QPSK signal spectrum.(d) The received signal spectrum after the PD and filter.

Figure 7 .
Figure 7.The measured constellations of the corresponding signals after the PD.(a) The constellation of the received and linearly equalized signals.(b) The constellation after the processing using the conventional BPS: Q = 14.54 dB and BER = 1.54 × 10 −2 .(c) The constellation after the processing using the proposed HBPS: Q = 17.90 dB and BER = 7.33 × 10 −4 .

Figure 8
Figure 8 shows the measured BER versus the ROP of 112 Gb/s 16-QAM when the transmission length varies from 5 km to 20 km.The BERs of the 16-QAM signal can still reach values below the HD-FEC threshold of 3.8 × 10 −3 for all the different transmission distances.At the HD-FEC threshold of 3.8 × 10 −3 , compared with the result after the 5 km transmission distance, a power penalty of about 3 dB is observed after transmission over 20 km.The BER performance degradation is mainly attributed to fiber dispersion.

Figure 8 .
Figure 8. BER versus ROP when the bit rate is 112Gb/s.

Figure 9 .
Figure 9. BER versus bit rate when the ROP is −13 dBm.

Figure 10 .
Figure 10.Q factor comparison of the synthesized 16-QAM using the proposed and conventional (Conv.)approaches under different ROPs.Sub-figures (a) and (b) show the electrical spectra of the synthesized 16-QAM after the PD reception using the proposed and conventional approaches, respectively.