With the advent of 5G commercialization, various new applications, such as unmanned driving, mobile X-haul, and smart health care, are gradually emerging, which brings huge wireless traffic and large demands on mobile networks^[1,2]. The radio-over-fiber (RoF) system has attracted much attention as a promising candidate for future broadband wireless communication due to its large fiber communication capacity, enhanced flexibility, and minimal propagation delay^[3,4]. Simple and cost-effective millimeter-wave (mmW) signal generation is essential for implementing RoF technology due to its abundant bandwidth resources and seamless integration between fiber and wireless communication^[5–7]. However, the current digital interfaces based on the Common Public Radio Interface (CPRI) protocol have extremely low bandwidth efficiency due to 15 quantization bits. Moreover, it is difficult to generate high-order vector mmW signals in the RoF system because of the higher requirements of the signal-to-noise ratio (SNR) and smaller nonlinear tolerance^[8–10].

Toward this issue, researchers have mainly focused on photonic beating and photonic frequency multiplication for the high-order vector mmW generation. In Refs. [11–13], the virtual carrier-assisted photonic beating scheme is proposed and the 16/64-quadrature amplitude modulation (QAM) vector mmW signals can be successfully generated. However, this approach only achieves double frequency, and the in-phase/quadrature (I/Q) modulator at the transmitter will also increase the system instability. Considering this issue, a photonic frequency-multiplied scheme is studied in Refs. [14–17], and the I/Q modulator can be replaced by a Mach–Zehnder modulator (MZM), which provides a simple and stabilized structure. However, the responses of different levels are distinct in nonlinear modulation of the MZM, which results in intensity-dependent distortion after photonic frequency multiplication, and the constellation will be distorted. To address this issue, additional transmitter precoding is required for the frequency multiplication. It not only increases the complexity of the transmitter but also reduces the Euclidean distance for the signal constellations, which will degrade the performance of the system. In Refs. [16,17], angle modulation is proposed to construct a constant-envelope signal, which tolerates signal–signal beating interference (SSBI) and avoids transmitter precoding. More importantly, a theoretical 6 dB SNR gain will be obtained with each doubling of the modulation index. However, in practice, it is far from enough to support the generation of higher-order vector mmW signals. Among these schemes^[11–17], only 64-QAM is supported, and the SNR is still insufficient for higher-order modulation formats vector mmW signal generation.

Recently, delta-sigma modulation (DSM) has become a hot topic in the wireless field^[18,19], as it can bring huge SNR gain and improve the capacity of optical and wireless access systems^[20–23]. Therefore, it is interesting to combine the DSM technology with phase modulation to generate the vector mmW signals with a simple structure and high-order modulation format. In Ref. [24], a dual-vector radio-frequency signal generation scheme enabled by bandpass DSM is proposed, and a single-carrier 64-QAM mmW signal and a single-carrier 128-QAM mmW signal are successfully generated. In Refs. [25,26] the 1024-QAM/4096-QAM mmW signals are generated with the aid of 1-bit DSM. However, an additional laser is required for photonic heterodyne detection^[24–26]. To clarify the differences between these schemes, a comparison of these schemes for generating high-order vector mmW signals is also listed in Table 1.

In this Letter, we propose a high-order vector mmW signal generation scheme enabled by photonic frequency multiplication and DSM. By applying one-bit DSM, the complex continuous analog signal is quantized to the NRZ signal. With the aid of phase modulation, the envelope of the CE-DSM signal stays constant, which can effectively avoid intensity-dependent distortion caused by photonic frequency multiplication and complex transmitter DSP. Meanwhile, the photonic frequency-multiplied mmW signal can be effectively generated without transmitter precoding^[14], a complex I/Q modulator^[11], or an additional laser^[24–26]. We experimentally verify the feasibility of the combination of phase modulation and DSM, and the 4096-QAM vector mmW signals can be successfully generated with high spectrum efficiency and a simple structure. Results show that the generated two-fold 0.5-Gbaud and four-fold 0.2-Gbaud photonic frequency-multiplied 4096-QAM vector mmW signals at 40 GHz can be successfully transmitted over 15-km standard single-mode fiber (SSMF) and 1-m wireless link when the bit error ratio (BER) meets the hard-decision forward error correction (HD-FEC) threshold of $3.8\times {10}^{-3}$ and the error vector magnitude (EVM) is lower than 1.29%.

Figure 1 illustrates the schematic diagram of our proposal comprising phase modulation, demodulation, and photonic frequency multiplication. The original signal shown in inset (a) is represented as $x(t)$, and after the phase modulation and upconversion, the baseband signal is transformed into a vector signal as inset (b), which can be expressed as $E_{\mathrm{PM}}(t)=E_P·\cos [w_{c}t+m·x(t)]$, where $E_P$ is the drive voltage, $w_c$ is the angular frequency, $m$ is the modulation index factor, and $E_{\mathrm{PM}}(t)$ is the drive voltage of the MZM. The optical field of continuous wave (CW) laser light wave at $f_0$ can be expressed as $E_{\text{in}}(t)=E_0·e^{j2\pi f_{0}t}$, where $E_0$ is the amplitude of the optical field. The output optical signal of the MZM is $$E_{\mathrm{MZM}}(t)=\frac{E_0}{2}·\{\begin{array}{c}{e}^{j\{w_{0}t+\frac{\pi ·E_P·\cos [w_{c}t+m·x(t)]+\pi ·V_{\mathrm{DC}}}{2V_{\pi }}\}}\end{array}+e^{j\{w_{0}t+\frac{\pi ·E_P·\cos [w_{c}t+m·x(t)+\pi ]-\pi ·V_{\mathrm{DC}}}{2V_{\pi }}\}}\},$$(1)where $V_{\pi }$ and $V_{\mathrm{DC}}$ are half-wave voltage and direct current (DC) bias voltage of the MZM, respectively. Let ${\phi }_{\mathrm{DC}}=\frac{\pi ·V_{\mathrm{DC}}}{2V_{\pi }}$ and $k=\frac{\pi ·E_P}{2V_{\pi }}$, and after applying the Jacobi–Anger identity, Eq. (1) can be transferred to Eq. (2). The phase difference between the upper and lower arms is $n·\pi -2{\phi }_{\mathrm{DC}}$. When the MZM is biased at its null point and peak point, Eq. (2) can be transformed into Eqs. (3) and (4), respectively. Insets (d) and (e) depict the output optical signal after MZM modulation, which corresponds to Eqs. (3) and (4), respectively. It can be observed from inset (d) that$$E_{\mathrm{MZM}}(t)=\frac{E_0}{2}·\{\begin{array}{c}\sum _{n=-\mathrm{\infty }}^{+\mathrm{\infty }}{J}_n(k)·e^{j[(w_0+n·w_c)t+\frac{n}{2}·\pi +n·m·x(t)+{\phi }_{\mathrm{DC}}]}\end{array}+\sum _{n=-\mathrm{\infty }}^{+\mathrm{\infty }}{J}_n(k)·e^{j[(w_0+n·w_c)t+\frac{3n}{2}·\pi +n·m·x(t)-{\phi }_{\mathrm{DC}}]}\},$$(2)and only odd sidebands are retained, while in contrast, in inset (e), only even sidebands are retained, $$E_{\mathrm{MZM}}(t)\propto E_0·\sum _{n=-\mathrm{\infty }}^{+\mathrm{\infty }}{J}_{2n+1}(k)·e^{j\{[w_0+(2n+1)·w_c]t+(2n+1)·m·x(t)\}},$$(3)$$E_{\mathrm{MZM}}(t)\propto E_0·\sum _{n=-\mathrm{\infty }}^{+\mathrm{\infty }}{J}_{2n}(k)·e^{j[(w_0+2n·w_c)t+2n·m·x(t)]}.$$(4)

After the PD detection, the mmW signals with 2n-fold frequency multiplication can be successfully generated. With the aid of the Bessel function, the generated mmW signals can be expressed as Eqs. (5) and (6). Equations (5) and (6) present the mmW signals generated when the MZM is biased at its null point and peak point. The frequency of the vector mmW signal is multiplied by 2 or 4 times or more. Inset (f) shows the electrical spectrum of the received signal after PD detection. After the downconversion and Rx DSP, finally, the baseband signal can be successfully recovered, $$I(t)\propto R{\left|E_0\right|}^2·\sum _{n=-\mathrm{\infty }}^{+\mathrm{\infty }}{|J_{2n+1}(k)|}^2\cos [2(2n+1)w_{c}t+2(2n+1)·m·x(t)],$$(5)$$I(t)\propto R{\left|E_0\right|}^2·\sum _{n=-\mathrm{\infty }}^{+\mathrm{\infty }}{|J_{2n}(k)|}^2\cos [4n{w}_{c}t+4n·m·x(t)].$$(6)

The experimental setup for the proposed 40 GHz CE-DSM 4096-QAM vector mmW signal generation system is illustrated in Fig. 2. The Tx and Rx DSP blocks are processed offline using MATLAB. First, at the transmitter, a pseudo-random binary sequence (PRBS) with a length of 2²³−1 is mapped into a complex-valued signal with an ultrahigh order of 4096 QAM, and the OFDM modulation is performed using a 1024-point inverse fast Fourier transform (IFFT). To obtain a real-valued and oversampled OFDM sequence, the input to the IFFT is a conjugate symmetric datum. The data of 0.5-Gbaud and 0.2-Gbaud OFDM signals are generated and loaded with 452 data subcarriers in MATLAB. After oversampling and one-bit fourth-order DSM, the baseband signals are converted to 4-GSa/s and 10-GSa/s NRZ signals, respectively. The generated DSM-NRZ signals are upsampled and passed through a root-raised cosine (RRC) filter. Then the phase modulation and upconversion are carried out as depicted in Fig. 1. Insets (a) and (b) in Fig. 2 show measured power spectral density (PSD) of the transmitted baseband signals after oversampling and one-bit DSM. It can be observed that the quantization noise component is pushed out of the signal bandwidth, which realizes the separation of noise and signal and greatly improves the in-band SNR. Insets (c) and (d) depict the zeros-poles plot and the realized frequency response of the square (RMS) gain of the discrete-time NTF in the signal band is about $-43\mathrm{dB}$.

The data generated by the Tx DSP block are uploaded into an arbitrary waveform generator (AWG, Keysight M8195A) with a sampling rate of 64 GSa/s. The output electrical signals with a peak-to-peak voltage of 600 mV are boosted by an electrical amplifier (EA) with a 23-dB gain before driving the 25-GHz MZM. The optical input of the MZM is a continuous-wavelength laser light wave at 1544.3 nm, which is generated from an external cavity laser (ECL) with a linewidth of 500 Hz and a maximum emitting optical power of 13.7 dBm. The output optical power of the MZM is about 2 dBm; the optical spectrum is depicted in Fig. 3. Figures 3(a) and 3(b) represent the optical spectra of twofold 0.5-Gbaud and fourfold 0.2-Gbaud vector mmW signals with an intermediate frequency (IF) of $f_{c1}=20\mathrm{GHz}$ and $f_{c2}=10\mathrm{GHz}$, respectively.

In Fig. 3(a), the MZM is biased at its null point, where only odd sidebands are preserved, and the $\pm 1$st-order optical sidebands are spaced by $2f_{c1}$ (40 GHz). In Fig. 3(b), the MZM is biased at its peak point, and the $\pm 2$nd-order optical sidebands are spaced by $4f_{c2}$ (40 GHz). After 15-km SSMF transmission, the optical vector mmW signal is sent into a high-speed PD with a 3-dB bandwidth of 50 GHz for heterodyning detection. Here we use a variable optical attenuator (VOA) before the PD for BER calculation. The generated electrical 40 GHz vector mmW signals are first amplified by EA2 and then loaded into the horn antenna (HA1) with a gain of 15 dBi. After 1-m wireless link transmission, the vector mmW signals are received by another HA2 and then amplified by EA3. Finally, the electrical signals are digitized at 160 GSa/s by a 59-GHz real-time digital signal analyzer (DSA, Keysight DSAZ594A). EA2 and EA3 are both broadband EAs with power gains of 23 and 10 dB, respectively.

Figure 4 shows the electrical spectra captured by the DSA as described by Eqs. (7) and (8). The electrical spectrum in Fig. 4(a) is converted from the optical spectrum in Fig. 3(a) after PD detection. The signal located at 40 GHz is generated through the beating of the $\pm 1$st-order optical sidebands. Similarly, the electrical spectrum in Fig. 4(b) corresponds to the spectrum in Fig. 3(b). However, unlike Fig. 4(a), the signal in Fig. 4(b) appears not only at 40 GHz but also at the surrounding areas of 30 and 50 GHz due to the bandpass effect of the antenna. It can be observed that the SNR of the signal is highest at 40 GHz because the fourfold frequency multiplied mmW signal can be obtained by beating both the $\pm 2$nd-order optical sidebands, the original optical carrier, and the $\pm 4$th-order optical sidebands as described by Eq. (8), $$I_o(t)\propto R{\left|E_0\right|}^2·\{2·J_1(k)·\cos [2w_{c}t+2·m·x(t)]\},$$(7)$$I(t)\propto R{\left|E_0\right|}^2·\{\begin{array}{l}2·J_0(k)·J_2(k)·\cos [2w_{c}t+2·m·x(t)]\end{array}+[2·J_0(k)·J_4(k)+2·J_2(k{)}^2]·\cos [4w_{c}t+4·m·x(t)]\}.$$(8)

As depicted in the Rx DSP block of Fig. 2, the offline process mainly includes three parts, i.e., phase demodulation, DSM demodulation, and OFDM demodulation. First, the phase demodulation involves downconversion and a phase demodulator, which is implemented with an arctangent calculator, followed by a phase unwrap. After the resampling and RRC filtering, an NRZ DSP is needed to recover the DSM-NRZ signal. We employ T/2-space equalization with a 21-tap feed-forward equalizer (FFE) and a 5-tap decision feedback equalizer (DFE) to solve the chromatic dispersion (CD) and nonlinearity caused by the fiber and wireless transmission and PD detection. Second, after recovering the NRZ signal, the DSM demodulation is carried out with a low-pass filter (LPF) to remove the out-of-band quantization noise introduced by noise shaping and restore the original analog signals. Finally, after downsampling, the OFDM demodulation is performed with synchronization, frequency domain equalization, fast Fourier transform (FFT), and 4096-QAM demapping.

We first analyze and discuss the experimental results of the NRZ signals, since the demodulation of DSM relies on the transmission quality of the quantized signals. The BER curves for 10-GSa/s and 4-GSa/s NRZ signals under different transmission scenarios, including BtB, 1-m wireless link, and 15-km SSMF hybrid with 1-m wireless link, are depicted in Fig. 5. The BER decreases gradually with increasing received optical power (ROP). In Fig. 5(a), for the twofold 10-GSa/s NRZ signal, the sensitivity penalty is about 2 and 2.5 dB for the 1-m wireless link and 15-km SSMF hybrid with 1-m wireless link compared with the BtB case at the BER of $1\times {10}^{-4}$. Similarly, for the fourfold 4-GSa/s NRZ signal in Fig. 5(b), there is an approximately 2.5 dB sensitivity penalty for both cases compared to BtB. Compared with optical fiber transmission, wireless transmission will bring greater power loss. The significant received sensitivity penalty in wireless transmission is mainly due to atmospheric attenuation and path loss, and thus the impairments of the two signals are basically the same. Additionally, the broadband amplifier also introduces additional noise, which will deteriorate the mmW signals^[10]. The frequency spectra of received DSM-NRZ signal with and without equalization and LPF are presented in Fig. 6(a), where the quantization noise is filtered out by an LPF, preserving the original features as inset (a) in Fig. 2.

Figure 7 illustrates the BER performance versus ROP for the 4096-QAM OFDM signal after DSM recovery at optical BtB, 1-m wireless link, and 15-km SSMF hybrid with 1-m wireless link transmission scenarios. Considering the HD-FEC threshold of $3.8\times {10}^{-3}$, the receiver sensitivities of the twofold 0.5-Gbaud and fourfold 0.2-Gbaud OFDM signals are $-8$ and $-8.5\mathrm{dBm}$ in the BtB case, respectively. When the ROP is greater than $-5\mathrm{dBm}$, the 4096-QAM vector mmW signals can be successfully recovered after fiber and wireless link transmission. The constellation diagram of the restored 0.2-Gbaud 4096-QAM OFDM vector mmW signal at an ROP of $-5\mathrm{dBm}$ is depicted in Fig. 6(b).

Finally, we discuss the SNR and the EVM of the 4096-QAM OFDM vector mmW signals as depicted in Fig. 8. The EVM and SNR are marked with blue and red markers, respectively. Figure 8(a) presents the SNR-EVM curves for the twofold 0.5-Gbaud vector mmW signal. It can be observed that for the BtB, 1-m wireless link, and 15-km SSMF hybrid with 1-m wireless link transmission scenarios, the EVM threshold requirement of 1.29% can be achieved with a maximum SNR of up to 48 dB when the ROP exceeds $-5\mathrm{dBm}$. Figure 8(b) shows the SNR-EVM curves for the fourfold 0.2-Gbaud vector mmW signal. The EVM threshold can be met for the BtB, 1-m wireless link, and 15-km SSMF hybrid with 1-m wireless link transmission scenarios, when the ROP is greater than $-9$, $-7.5$, and $-7\mathrm{dBm}$, respectively. With the increase of the ROP, the SNR is improved with a maximum SNR of 54 dB after 15-km SSMF and 1-m wireless link transmission when the ROP is greater than $-5\mathrm{dBm}$.

In conclusion, we propose a photonic frequency-multiplied 4096-QAM vector mmW signal generation scheme based on CE-DSM. Benefiting from the CE characteristic of phase modulation, the transmitter precoding and intensity-dependent nonlinear distortion can be effectively avoided when generating a vector mmW signal by photonic frequency multiplication. Additionally, combined with one-bit DSM, the in-band SNR can be dramatically improved, and the spectrum-efficient high-order QAM vector mmW signal can be well generated. We experimentally demonstrate the generation of twofold 0.5-Gbaud and fourfold 0.2-Gbaud 40 GHz 4096-QAM OFDM vector mmW signals and transmission over BtB, 1-m wireless link, and 15-km SSMF hybrid with 1-m wireless link. Results indicate that the BER reaches the HD-FEC threshold of $3.8\times {10}^{-3}$, and the EVM meets the threshold of 1.29%, providing a high spectral efficiency and high-fidelity solution for next-generation MFH systems.