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Abstract
Channel estimation is a key technology in MIMO-OFDM wireless communication systems. Increasingly extensive application scenarios and exponentially growing data volumes of MIMO-OFDM systems have imposed greater challenges on the speed, latency, and parallelism of channel estimation based on electronic processors. Here, we propose a photonic parallel channel estimation (PPCE) architecture which features radio-frequency direct processing. Proof-of-concept experiment is carried out to demonstrate the general feasibility of the proposed architecture at different frequency bands (100 MHz, 4 GHz, and 10 GHz). The mean square errors (MSEs) between the experimental channel estimation results and the theoretically simulated ones lie on the order of 10−3. The bit error rates (BERs) are below the pre-forward error correction (pre-FEC) threshold. Besides, we analyze the performance of PPCE under different signal-to-noise ratios (SNRs), baseband symbol forms, and weight tuning precisions. The proposed PPCE architecture has the potential to achieve high-speed, highly parallel channel estimation in large-scale MIMO-OFDM systems after the photonic-electronic chip integration.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Orthogonal frequency division multiplexing (OFDM) technology and multi-input multi-output (MIMO) technology are widely used in wireless communication systems, improving spectral efficiency, data transmission quality, and system capacity [1]. In MIMO-OFDM wireless communication systems, the channel state information (CSI) obtained by channel estimation techniques is critical, as it has a significant impact on the accurate implementation of coherent detection and decoding [2] and directly guides the configuration of analog and digital beamformers [3,4]. Currently, complex and extensive application scenarios and exponentially growing data volumes are placing increasingly high demands on the data transmission rate and latency of the systems (e.g., 5 G requires 10-Gbits/s ∼ 20-Gbits/s peak rate and sub-1 ms round-trip latency) [5]. Especially in channel estimation, an increasing number of channel coefficients and long pilot sequences need to be trained, and increasingly stringent latency constraints are imposed [2,6]. These pose growing challenges to existing channel estimation based on electronic processors in terms of computing power proportional to parallelism, data storage, and data transmission [7]. Specifically, channel estimation entails large-scale complex matrix computations, which in turn, requires a large number of transistors working together and additional scheduling procedures to coordinate the movement of data involving weights, resulting in an overall latency on the order of milliseconds [8,9]. Besides, in other electrical signal processing associated with channel estimation (e.g., serial-to-parallel conversion and fast Fourier transform), there is additional latency of microseconds in signal access, processing, storage, and transmission [10,11]. Thus, key performances of channel estimation still have room for improvement in terms of computational speed, latency, and parallelism and our research aims to reduce the latency of the entire channel estimation process and improve the computational speed and parallelism of channel estimation.
Integrated photonic circuits feature ultra-wideband, low-latency, and low energy-consumption. In addition, light has multiple physical dimensions including wavelength, polarization, and spatial modes, enabling highly parallel data processing [9]. Based on these physical advantages, photonic computing architectures for deep neural networks are proposed using cascaded Mach-Zehnder modulators (MZMs) [12], cascaded Mach-Zehnder interferometers (MZIs) [13], cascaded diffractive optical elements (DOEs) [14,15], spatial light modulators (SLMs) [16], micro-ring resonators (MRRs) [17,18], and phase-change materials (PCMs) [19]. Among them, the photonic computing schemes in [13], [17], and [19] can achieve ultra-low sub-nanosecond latency, those in [17] and [19] can achieve ultra-high computing density of tens of tera MACs/s/mm2, and those in [15] and [17] can achieve ultra-low energy consumption on the order of femtojoules per MAC (10−15 J/MAC). Besides, the computing precision of the photonic computing schemes in [13], [15], and [18] is demonstrated over 8 bits [20,21].
In this paper, we propose a photonic parallel channel estimation (PPCE) architecture in the analog domain. The multi-band RF signals received by MIMO antennas without analog-to-digital conversion (ADC) and digital OFDM demodulation are directly fed into the PPCE architecture. Subcarrier demodulation signal loading, channel estimation weight loading, and temporal integration are then conducted in the analog domain of the photonics/electronics hybrid system. The channel estimation results are obtained at the output of the architecture in parallel. Low-speed parallel analog-to-digital converters (ADCs) are used to record the estimated CSI. This architecture has the advantages of parallelism, RF direct processing, and processing signals at different frequency bands in a single system. We design a proof-of-concept experiment to demonstrate the feasibility of the proposed PPCE architecture at multiple frequency bands (100 MHz, 4 GHz, and 10 GHz). The experimental channel estimation results are all consistent with the theoretically simulated ones. The mean square errors (MSEs) of the channel estimation results lie on the order of 10−3, and the bit error rates (BERs) of wireless communication systems are below the pre-forward error correction (pre-FEC) threshold. Furthermore, we analyze the performance of the PPCE under different signal-to-noise ratios (SNRs), baseband symbol forms, and weight tuning precisions. Simulation results indicate that the PPCE can be implemented with current photonic-electronic integration technologies.
2. Basic principles
2.1 Channel estimation in MIMO-OFDM wireless communication systems
Channel estimation is a key technology used to obtain CSI. In the MIMO-OFDM wireless communication system, the signal emitted by the transmitter is transmitted through the wireless channel to the receiver. Due to the inter-symbol interference (ISI) caused by the wireless channel, the MIMO-OFDM wireless communication system needs to obtain CSI through channel estimation techniques, and thus perform channel equalization based on the obtained CSI to reduce the erroneous symbols caused by ISI. Channel estimation techniques can be classified into pilot-aided channel estimation, blind channel estimation, and semi-blind channel estimation [22]. Among them, the pilot-aided channel estimation is implemented by extracting the CSI from pilot symbols known to both transmitter and receiver according to the least squares (LS) criterion or the minimum mean squared error (MMSE) criterion and is selected for its lower computational complexity and higher accuracy [23]. As shown in Fig. 1(a), the conventional electrical implementation of pilot-aided channel estimation requires high-speed ADC after RF reception, OFDM demodulation of digital signals, and electronic matrix multiplication computation based on a certain criterion in sequence to obtain the CSI.
Fig. 1. (a) The conventional wireless communication system with pilot-aided channel estimation. (b) The improved wireless communication system. Only its receiver has been improved, but its transmitter remains the same as that of the conventional one. The channel estimation conventionally implemented by the electronic processor after OFDM demodulation is transformed into the channel estimation implemented by the channel estimation module after RF reception. (c) The channel estimation module based on the PPCE architecture in the improved wireless communication system. It mainly consists of cascaded MZMs, PDs, and electrical power combiners. Besides, the spectrum of a high-speed serial RF signal which is an OFDM signal at 10-GHz carrier frequency and the spectrum of a low-speed parallel baseband signal transformed from the high-speed serial signal by the MZM array are shown above. Here, the OFDM signal has four subcarriers with 100-MHz subcarrier intervals.
Specifically, in MIMO-OFDM systems, the wireless communication process can be expressed as
Using the block-type pilot symbols to obtain the CSI, the transmitted pilot symbol corresponding to transmitting antenna i can be denoted as XiP = (XiP[0],…, XiP[N-1])T, the received pilot symbol corresponding to receiving antenna j can be denoted as YjP = (YjP[0],…, YjP[N-1])T, and the synthesis matrix above can be rewritten as Q = (diag{X1P}FL,…, diag{XMTP}FL) [25]. Then, according to the least squares criterion, the estimated time-domain channel matrix corresponding to receiving antenna j can be expressed as
According to the above principle, if the matrix multiplication computing in Eq. (5) is completed, the channel estimation in MIMO-OFDM systems can be implemented.
2.2 Architecture of photonic parallel channel estimation (PPCE)
The proposed PPCE architecture, shown in Fig. 1(c), mainly consists of cascaded MZMs, photodetectors (PDs), and electrical power combiners. It can realize the photonic matrix multiplication applicable to analog signals. When the MZM is in the push-pull mode, its transfer function can be expressed as
Satisfing -Vπ/2 < uRF(t)<Vπ/2, the output optical field of the MZM does not introduce a phase shift with respect to the input optical field. When the amplitude range of uRF(t) is [-Vπ/8,Vπ/8], our MZM can approximate a linear modulation of the output intensity. Similarly, by cascaded MZMs, one RF signal can implement the linear modulation of the other one loaded on the optical carrier when the two RF signals are synchronized. Besides, with E(t) denoting the optical field, υ0 denoting the frequency of the optical carrier, and P(t) denoting the intensity of the optical carrier, according to the response current of the PD expressed as
2.3 Utilization of PCCE for MIMO-OFDM systems
In OFDM systems, a transmitted RF signal corresponding to the m-th OFDM symbol can be expressed as
where sm(k) is a QAM/PSK symbol mapped at the transmitter and loaded onto the k-th subcarrier of the m-th OFDM symbol by OFDM modulation [27]. The duration range of the m-th OFDM symbol is from (m-1)Tsym to mTsym, where Tsym is the period of an OFDM symbol and can be described as Tsym = 1/Δf. The value of fk is fc + kΔf (k = 0,…, N-1), where fc is the carrier frequency, Δf is the subcarrier interval, and N is the number of subcarriers. When the carrier frequency is equal to an integer multiple of the subcarrier interval, the original transmitted symbol can be recovered from the received RF signal due to the orthogonality between the individual subcarriers. The corresponding equation can be expressed asThus, the element of estimated time-domain channel matrix can be expressed as
Following the above basic principles, we improve the wireless communication system shown in Fig. 1(a) into the system shown in Fig. 1(b) and propose the PPCE architecture shown in Fig. 1(c). Compared with the conventional system in Fig. 1(a), the RF signal received by a MIMO antenna can be directly fed into the channel estimation module in the improved wireless communication system shown in Fig. 1(b) without ADC and digital OFDM demodulation. It simplifies the signal processing associated with channel estimation and reduces the latency of channel estimation, which is a major feature and advantage of our proposed PPCE.
The channel estimation module based on the PPCE architecture in the improved wireless communication system is shown in Fig. 1(c). Due to the ultra-wideband feature of photonic circuits, this architecture can accommodate the processing of multi-band signals received directly from MIMO antennas, which is further illustrated by the proof-of-concept experiment in Section 4. Besides, the signal processings based on this architecture are identical for different received RF signals. Take one of the received RF signals in the MIMO-OFDM system as an example. Firstly, the received RF signal yj(t) is loaded onto the optical field using an MZM, and the output of the MZM is split into identical N optical signals by an optical splitter. Next, the subcarrier demodulation signals obtained from the subcarrier information, i.e. e-j2πfkt k = 0,…, N-1, are loaded onto the N parallel optical signals by the MZM array 1 in parallel, and the output of each MZM in this array is split into identical MTL optical signals. Then, the channel estimation weights obtained from the pilot information known to both the transmitter and receiver, a(i-1)L + l + 1,k + 1, are loaded onto the optical signals by the MZM array 2 in parallel, realizing weighted computations of RF signals. Next, the weighted RF signals loaded on the optical field are detected by the PDs that enable photoelectric conversion, and the outputs of PDs are fed into corresponding electrical power combiners for the summation of the branched electrical signals. Finally, the temporal integral operations of the analog electrical signals are performed by the integrators. According to Eq. (12), the CSI corresponding to each time-domain path of the wireless channel in the MIMO-OFDM system can be obtained by the architecture shown in Fig. 1(c).
Based on the MZM arrays in Fig. 1(c), all subcarrier demodulation signals and all channel estimation weights are loaded onto optical signals in parallel, so that the CSI of all time-domain paths corresponding to one of the receiving antennas can be obtained in parallel. Besides, according to Eq. (4), the channel estimation weights in the matrix QLS, and the subcarrier demodulation signals are identical to the RF signals received by different receiving antennas, so that we can use a wavelength multiplexer (MUX) of the WDM system to achieve parallel processing of all RF signals in the wavelength dimension, obtaining all of the CSI in parallel. For the parallel processing achieved by WDM and MZM arrays and the high signal processing speed mainly limited by the bandwidth of the MZMs and PDs, our proposed PPCE can fulfill its potential as an alternative solution for electronic processors to increase the computational speed and reduce the latency of channel estimation in wireless communication systems.
The spectrum of the received RF signal before the MZM array and the spectrum of one of the parallel signals after the MZM array are also shown in Fig. 1(c). Comparing the two spectrums above, we can see that the high-speed serial RF signal is converted into multiple low-speed parallel baseband signals by the MZM array. Thus, the subsequent signal conversions can be implemented by low-speed parallel ADCs, which is further illustrated by the experimental results in Section 4.
The main advantages of the proposed PPCE are summarized as follows.
- • It replaces the conventional electrical implementation of channel estimation, with the potential to achieve high parallelism, low latency, ultra-wideband, and low energy consumption.
- • As the received RF signals are directly fed into the channel estimation module for PPCE, without ADC and digital OFDM demodulation, it can reduce the latency corresponding to the entire process of channel estimation.
- • Through the MZM arrays in the channel estimation module, high-speed serial RF signals are converted into low-speed parallel baseband signals, allowing for fully parallel signal processing.
- • It is able to process multi-band analog signals using an identical system, reducing the complexity of the hardware system and saving hardware resources.
3. Experimental demonstration
3.1 Experimental setup
We design a proof-of-concept experiment based on the PPCE architecture. The corresponding experimental setup, shown in Fig. 2, contains two branches. A continuous-wave laser diode (Alnair Labs TLG-200) serves as the stable optical source for the first-stage MZM (EOSPACE AX-1 × 2-0MSS-20-PFA-PFA-LV). The RF signals are generated by a multi-channel arbitrary waveform generator (AWG, NI PXIe-8880) and input to the first-stage MZM and the second-stage MZMs, respectively. The channel estimation weights are generated by a voltage source (Keithley 2230G-30-1) and input to the third-stage MZMs. Thus, the weighted computations are realized through cascaded MZMs. The experimental setup currently can load real weights and real signals, using the MZMs in push-pull mode. When the weights or signals are in complex form, their real and imaginary parts can be separately loaded by multiplexing the experimental setup twice. The outputs of the third-stage MZMs are fed into PDs (EOT ET-3600F) in parallel to realize the photoelectric conversions. The detected electrical signals are summed by an electrical power combiner (Talent Microwave RS2W05400-K), whose output is collected by an oscilloscope (Keysight UXR033) for subsequent processing and analysis. The experimental setup is identical to the overall PPCE architecture in functions, so the feasibility of the proposed PPCE can be demonstrated by completing the proof-of-concept experiment.
Fig. 2. The experimental setup of the proof-of-concept experiment. It mainly consists of cascaded MZMs, PDs, and an electrical power combiner which is used for the summation of signals of the two branches. And it can be used to demonstrate the weighted computing function, the photoelectric conversion function, and the summation function of the channel estimation module. Besides, the amplitude-frequency response curve of the electrical power combiner is also shown above.
Since the maximum sampling rate of the multi-channel AWG (NI PXIe-8880) is 100 MSa/s, we adapt the AWG (KEYSIGHT M8195A) to demonstrate the PPCE with higher carrier frequency, e.g., 4 GHz and 10 GHz. Limited by the number of channels, we separately conduct the matrix multiplication of each branch. Figure 2 shows that the amplitude-frequency response curve of the electrical power combiner is relatively flat. If the summation function of the electrical power combiner has been verified in the proof-of-concept experiment at a lower frequency band, the electrical power combiner will still perform the summation at a higher frequency band. Therefore, the proof-of-concept experiment can be implemented at multiple frequency bands including 4 GHz and 10 GHz.
3.2 Experimental results
In the proof-of-concept experiment, we set the carrier frequencies of the RF signals input to the MZMs to 100 MHz, 4 GHz, and 10 GHz, respectively. We first theoretically simulate a MIMO-OFDM wireless communication system based on QPSK/16QAM symbols with two transmitting antennas, two receiving antennas, and four subcarriers. Then, the corresponding signal generation, processing, and acquisition are achieved by the experimental setup described above. Next, the signals acquired through the high-speed oscilloscope are subsampled digitally, which is equal to acquiring the experimental signals with low-speed ADCs. The subsampled experimental signals and theoretically simulated signals are displayed in Fig. 3. The waveforms of the above two types of signals are similar, although some noise is introduced into the experimental signals. The final experimental and simulation results of channel estimation are also displayed in each panel of Fig. 3. The experimental channel estimation results are all consistent with the theoretically simulated ones. From the MSEs between the experimental and simulation results shown in Table 1, we can see that the MSEs based on QPSK/16QAM symbols under different frequency bands are similar and lie on the order of 10-3, which can satisfy the basic requirements of channel estimation. These demonstrate that the correct channel estimation results can be achieved and the low-speed ADCs can meet the signal conversion requirements of channel estimation after converting high-speed serial RF signals into low-speed parallel baseband signals by the MZM arrays.
Fig. 3. The experimental signals from the proof-of-concept experiment, the theoretically simulated signals, and their corresponding channel estimation results, including (a) four sets of the results at 100-MHz carrier frequency with QPSK symbols, (b) four sets of the results at 4-GHz carrier frequency with QPSK symbols, (c) four sets of the results at 10-GHz carrier frequency with QPSK symbols, and (d) four sets of the results at 4-GHz carrier frequency with 16QAM symbols. The subcarrier intervals in (a), (b), (c), and (d) are 1 MHz, 40 MHz, 100 MHz, and 40 MHz, respectively, the sampling rates in (a), (b), (c), and (d) are 10 MSa/s (subsampled from 1 GSa/s digitally), 400 MSa/s (subsampled from 80 GSa/s digitally), 1 GSa/s (subsampled from 80 GSa/s digitally), and 400 MSa/s (subsampled from 128 GSa/s digitally), respectively, and the subsampled signals all contain 10 samples. By recovering the amplitude of the experimental signals with reference to the calibration signals, performing the integration computations, and eliminating the external DC components with noise, the final experimental results of channel estimation can be obtained, as shown in each panel of (a), (b), (c), and (d), respectively. Besides, the simulation results of channel estimation are also shown in each panel of (a), (b), (c), and (d), respectively.
Table 1. The MSEs between the experimental results and the simulation results
3.3 Performance analysis of experimental results
Based on the channel estimation results of the proof-of-concept experiment, the channel equalization in the 2 × 2 MIMO-OFDM wireless communication system can be realized, and the corresponding constellation diagrams after channel equalization can be obtained. After demapping the received symbols into binary bitstreams through the demapper, the BER-SNR curves can also be obtained. Besides, in wireless communication systems, forward error correction (FEC) techniques are often used to increase the reliability of wireless communication. As shown in Fig. 1(a), FEC coding is performed before mapping at the transmitter and FEC decoding after demapping at the receiver. Among FEC techniques, the FEC technique based on soft decision (SD-FEC) has a superb BER correction capability, while SD-FEC decoding can introduce latency of hundreds of microseconds, posing a challenge to MIMO-OFDM wireless communications [28]. It is encouraged to investigate how to use photonic matrix computing techniques to accelerate FEC decoding as well, tackling the latency challenge imposed on MIMO-OFDM wireless communications. Currently, the pre-FEC BER corresponding to the 1 × 10−15 post-FEC BER, i.e. the pre-FEC threshold, has reached 1.8 × 10−2 ∼ 2.5 × 10−2 [29–32]. In other words, before FEC decoding at the receiver, if the BER is below the above threshold, the basic requirement of the wireless communication systems can be met.
In the form of BER-SNR curves with the pre-FEC threshold and constellation diagrams, the performance analyses of the experimental results are shown in Fig. 4. As shown in Fig. 4(a), the BER-SNR curve corresponding to the experimental results at the 100-MHz carrier frequency is close to the curves corresponding to the simulation results. Compared with the case without channel equalization, the reliability of the MIMO-OFDM wireless communication system with channel estimation and channel equalization is improved, which can meet the basic requirement of wireless communication systems.
Fig. 4. The performance analyses of the experimental results at multiple carrier frequencies. (a) shows the BER-SNR curves in the 2 × 2 MIMO-OFDM system with QPSK symbols at 100-MHz carrier frequency. (b) and (c) respectively show the constellation diagrams before and after channel equalization corresponding to the case in (a) at 0-dB SNR. (d) shows the BER-SNR curves in the 2 × 2 MIMO-OFDM system with QPSK symbols at 4-GHz carrier frequency. (e) and (f) respectively show the constellation diagrams before and after channel equalization corresponding to the case in (d) at -8-dB SNR. (g) shows the BER-SNR curves in the 2 × 2 MIMO-OFDM system with QPSK symbols at 10-GHz carrier frequency. (h) and (i) respectively show the constellation diagrams before and after channel equalization corresponding to the case in (g) at -4-dB SNR. (j) shows the BER-SNR curves in the 2 × 2 MIMO-OFDM system with 16QAM symbols at 4-GHz carrier frequency. (k) and (l) respectively show the constellation diagrams before and after channel equalization corresponding to the case in (j) at 8-dB SNR. Besides, in (a), (d), (g), and (j), from top to bottom are the BER-SNR curves corresponding to two antennas in the cases of no channel equalization, channel equalization based on the experimental results, and channel equalization based on the simulation results.
The role of the channel estimation module can be illustrated more intuitively in the form of constellation diagrams. After transmission over the wireless channel, the symbols which are initially located in the second quadrant of the constellation diagram are shifted to the fourth quadrant. As shown in Figs. 4(b) and (c), the received symbols are restored to the second quadrant, which significantly reduces the BER of the MIMO-OFDM wireless communication system. What’s more, similar conclusions can be drawn from the performance analyses of the experimental results at the 4 GHz with QPSK symbols in Figs. 4(d), (e), and (f), experimental results at the 10 GHz with QPSK symbols in Figs. 4(g), (h), and (i), and experimental results at the 4 GHz with 16QAM symbols in Figs. 4(j), (k), and (l). In short, the experimental channel estimation results are all consistent with the theoretically simulated ones; the MSEs of the channel estimation results lie on the order of 10−3; and the BERs of wireless communication systems are below the pre-FEC threshold. Thus, our proposed PPCE is feasible and is able to process multi-band analog signals using an identical system.
4. Discussion
The noise and losses introduced by the channel estimation module measured in the form of SNR, the weight tuning precision, and the baseband symbol forms can affect the performance of the PPCE. In this section, we firstly analyze the performance of the PPCE under different SNRs, baseband symbol forms, and weight tuning precisions in the 2 × 2 MIMO-OFDM system with four subcarriers. The BER-SNR curves obtained from the above simulation analyses are shown in Fig. 5. The BER-SNR curves corresponding to experimental results with QPSK/16QAM symbols are shown in Fig. 5 as well. As shown in Fig. 5(a), the BER-SNR curve corresponding to the experimental results with QPSK symbols is close to the BER-SNR curve under 7-bit precision and 20-dB SNR. The basic requirements of wireless communication systems based on QPSK symbols can be met under 5-bit precision and 13-dB SNR. As shown in Fig. 5(b), the BER-SNR curve corresponding to the experimental results with 16QAM symbols is close to the BER-SNR curve under 7-bit precision and 20-dB SNR. The basic requirements of wireless communication systems based on 16QAM symbols can be met under 6-bit precision and 20-dB SNR.
Fig. 5. The BER-SNR curves with experimental results. (a) is in the 2 × 2 MIMO-OFDM system based on QPSK symbols. The precisions include 9 bits, 7 bits, and 5 bits. The SNRs include infinity, 20 dB, and 13 dB. The BER-SNR curve from one set of experimental results with QPSK symbols is also shown in (a) as a contrast. (b) is in the 2 × 2 MIMO-OFDM system based on 16QAM symbols. The precisions include 9 bits, 7 bits, and 6 bits. The SNRs include infinity, 27 dB, and 20 dB. The BER-SNR curve from one set of experimental results with 16QAM symbols is also shown in (b) as a contrast.
Then, we analyze the performance of the PPCE in the 4 × 4 and 8 × 8 MIMO-OFDM systems both with 128 subcarriers. As shown in Fig. 6, the wireless communication systems based on high-order baseband symbols like 64QAM symbols have stricter restrictions on the precision and the SNR of the channel estimation module. Specifically, the basic requirements of wireless communication systems based on 64QAM symbols can be met under 7-bit precision and 27-dB SNR.
Fig. 6. The BER-SNR curves. (a) is in the 4 × 4 MIMO-OFDM system based on QPSK symbols. (b) is in the 8 × 8 MIMO-OFDM system based on QPSK symbols. In (a) and (b), the precisions include 9 bits, 7 bits, and 5 bits and the SNRs include infinity, 20 dB, and 13 dB. (c) is in the 4 × 4 MIMO-OFDM system based on 16QAM symbols. (d) is in the 8 × 8 MIMO-OFDM system based on 16QAM symbols. In (c) and (d), the precisions include 9 bits, 7 bits, and 6 bits and the SNRs include infinity, 27 dB, and 20 dB. (e) is in the 4 × 4 MIMO-OFDM system based on 64QAM symbols. (f) is in the 8 × 8 MIMO-OFDM system based on 64QAM symbols. In (e) and (f), the precisions include 9 bits, 8 bits, and 7 bits and the SNRs include infinity, 34 dB, and 27 dB. In all the above figures, the number of subcarriers is 128.
The above requirements for precision and SNR can be implemented with current photonic-electronic integration technologies in the PPCE architecture. Besides, due to the booming development of the chip-scale photonic-electronic hybrid integration technology, the manufacture of the large-scale integrated channel estimation module is promising [33]. With the large-scale integration of the channel estimation module, high-speed, highly parallel channel estimation will be achieved in MIMO-OFDM wireless communication systems with much more subcarriers and antennas. Thus, the above simulations and analyses further demonstrate the feasibility and development prospects of our proposed PPCE.
5. Conclusion
We have proposed a photonic parallel channel estimation (PPCE) architecture in the analog domain. This architecture has the advantages of parallelism and RF direct processing. Besides, it can process RF signals at different frequency bands in a single system. We have designed a proof-of-concept experiment and corresponding experimental setup to examine the feasibility of the proposed PPCE architecture at multiple frequency bands (100 MHz, 4 GHz, and 10 GHz). The experimental channel estimation results are all consistent with the theoretically simulated ones. The MSEs of the channel estimation results lie on the order of 10−3, and the BERs of wireless communication systems are below the pre-FEC threshold, which can meet the basic requirements of MIMO-OFDM wireless communication, proving the feasibility of PPCE. Furthermore, we have analyzed the performance of the PPCE under different SNRs, baseband symbol forms, and weight tuning precisions. Simulation results indicate that the PPCE can be implemented with current photonic-electronic integration technologies.
Faced with the 10-µs round-trip latency and tens of Peta MACs per second for beyond-5 G wireless communications, our proposed PPCE has the potential to meet these requirements, despite introducing additional lasers, modulators, and PDs [34]. Besides, in the near future, the chip-scale photonic-electronic hybrid integration technology will increase the parallelism of the channel estimation module, supporting photonic channel estimation in larger-scale MIMO-OFDM systems and reducing the reuse of the channel estimation module. Based on the trade-off between optimal computing power and minimal complexity achieved by matrix tiling [8], the hardware implementation complexity and cost will be reduced. By improving the weight loading method based on MZMs, the multiplication of complex matrices will be achieved, reducing the reuse of the channel estimation module and the overall latency of channel estimation. Furthermore, higher-speed MZMs and PDs will also effectively increase the computational speed of the PPCE. In a word, the proposed PPCE has the potential to better exploit the advantages of photonic computing and achieve higher speed and parallelism.
Funding
National Key Research and Development Program of China (2019YFB2203700); National Natural Science Foundation of China (62205203, T2225023).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but can be obtained from the authors upon reasonable request.
References
1. P. Zhang, K. Niu, H. Tian, G. Nie, X. Qin, Q. Qi, and J. Zhang, “Technology prospect of 6 G mobile communications,” Journal on Communications 40(1), 141–148 (2019).
2. H. Ye, G. Y. Li, and B. Juang, “Power of Deep Learning for Channel Estimation and Signal Detection in OFDM Systems,” IEEE Wireless Commun. Lett. 7(1), 114–117 (2018). [CrossRef]
3. H. Ye and G. Y. Li, “Initial Results on Deep Learning for Joint Channel Equalization and Decoding,” 2017 IEEE 86th Vehicular Technology Conference (VTC-Fall), 1–5 (2017).
4. W. Ma, C. Qi, Z. Zhang, and J. Cheng, “Sparse Channel Estimation and Hybrid Precoding Using Deep Learning for Millimeter Wave Massive MIMO,” IEEE Trans. Commun. 68(5), 2838–2849 (2020). [CrossRef]
5. N. Hassan, K. L. A. Yau, and C. Wu, “Edge Computing in 5G: A Review,” IEEE Access 7, 127276–127289 (2019). [CrossRef]
6. H. Hua, X. Wang, and Y. Xu, “Signal Detection in Uplink Pilot-Assisted Multi-User MIMO Systems with Deep Learning,” 2019 Computing, Communications and IoT Applications (ComComAp), 369–373 (2019).
7. C. Li, X. Zhang, J. Li, T. Fang, and X. Dong, “The challenges of modern computing and new opportunities for optics,” PhotoniX 2(1), 1–31 (2021). [CrossRef]
8. M. Salmani, A. Eshaghi, E. Luan, and S. Saha, “Photonic computing to accelerate data processing in wireless communications,” Opt. Express 29(14), 22299–22314 (2021). [CrossRef]
9. J. Cheng, H. Zhou, and J. Dong, “Photonic Matrix Computing: From Fundamentals to Applications,” Nanomaterials 11(7), 1683 (2021). [CrossRef]
10. S. Liu and D. Liu, “A high-flexible low-latency memory-based FFT processor for 4 G, WLAN, and future 5 G,” IEEE Trans. VLSI Syst. 27(3), 511–523 (2019). [CrossRef]
11. M. Garrido, “A survey on pipelined FFT hardware architectures,” J. Sign. Process Syst. 94(6), 1–20 (2021). [CrossRef]
12. S. Xu, J. Wang, H. Shu, Z. Zhang, S. Yi, B. Bai, X. Wang, J. Liu, and W. Zou, “Optical coherent dot-product chip for sophisticated deep learning regression,” Light: Sci. Appl. 10(1), 221 (2021). [CrossRef]
13. Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englind, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11(7), 441–446 (2017). [CrossRef]
14. X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018). [CrossRef]
15. T. Zhou, X. Lin, J. Wu, Y. Chen, H. Xie, Y. Li, J. Fan, H. Wu, L. Fang, and Q. Dai, “Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit,” Nat. Photonics 15(5), 367–373 (2021). [CrossRef]
16. Y. Zuo, B. Li, Y. Zhao, Y. Jiang, Y. C. Chen, P. Chen, G. B. Jo, J. Liu, and S. Du, “All-optical neural network with nonlinear activation functions,” Optica 6(9), 1132–1137 (2019). [CrossRef]
17. A. N. Tait, T. F. De Lima, M. A. Nahmias, H. B. Miller, H. T. Peng, B. J. Shastri, and P. R. Prucnal, “Silicon photonic modulator neuron,” Phys. Rev. Appl. 11(6), 064043 (2019). [CrossRef]
18. X. Xu, M. Tan, B. Corcoran, J. Wu, A. Boes, T. G. Nguyen, S. T. Chu, B. E. Little, D. G. Hicks, R. Morandotti, A. Mitchell, and D. J. Moss, “11 TOPS photonic convolutional accelerator for optical neural networks,” Nature 589(7840), 44–51 (2021). [CrossRef]
19. J. Feldmann, N. Youngblood, M. Karpov, H. Gehring, X. Li, M. Stappers, M. Le Gallo, X. Fu, A. Lukashchuk, A. S. Raja, J. Liu, C. D. Wright, A. Sebastian, T. J. Kippenberg, W. H. P. Pernice, and H. Bhaskaran, “Parallel convolutional processing using an integrated photonic tensor core,” Nature 589(7840), 52–58 (2021). [CrossRef]
20. H. Zhou, J. Dong, J. Cheng, W. Dong, C. Huang, Y. Shen, Q. Zhang, M. Gu, C. Qian, H. Chen, Z. Ruan, and X. Zhang, “Photonic matrix multiplication lights up photonic accelerator and beyond,” Light: Sci. Appl. 11(1), 30 (2022). [CrossRef]
21. J. Wu, X. Lin, Y. Guo, J. Liu, L. Fang, S. Jiao, and Q. Dai, “Analog Optical Computing for Artificial Intelligence,” Engineering 10(1), 133–145 (2022). [CrossRef]
22. Z. Gao, L. Dai, C. Hu, X. Gao, and Z. Wang, Channel estimation for mmWave massive MIMO systems, Academic Press, online at https://doi.org/10.1016/B978-0-12-804418-6.00006-6, 113–139 (2017).
23. M. K. Ozdemir and H. Arslan, “Channel estimation for wireless OFDM systems,” IEEE Commun. Surv. Tutorials 9(2), 18–48 (2007). [CrossRef]
24. Y. S. Cho, J. Kim, W. Y. Yang, and C. G. Kang, MIMO-OFDM Wireless Communications with MATLAB, John Wiley & Sons111–136 (2010).
25. L. Li, Principles, applications and simulations for MIMO-OFDM systems, (China Machine Press, 2014), pp. 89–121.
26. Y. Li, Y. Zhang, and Y. Huang, “Any Bias Point Control Technique for Mach-Zehnder Modulator,” IEEE Photonics Technol. Lett. 25(24), 2412–2415 (2013). [CrossRef]
27. A. Goldsmith, Multicarrier Modulation with Overlapping Subchannels (Cambridge university press, 2005), pp. 374–401.
28. C. Tarver, M. Tonnemacher, H. Chen, J. Zhang, and J. R. Cavallaro, “GPU-based, LDPC decoding for 5 G and beyond,” IEEE Open J. Circuits Syst. 2, 278–290 (2021). [CrossRef]
29. G. Tzimpragos, C. Kachris, I. B. Djordjevic, M. Cvijetic, D. Soudris, and I. Tomkos, “A Survey on FEC Codes for 100 G and Beyond Optical Networks,” IEEE Commun. Surv. Tutorials 18(1), 209–221 (2016). [CrossRef]
30. T. Yoshida, M. Karlsson, and E. Agrell, “Performance Metrics for Systems With Soft-Decision FEC and Probabilistic Shaping,” IEEE Photonics Technol. Lett. 29(23), 2111–2114 (2017). [CrossRef]
31. T. Yoshida, A. Alvarado, M. Karlsson, and E. Agrell, “Post-FEC BER Benchmarking for Bit-Interleaved Coded Modulation With Probabilistic Shaping,” J. Lightwave Technol. 38(16), 4292–4306 (2020). [CrossRef]
32. X. Liu, Optical Communications in the 5 G Era (Academic Press, 2021), Chap. 8.
33. A. H. Atabaki, S. Moazeni, F. Pavanello, H. Gevorgyan, J. Notaros, L. Alloatti, M. T. Wade, C. Sun, S. A. Kruger, H. Meng, K. A. Qubaisi, I. Wang, B. Zhang, A. Khilo, C. V. Baiocco, M. A. Popović, V. M. Stojanović, and R. J. Ram, “Integrating photonics with silicon nanoelectronics for the next generation of systems on a chip,” Nature 556(7701), 349–354 (2018). [CrossRef]
34. D. C. Nguyen, M. Ding, P. N. Pathirana, A. Seneviratne, J. Li, D. Niyato, O. Dobre, and H. V. Poor, “6 G Internet of Things: A comprehensive survey,” IEEE Internet Things J. 9(1), 359–383 (2022). [CrossRef]
