The advent of 5G technology has resulted in an exponential increase in mobile traffic data and increased demands on mobile networks due to the development of new technologies like augmented reality, smart healthcare, and drones^[1]. Because of its considerable advantages over rivals, centralized/cloud radio access network (C-RAN) architecture has improved its ability to respond to market conditions in recent years. In Ref. [2], baseband units (BBUs), which are centralized in a single site or even in the cloud, are kept apart from the system’s remote radio heads (RRHs) via the C-RAN technique. This method increases the demands for high speed, low latency, and precise synchronization on the network connection between RRHs and BBUs while simultaneously lowering the cost of equipment and making the radio unit layout less complicated. These crucial needs can be satisfied by mobile front-end (MFD) networks based on radio-over-fiber (RoF)^[3]. But not every location is appropriate for the deployment of fiber. The fiber deployment is expensive in hilly and metropolitan locations. As a result, developing radio access networks (RANs) with high communication capacity, high flexibility, and cheap engineering cost has drawn attention. The advantages of millimeter wave (MMW) transmission include a broad frequency range and very little air attenuation. For high-speed RoF transmission that goes beyond sub-6G, this frequency range is perfect. It has been claimed several times^[4,5] that photonics-aided W-band long-distance high-speed communication can provide flexible transmission for MFD customers in the last mile. W-band (75–110 GHz) radio, in particular, provides high precision and low air attenuation. As a result, a W-band RoF system can increase the transmission range and capacity of wireless services^[6-8]. However, the bulk of MMW-RoF techniques now in use rely on expensive and intricate coherent receivers to transmit signals^[9]. In addition to avoiding complicated and expensive high-speed mixers, millimeter-wave local oscillators, and high-speed DACs in order to save equipment costs, intensity modulation and direct detection (IM-DD) schemes using the envelope detector (ED) also prevent frequency drift in the photon-assisted MMW system^[10].

Furthermore, the probabilistic shaping (PS) constellation may be utilized for rate adaptation and is viewed as a promising way to escape Shannon’s limit^[11]. Recently, the Gallager many-to-one mapping (MTO), the hierarchical distribution matcher (HiDM), the constant composition distribution matcher (CCDM), bit-weighted distribution matching (BWDM), and prefix-free code distribution matching (PCDM) are a few PS approaches that have been presented^[12-14]. Only PCDM, BWDM, and HiDM have had field programmable gate array (FPGA) implementations^[13-15]. To employ the MTO shaping technique, the receiver must design an iterative strategy that applies both inner and outer iterations to the low-density parity-check (LDPC) decoder and the PS decoder. This demonstrates that the technique is costly in terms of computation time, memory utilization, power consumption, and hardware implementation complexity. Furthermore, the CCDM requires resource-intensive division and multiplication operations^[16]. In Ref. [17], a low-complexity PS-16QAM scheme based on BWDM for orthogonal frequency division multiplexing (OFDM) symbols in an IM-DD system is presented. Zhang et al. demonstrated it in a high-speed real-time system^[15]. The experimental results show that the system does not require complicated multiplication and division operations and, thus, has reduced computational and hardware complexity. The shortcoming of this method is that it cannot be used directly to higher order 64-ary quadrature amplitude modulation (QAM).

In this work, we propose and experimentally demonstrate a novel PS-64QAM-OFDM based on two-stage bit weight distribution matching (TS-BWDM) for an IM-DD-based W-band RoF system. The signal is transmitted over 45 km standard single-mode fiber (SSMF) and 4 m wireless links. Compared to high-cost coherent reception, this system uses a low-cost W-band ED to recover the received signals to the baseband. After 45 km SSMF and 4 m wireless transmission, 28.13 Gb/s PS-64QAM-OFDM signal transmission is obtained with a bit error rate (BER) smaller than 2.2×10−2. The experimental results show that the receiver sensitivity and the system fiber nonlinear effect tolerance can be significantly improved.

The process of TS-BWDM in detail is depicted in Fig. 1. First, the original input bit stream is divided into three parallel data streams, U1, U2, and U3, with the matching bit lengths of n1, n2, and n3 following the serial-to-parallel conversion. Here, U1-path performs flag bit insertion, U2-path mainly realizes two-stage bit-weighted inversion, and U3-path performs the judgment of the second bit-weighted inversion to realize approximate Gaussian distribution (GD). The three parallel data streams can be expressed as Ui={Di,1,Di,2,…,Di,ni},(1)where D∈{0,1} and i is the index of the parallel bit streams. The U2 is then subjected to the two-stage bit-weighted inversion processing procedure, which is a crucial component of TS-BWDM. In the two-stage bit-weighted inversion, U2 is bitwise separated into a number of sets, each of which contains k bits, and one flag bit, the newly added most significant bit (MSB), is added to the U1 set via weight computation based on the original k elements of U2. The constellation labeling design with gray mapping rules for PS-PAM8 is shown in Fig. 2(a). The yellow marked bit represents the symbol bit. It is obvious that the PS can be achieved by increasing the probability of “1” in the inner circle of U2. After the weight calculation, if the probability of “1” is greater than k/2, the corresponding MSB is defined as “1.” If not, the MSB is set to “0,” and the k bits of the set undergo a bit negation operation.

Figure 2(b) shows the probability distribution of PS-PAM8 symbols for k=3 after first stage inversion. To achieve the PS-PAM8 signals following approximate GD, similarly, the U3 is divided into several sets according to the flag bits inserted by the first bit-weighted reversion operation, and each set also includes k bits. After calculating the weight of the subset in U3, the bits in the subset of U2 corresponding to “1” in the subset of U3 are subject to the bit inversion operation if the probability of “1” is greater than k/2. If not, these bits remain unchanged. It is worth noting that the two-stage bit-weighted inversion here is performed on U2, and only one-stage flag bit insertion operation is performed on U1. Using the first stage bit-weighted inversion processing procedure, the probabilities of “1” and “0” in the U2′ can be written as P(U2′)={12k(∑x=⌈k/2⌉kx+1k+1Ckx+∑x=⌊k/2⌋+1kxk+1Ckx),U2′=1,1−12k(∑x=⌈k/2⌉kx+1k+1Ckx+∑x=⌊k/2⌋+1kxk+1Ckx),U2′=0,(2)where ⌈·⌉ means the operation for the minimal integer larger than the value inside it. ⌊·⌋ indicates the opposite operation.

The key to the second stage bit-weighted reversion is to re-reverse the subset in U2′ according to the distribution of “1” and “0” in U3′, which includes three steps as follows. (1) Use the flag bits added by the initial bit-weighted reversion operation to partition the U3′ into a number of sets, each of which also contains k bits. (2) Calculate the weight of the subset in U3′. (3) Find the bits in the subset of U2′ corresponding to “1” in the subset of U3′, if Z is greater than k/2, and re-reverse these found bits. If not, these bits remain unchanged. The probability distribution of PS-PAM8 symbols for k=3 after second stage inversion is shown in Fig. 2(c). The detail LDPC-coded PS-64QAM based on the two-stage BWDM generation procedure is shown in Fig. 2(d). After the 64QAM mapping operation, the generated PS-64QAM constellation is shown in Fig. 3.

The mutual information (MI) of the modulated signal for an N-order constellation set X transmitted in the additive Gaussian white noise (AWGN) channel can be represented by $$\begin{gathered} I(X;Y)=H(Y)−H(Y/X)=H(X+N)−H(N) \\ =∑x∈X∑y∈Yp(x,y)logp(x,y)p(x)p(y) \\ =∑xp(x)[∑yp(y/x)logp(y/x)] \\ −∑ylogp(y)∑xp(x,y) \\ =−∑xp(x)H(Y/X=x)−∑ylogp(y)p(y), \end{gathered}$$(3)where p(y/x) and H(·) indicate the conditional transition probability density and the information entropy, respectively. It is feasible to communicate reliably across the AWGN channel if the transmission rate per real dimension does not exceed the channel capacity C. It can be written as C=maxI(X;Y).(4)

Figure 4 illustrates the channel capacity for uniformly distributed 64QAM (UD-64QAM) and TS-BWDM-based PS-64QAM in the cases of k=3, respectively. Obviously, approximately 0.61 dB shaping gain can be correspondingly obtained in the case of k=3, compared with the UD-64QAM. Additionally, in the case of k=3 and 9, the net rate of BWDM-based PS-64QAM is 5.76 and 5.93 bits/symbol regardless of FEC redundancy.

Figure 5 shows the experimental setup of the LDPC-coded PS-64QAM OFDM for the IM-DD-based W-band RoF system. At the transmitter, the modulated signal is sent to the AWG (Tektronix AWG7122C). After then, the MZM (FTM7938EZ) is driven by this data sequence. With the bias voltage adjusted to −4.5V, the MZM functions close to the quadrature point. The signal amplitude stays within the linear driving voltage range of the MZM. Two external cavity lasers with a 100 kHz linewidth produce beams at 1550 nm and 1550.7 nm with a channel spacing of 87 GHz. The modulator has an insertion loss of 9 dB and combines the two laser beams via the polarization-maintaining optical coupler (PM-OC) before sending them to the MZM as an optical carrier. A range of 0 dBm to 3 dBm is maintained for the optical power prior to PD detection. The light waves are combined by the PM-OC with the optical spectrum in Fig. 5(a). The optical signal is square-law detected by the 50 GHz bandwidth PD (XPDV21), which then modulates the signal onto the 87 GHz center carrier. The W-band signal is sent to free space via a horn antenna with a gain of 25 dBi after being amplified by an electrical amplifier (EA) operating at 75–100 GHz with a gain of 21 dB. The MMW signal is down-converted to the baseband OFDM signal through the ED via 45 km SSMF and 4 m wireless propagation and amplified by a horn antenna with a gain of 25 dBi, a lens with a gain of 15 dBi, and a W-band LNA with a gain of 30 dB. After being amplified by an EA with a gain of 30 dB, the signal is captured offline by a real-time oscilloscope operating at a sampling rate of 50 GSa/s and a bandwidth of 16 GHz. Figure 5(a) illustrates the electrical spectrum of the PA-64QAM OFDM signal.

Figures 6(a) and 6(b) show the DSP at the transmitter and the receiver, respectively. The IFFT size is 1024, and 400 subcarriers are loaded with data. The length of both the cyclic prefix and suffix is 32. The number of ISFA taps is 4. One OFDM frame comprises 9 TSs and 243 data-carrying OFDM symbols. The bandwidths of LDPC-coded UD-64QAM, PS-64QAM OFDM signals of k=9 and k=3 are about 4.18 GHz, 4.34 GHz, and 4.69 GHz, respectively. The LDPC code length and rate are 46,800 and 3/4 in our experiment. Here, the binary data after parallel-to-serial conversion are used to generate 64,800 bits per LDPC block via the FEC encoder in consideration of the cooperation with LDPC codes for more dependable transmission. The maximum number of iterations is 30. The decoder for LDPC codes is the belief propagation decoding algorithm. Here, the belief propagation decoding algorithm and a maximum of 30 iterations are used to decode the logarithmic likelihood ratio; some key parameters used in the experiment are shown in Table 1.

Figure 7 shows the estimated SNR across the data subcarrier index for the PS-64QAM OFDM with k=3. The ISFA-enhanced channel estimation method can provide more accurate channel estimation for subcarriers and achieve improved SNR performance.

Figure 8 shows the BER performance for UD/PS-64QAM OFDM signals over 4 m wireless transmission. For fair comparison, the bit rates of all three signals (UD, k=3 and k=9) are 28.13 Gb/s. For the post-FEC BER performance, the received optical power (RPS) improvement for k=3 and k=9 signals after 4 m wireless transmission is 0.97 and 0.48 dB compared with the UD-64QAM at the BER of 2.2×10−5, respectively. The insets of Figs. 8(a), 8(b), and 8(c) show the recovered constellation diagrams of the OFDM for the three cases of UD, k=9, and k=3, respectively.

According to the result of the 4 m wireless transmission experiment, we carried out the 4 m wireless + 45 km SSMF transmission experiment of UD/PS-64QAM OFDM. Figure 9 illustrates the BER performance of UD/PS-OFDM versus different ROPs over 45 km SSMF + 4 m wireless transmission. Compared with UD-OFDM, PS-OFDM with k=3 and 9 can reach the BER of 2.4×10−2. In addition, the receiver sensitivities of the PS-OFDM receivers with k=3 in terms of the ROP can be improved by more than 1.4 dB at the BER of 1.8×10−5 compared to UD-OFDM. The reduced signal average power by the PS technique, which may lessen the harm on the transmitted signal produced by the fiber nonlinear effect, can benefit both the IM-DD and the coherent detection systems with negative electrical field^[18]. The reconstructed constellation diagrams of the OFDM for the three situations of UD, k=9, and k=3, are displayed in the insets of Figs. 9(a), 9(b), and 9(c), respectively. In Figs. 8 and 9, the post-FEC is referring to after the LDPC decoding and without ITS-BWDM.

In conclusion, a novel PS 64QAM-OFDM with LDPC-coded modulation in a W-band RoF system using envelope detection is proposed and experimentally demonstrated. The proposed PS scheme has the advantages of no complex multiplication and division operations and low hardware implementation complexity. Apart from shaping gain, the PS-64QAM OFDM signal outperforms the UD-64QAM OFDM signal in terms of receiver power sensitivity and fiber nonlinear effect tolerance. The power sensitivity of the optical receiver in the experiment has increased by at least 1.4 dB higher than that of UD, according to the experimental data.