To meet the rapid growth of mobile data caused by prosperous mobile applications, the fifth generation (5G) mobile communication network will offer 1000 times data traffic compared to the current fourth generation (4G) system ^[1,2]. The radio over fiber (RoF) technique is considered as a promising candidate for the 5G system because it directly transports radio frequency (RF) signals between the baseband units (BBUs) and remote radio heads (RRHs). It allows for centralization of signal processing and network management, resulting in simple remote antenna unit (RAU) design and low-cost implementation ^[3–6]. However, for massive access in an RoF-based mobile fronthaul, a multiple-channel, broadband, high-linearity, and low-noise analog optical transceiver is highly desired ^[7]. In addition to the modulation bandwidth, linearity, noise figure, and spurious-free dynamic range (SFDR) are the primary factors for analog application. The design and encapsulation for an analog optical transceiver is a very challenging process, and many technical issues should be considered, such as signal and power integrity, optical coupling, and heat dissipation design. Many works have presented the design of a transmitter optical subassembly (TOSA) and a receiver optical subassembly (ROSA) ^[8–12]. However, almost all the above researches are focusing on a single channel, external modulation, and digital optical transceiver rather than the integrated multichannel, directly modulated, and analog optical transceiver. In our previous work ^[13], an integrated four-channel directly modulated optical transceiver has been designed and fabricated for the first time. However, the optical coupling loss is 7 dB for the TOSA, and the optical coupling efficiency needs to be improved. Moreover, the noise floor of the designed four-channel optical module is about −140dBm/Hz ^[13,14], which is much higher than that of the single-channel optical module (about −160dBm/Hz) ^[15]. The large additive noise would degrade the performance of the received signal. Therefore, new techniques that can reduce the noise influence for signal demodulation are required.

On the other hand, to further improve the signal performance and capacity, the multi-input multioutput (MIMO) technique is adopted in multiple antenna subsystems ^[2,16]. This technique could both increase data capacity through spatial multiplexing and improve system reliability through antenna diversity without occupying additional spectrum. The simplest zero-forcing (ZF) MIMO equalizer algorithm is widely used in the MIMO-RoF system ^[5,6]. However, the performance of the ZF algorithm is easily deteriorated due to the noise amplification problem. The well-known optimal detection algorithm is the maximum-likelihood sequence estimation (MLSE). It searches exhaustively all possible transmitted symbols in the signal space and then chooses the symbols that have minimum Euclidean distance with the received signal ^[17]. However, the complexity of this algorithm grows exponentially with the problem dimension, and the MLSE is proven to be nondeterministic polynomial-time hard (NP hard) ^[18]. Obviously, to benefit from joint detection in MIMO systems, more efficient suboptimal MIMO detection algorithms are highly desired. In this case, lattice theories are used to develop powerful algorithms for MIMO detection ^[19]. Various lattice reduction (LR) algorithms have been proposed for MIMO detection ^[20–22], and the most famous one is the Lenstra–Lenstra–Lovasz (LLL) algorithm. Although the average complexity of the LLL algorithm is a polynomial in the length of basis, the complexity of the worst case is unbounded. To address this issue, a modified LLL algorithm that contains four LLL loops is reported in Ref. ^[23], and it achieves nearly the same performance as the original LLL algorithm. By optimizing the algorithm, a lower complexity algorithm that contains only one LLL loop is proposed in our scheme, which can make the MIMO channel matrix more orthogonal and reduce the noise influence for signal demodulation.

In this paper, a cost-effective integrated O-band four-channel directly modulated optical transceiver has been developed. After optical coupling optimization, the measured 3 dB bandwidth of this optical transceiver is about 20 GHz, and the spurious-free dynamic range (SFDR) is up to 91.2dB·Hz2/3 when the input RF frequency is below 14 GHz for all lanes. To mitigate the channel interference and the additive noise in our optical transceiver, a low-complexity MIMO demodulation algorithm based on lattice reduction zero-forcing (LR-ZF) is proposed and designed. By the cooperation of the fabricated optical transceiver and the proposed LR-ZF MIMO demodulation algorithm, a 4×4 MIMO orthogonal frequency division multiplexing (OFDM) RoF system with 15.5 km standard single-mode fiber (SSMF) and 1.2 m wireless transmission has been demonstrated for both uplink and downlink, and the achieved data rate is 6.624 Gbit/s.

Figure 1 shows the structure of the proposed TOSA and ROSA. As shown in Fig. 1(a), four discrete distributed feedback (DFB) laser chips, four nonspherical lenses, a flexible printed circuit (FPC), and an arrayed waveguide grating using a silica-based planar lightwave circuit (AWG-PLC) are contained in this TOSA. All these components are packaged in a small metal box with the size of 16mm×18mm×6mm. The central wavelengths of these four DFB chips are 1271.4 nm, 1290.7 nm, 1311.6 nm, and 1330.1 nm, respectively. The fabrication process of this TOSA is as follows. First, the DFB chips are eutectic-bonded to the silicon submount. Then, the pads of the DFB chips and the submount are connected by gold bonding wire. The AWG-PLC and FPC are manually fixed on the metal bench with epoxy. Consequently, these DFB chips are aligned with four channels of the waveguide, and the submount and FPC are connected by gold bonding wire. At last, a six-axis precise alignment optical platform is used to adjust the lens for optical coupling. As shown in Fig. 1(b), an AWG-PLC demultiplexer (De-mux) integrated with a pigtail fiber, a PIN-type photodetector (PD) array chip, a four-channel linear transimpedance amplifier (TIA), and an FPC are contained in the ROSA. Similarly, all these components are packaged in a small metal box with the size of 16mm×20mm×6mm. Note that the beveled facet of the De-mux AWG-PLC is polished with an inclined surface. The total power consumption of the proposed optical transceiver module is about 1.111 W when all lanes are working simultaneously.

In contrast to direct butt-joint optical coupling, optical coupling using a lens has the advantage of preventing laser instability induced by reflection from the end facet of the waveguide. That is to say, the performance of reflection coefficient S11 using an optical lens for optical coupling will be better than that using direct butt-coupling ^[24]. However, the optical coupling efficiency (CE) is very sensitive to the position deviation of the lens. Therefore, these four optical lenses must be actively aligned after mounting the DFB chips and AWG-PLC, because the multiple input cores of the AWG-PLC cannot be relocated. To address this issue, a precise submicron alignment technique for optical lenses that is proposed in Ref. ^[24] is used in our test, and the optical CE is about −1.3dB for all lanes with the alignment tolerance of ±0.3μm. In the package, the insertion loss from the AWG-PLC to the output fiber is 3.22 dB, 3.02 dB, 3.03 dB, and 2.92 dB for four lanes, respectively. In this way, the total optical loss of the TOSA is less than 4.6 dB.

To improve the performance of the scattering parameter and minimize the electrical crosstalk, some useful methods are applied in our work. As shown in Fig. 1(c), there is a ground line between two signal lines of each channel on the FPC. The ground–signal–signal–ground structure can effectively reduce crosstalk from the adjacent channel. The high frequency matching resistance should be close to the DFB laser, which can reduce the reflection coefficient S11 performance of the TOSA. What is more, the short and thick wire bonding is helpful to not only carry a higher current at high frequency but also have smaller effective inductance and less signal crosstalk ^[9,25]. In our experiment, by comprehensively considering the high-frequency characteristics and the implementation complexity, two gold wires are used to connect the submount and the transmission line of the FPC. Furthermore, making the side of transmission line metallization on the printed circuit board (PCB) is helpful to decrease the electrical crosstalk and guarantee the signal integrity.

To improve the optical CE of the ROSA, the end facet of the De-mux AWG-PLC with an oblique angle is used as shown in Fig. 1(d). To optimize the oblique angle, a simulation is set up by the finite-difference time-domain (FDTD) method. The refractive indexes of the cladding material (SiO2) and the core material (SiO2–GeO2) are 1.4475 and 1.4692, respectively. The sizes of the core layer and the photosensitive surface of the PD are set at 4μm×4μm and 16μm×16μm, respectively. Figure 2 shows the optical CE versus the distance and oblique angle. As shown in Fig. 2(a), the optical CE decreases with the increase of distance between the AWG-PLC and PD. However, if the distance is too short, the polished end of the AWG-PLC and photosensitive surface of the PD are easy to damage during processing fabrication. Therefore, this distance value is usually set in the range of 10–30 μm. Figure 2(b) shows that the highest optical CE is achieved when the oblique angle is set at 42°, and the value of the optical CE is −0.335 dB if the distance is set to 10 μm. Moreover, the optical CE is −1.255dB even as the distance increases to 30 μm, which means that the large alignment tolerance of the distance between the bottom of the AWG-PLC and the PD can be achieved. At last, the TOSA and the ROSA are connected by an RF PCB, and the photographs of the fabricated optical transceiver, PD array, TIA array, AWG-PLC, and DFB chips are shown in Fig. 3.

Figure 4 shows the measured scattering parameter performances of the designed optical transceiver by using a vector network analyzer (R&S ZNB40). As shown in Fig. 4(a), the measured reflection coefficient S11 is below −20dB for all the lanes when the bias current is 35 mA for each lane. Figure 4(b) shows the measured forward transmission coefficient S21, and it can be easily observed that the 3 dB bandwidth of this transceiver is about 20 GHz for each lane. In our test, a two-tone RF signal with the frequency interval of 10 MHz and different central frequency is generated by a vector signal generator (R&S SMW200A), and it is used to measure the SFDR. The bias current of the TOSA for each lane is set to 35 mA, and the received optical power for ROSA is set to −6dBm for each lane. It can be clearly observed in Fig. 4(c) that the measured SFDR is above 91.2dB·Hz2/3 for all lanes when the central frequency is 2–14 GHz. As shown in Fig. 4(d), the highest SFDR value is 94.27dB·Hz2/3 for lane 3 when the central frequency is 6 GHz.

An N×N MIMO system consists of N transmitters and N receivers, and the relationship between the transmitted column vector x and the received vector y is determined by where H and n represent the transmission matrix and the additive noise of the MIMO channel, respectively. After orthogonal-triangular (QR) decomposition for H, Q is the unitary matrix that contains orthogonal columns, and R is upper triangular. By using the proposed algorithm, Eq. (1) can be modified as Then, multiplying two sides of Eq. (2) by QLLLH, the above equation can be written as Making y˜=QLLLHy,x˜=TLLL−1x,n˜=QLLLHn, Eq. (3) can be expressed as Subsequently, we can recover the input signal by using Eq. (4). To get the QLLL, RLLL, and TLLL, an LR algorithm is proposed in our scheme. Figure 5 presents the schematic diagram of the modified single-loop LLL algorithm. The transmission matrix H is estimated by training sequences, after QR decomposition, size reduction, and column swapping. Then the MIMO channel matrix becomes more orthogonal, which means that the new channel matrix RLLL has a lower condition number than the original channel matrix H. At last, the conventional linear detection algorithm can benefit from such a transformation and achieve a better performance. It is noteworthy that the proposed single-loop LLL algorithm has three differences from the original LLL algorithm reported in Ref. ^[26]. First, step 16 in the original algorithm has been eliminated which can greatly reduce the complexity. Second, operations on matrix Q are shifted to matrix H to get the desired new channel matrix directly. Third, only one single loop can be extracted from the original LLL algorithm, and the loop flow can be predefined when performing the algorithm. Table 1 shows the average complexity of the proposed LR algorithm, the LLL algorithm reported in Ref. ^[23], and the optimal MLSE based on real number multiplication. Obviously, the proposed single-loop LLL algorithm has the lowest algorithm complexity.

To investigate the feasibility of broadband wireless access based on the proposed LR-ZF algorithm and integrated optical transceiver, an experiment is set up as shown in Fig. 6. Both uplink and downlink transmissions are evaluated. As shown in Fig. 6(a), for downlink transmission, at the transmitter a pseudorandom bit sequence (PRBS) with a length of 215−1 is generated and then mapped onto 128 subcarriers. In each subcarrier, 16-quadrature amplitude modulation (16QAM) and 256-point inverse fast Fourier transform (IFFT) are used. The cyclic prefix (CP) length is set to 10%, eight training sequences for every 100 payload symbols are employed, and the first training symbol is used for time synchronization. Then the produced four independent 16QAM-OFDM signals are upconverted to 5.5 GHz by a four-channel arbitrary waveform generator (AWG, Keysight M8195A) with a 3 dB bandwidth of 20 GHz. The sampling rate of this AWG is set to 40 GSa/s, and the generated RF signal has a data rate of 6.624 Gbit/s [4×(40GSa/s/40)×4×(100−8)/100×90%×128/256] with a bandwidth of 500 MHz [(40GSa/s/40)×128/256] and spectrum efficiency (SE) of 13.248 bit/(s·Hz).

These four electrical RF signals are used to drive four channels of the TOSA. After 15.5 km SSMF propagation, a variable optical attenuator (VOA) is adopted to adjust the received optical power at the ROSA. The received four-channel RF signals are then fed into four antennas after a four-channel electrical amplifier with 24 dB gain. After 1.2 m air transmission, four antennas and a four-channel digital storage oscilloscope (DSO, Tektronix MSO72004C) with a 25 GSa/s sampling rate are used to capture these four wireless signals. The operation bandwidth and the gain of the transmitter and receiver antennas (PBTX580060V15DA) are 5150–5850 MHz and 15 dBi, respectively. The horizontal spacing between every two Tx antennas is 0.25 m. Offline signal demodulation is then performed by a digital signal processing (DSP)-based receiver consisting of resampling, synchronization, 4×4 MIMO channel estimation, data mapping, and bit error ratio (BER) counting. To evaluate the performance of different algorithms, three MIMO channel estimate algorithms including ZF, LR-ZF, and MLSE are tested for both uplink and downlink transmissions.

For uplink transmission as shown in Fig. 6(b), the generated four-channel 16QAM-OFDM RF signals with 5.5 GHz carrier frequency are fed into four transmitter antennas. After 1.2 m air transmission, the received upstream wireless signals are used to drive four channels of the TOSA. The optical upstream signals are captured by the ROSA and 25 GSa/s DSO after 15.5 km SSMF propagation. The same digital signal process as used in downstream transmission is performed, and the net rate of the upstream is also 6.624 Gbit/s for 4×4 MIMO 16QAM-OFDM due to the use of the same modulation parameters.

Figures 7(a)–7(c) show the measured BER performance in terms of the received optical power in the ROSA for 4×4 MIMO 16QAM-OFDM signals with different algorithms in downlink. As shown in Fig. 7(a), it could be clearly observed that the receiver’s sensitivity at the forward-error correction (FEC) limit (BER of 3.8×10−3) is −8.4dBm, −8dBm, −7dBm, and −7.7dBm for four lanes, respectively, by using the traditional ZF algorithm. Similarly, Fig. 7(b) shows that the receiver’s sensitivity is −9.6dBm, −9.6dBm, −9.5dBm, and −9.6dBm for four channels, corresponding to 1.2 dB, 1.6 dB, 2.5 dB, and 1.9 dB sensitivity improvement when the MLSE algorithm is adopted. As shown in Fig. 7(c), the measured receiver’s sensitivity by using the proposed LR-ZF algorithm is evaluated for comparison. Obviously, the receiver’s sensitivity is −9.3dBm, −9.4dBm, −9dBm, and −9.4dBm for each lane, respectively, and negligible sensitivity deterioration (around 0.2 dB) among four lanes is observed. It means that compared to the MLSE algorithm, the proposed LR-ZF algorithm could achieve a close BER performance with much less algorithm complexity. The constellations of the received 4×4 MIMO 16QAM-OFDM signals by using the proposed LR-ZF algorithm are all shown in the insets of Fig. 7(c).

Figures 7(d)–7(f) show the measured BER performance in terms of received optical power for the uplink transmission. It can be easily observed in Figs. 7(d) and 7(e) that the measured receiver’s sensitivity at the FEC limit is improved from −7.6dBm to −9.2dBm with about 1.8 dB performance improvement for each lane by using the MLSE algorithm. As shown in Figs. 7(e) and 7(f), there is only 0.2 dB power penalty between the MLSE algorithm case and the proposed LR-ZF algorithm case. It means that compared to the MLSE algorithm, LR-ZF algorithm has a close BER performance but lower algorithm complexity. The constellations of the received 4×4 MIMO 16QAM-OFDM signals by using the proposed LR-ZF algorithm are all shown in the insets of Fig. 7(f).

We have designed and fabricated a broadband, high linearity, and integrated four-channel directly modulated analog optical transceiver. A precise submicron alignment technique for lens coupling in the TOSA and the 42° oblique angle De-mux AWG-PLC in ROSA are used to optimize the optical coupling efficiency. Based on this optical transceiver, we have successfully demonstrated 6.624 Gbit/s 4×4 MIMO 16QAM-OFDM radio signal transmission over 15.5 km SSMF and 1.2 m wireless transmission for both downlink and uplink. Moreover, the proposed LR-ZF algorithm is proven to effectively mitigate the noise and crosstalk in the optical transceiver with lower algorithm complexity. The proposed four-channel integrated directly modulated optical module and LR-ZF algorithm have the potential to be used in a future 5G cellular system.

Acknowledgment. Thanks to Accelink Techn. Co., Ltd., Henan Shijia Photons Techn. Co., Ltd., and Institute of Semiconductors, Chinese Academy of Sciences.