Abstract
A novel wide-band RF receiver based on a dual-OFC-based channelization and spectrum stitching technique is proposed and demonstrated experimentally. In the scheme, a dual-OFC-based channelizer is utilized as the front-end to slice the RF signals into multiple channels. In the back-end, through the channel estimation and spectrum stitching, the received signals can be well reconstructed in the digital domain. A proof-of–concept experiment is performed, in which signals with 3 GHz bandwidths are sliced and reconstructed using the proposed receiver with a normalized mean squared error (NMSE) of 7.9×10−3. The performances of the reconstructed signals on pulse compression are also demonstrated to evaluate the potential of the proposed technique in practical applications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Wide-band RF signal reception is essential in numerous applications, such as telecommunications, electronic warfare, and remote sensing [1,2]. Conventional electronic superheterodyne receiver with direct analog-to-digital conversion can hardly satisfy the increasing bandwidth requirements due to time jitter and sampling rate limits of analog-to-digital converters (ADCs) under large dynamic range [3]. To address the challenge, channelized RF receivers were proposed, theoretically avoiding the tradeoff between the dynamic range and the sampling rate, and further improving the bandwidth, sensitivity, and interference rejection. Consequently, channelized RF receivers have been considered as competitive alternatives for wide-band signal reception [1,4].
Conventional electronic channelized receiver faces two problems: 1) channel equalization is difficult due to poor gain flatness and inconsistency of analog electronic devices over large bandwidths; 2) system complexity increases rapidly as the number of channels increases, leading to problems associated with the increased size, weight, and power consumption (SWaP) of the receiver [1]. Recently, photonic channelized RF receivers are proposed. With the aid of photonic components and technologies, photonic channelized RF receivers have better inter-channel consistency, much wider instantaneous bandwidth, and much smaller SWaP [5]. Furthermore, most of the photonic channelized RF receivers have abilities of reconfiguration in channel bandwidth, channel spacing, and operation frequency range [5–7]. Present photonic channelized receivers can be mostly classified into four categories: direct spectrum slicing [8], single optical frequency comb (OFC) based channelization [9–15], optical superheterodyne channelization [16–18], and dual-OFC-based channelization [6,19–21]. However, most of the studies on photonic channelized receivers neglected the amplitude and phase inconsistency among channels, making it difficult to reconstruct those RF signals with wider bandwidths which would fall into multi-channels. Therefore, these photonic channelized receivers are applied specifically in some electronic warfare applications where only rough power spectrum information is demanded, such as channel detection and frequency measurement. The literature [18] proposed a RF receiver with the capacity in the spectrum reconstruction of the entire RF spectrum based on a superheterodyne channelizer and demonstrated the scheme in a computer simulation experiment. The differences among channels were estimated from the overlap of adjacent channels with the maximum likelihood estimation. But the practicality of the scheme is limited since the statistical characteristics of the received signals are required in the maximum likelihood estimation, which cannot be met in most conditions.
In this paper, a wide-band RF receiver based on dual-OFC-based photonic channelization and spectrum stitching technique is proposed and demonstrated experimentally to increase the reception bandwidth of RF receivers while keeping large dynamic range. In the front-end, the dual-OFC-based photonic channelizer is chosen to slice the RF signal into multiple channels and convert all slices to intermediate frequency (IF) bands, due to its inherent advantages in immunity to the spectrum aliasing problem caused by the square-law detection of photodetectors (PD) [21] and advantages in channel tuning and equalization capabilities brought by OFCs [6,22]. Then, the spectrum stitching is performed in three steps: 1) estimating and compensating the transfer functions of all channels by analyzing the responses of stepped frequency continuous wave (SFCW) pilot signals; 2) estimating and compensating the residual terms of transfer functions, which varies rapidly, from the redundant information contained in the overlaps between adjacent channels; 3) stitching the compensated signals of all channels together. Experiments have been carried out for receiving and precisely reconstructing a nonlinear frequency modulation (NLFM) signal and a band-limited random phase signal both with bandwidths of 3 GHz. To the best of our knowledge, it is the first experimental demonstration of receiving and reconstructing wide-band RF signals fall into multi-channels through a photonic channelizer. The phase error of the reconstructed signals and the performance on pulse compression are also analyzed, verifying the potential of the proposed receiver in practical applications.
2. Principle
As shown in Fig. 1(a), the scheme of the proposed wide-band RF receiver comprises an analog front-end and a digital back-end. In the front-end, a dual-OFC-based channelizer is utilized to slice received wide-band RF signals into different channels and down-convert the sliced signals to IF bands. In the back-end, the digitized sliced signals in different channels are compensated and stitched together using the spectrum stitching technique to reconstruct the received RF signals. The detailed principles are specified as follows.
In the front-end, a carrier OFC with a free spectrum range (FSR) of δsig is modulated by the received wide-band RF signals on a Mach-Zehnder modulator (MZM) biased at the double-sideband suppressed-carrier (DSB-SC) modulation mode to generate the optical signal. Then, in each channel, the upper sideband around a comb line of the optical signal is selected and demodulated by the corresponding comb line of the local OFC (with an FSR of δLO, which is slightly different from the δsig) through a quadrature coherent optical receiver, which is composed of a 90° hybrid coupler (HC), a pair of balanced photodetectors (BPD), and ADCs.
The carrier OFC and the local OFC can be expressed in the frequency domain as
Since the MZM is biased at the DSB-SC modulation mode, the optical signal can be expressed as
Through a demultiplexer with sufficient crosstalk suppression, both the optical signal and the local OFC are multicast into different channels. Subsequently, for the mth channel (m equals to 0, 1, 2, …), the mth copy of the received wide-band RF signal is mixed with the mth comb line of the local OFC in the optical quadrature coherent optical receiver. The process can be written as
In fact, the responses of channels are not ideal. In a practical scenario, the I path and the Q path in the coherent optical receiver are not perfectly matched, and photonic links are sensitive to temperature variation, mechanical vibration, and stress change, due to the micrometer-scale wavelength of lightwave. As a result, under the condition that the nonlinearity of channels can be neglected, the digitized sliced signals in the mth channel can be expressed as
To reconstruct the received wide-band RF signal precisely, the spectrum stitching technique is utilized in the back-end. Firstly, a primary channel estimation and compensation under the assistance of pilot signals is performed. In each channel, a SFCW signal is chosen as the pilot signal for its comb-like spectrum. The center frequency of the pilot signal is set to the same value of the center frequency of the corresponding channel while the bandwidth is slightly larger than the channel bandwidth Bch. The pilot signals of all channels are fed into the dual-OFC-based channelizer in turn, and by recoding the output of each channel, the responses of all comb lines of the pilot signals can be calculated. By estimating the absent values between adjacent comb lines of pilot signals with spline interpolation, the transfer functions Hm,I(f;t) and Hm,Q(f;t) of all channels can be estimated.
However, the repeat rate of pilot signals is limited due to the fact that the channelizer cannot work when the pilot signals exist. As a result, rapid variant terms of the transfer functions can’t be estimated with the pilot-assisted estimation. To solve the problem, a secondary channel estimation is performed. We rewrite Hm,I(f;t) and Hm,Q(f;t) as Gm,I(f;n·Tpilot)·Wm,I(f;t) and Gm,Q(f; n·Tpilot)·Wm,Q(f;t), where Gm,I(f;n·Tpilot) and Gm,Q(f;n·Tpilot) are the transfer function of I path and Q path in the mth channel estimated from the response of pilot signals at the time of nth pilot signal pulse (n equals to 1, 2, 3, …), Tpilot is the repetition period of pilot signals; Wm,I(f;t) and Wm,Q(f;t) are the residual terms of transfer functions. Note that Gm,I(f;n·Tpilot) and Gm,Q(f;n·Tpilot) have been well estimated and compensated in the primary channel estimation and compensation, the signal of the mth channel can be expressed as
All the channel differences can be compensated after the channel estimation and compensation processes discussed above. And the received RF signal can be reconstructed through simply combining the compensated signals of all channels together. Since all the compensations in the back-end are performed with additions and convolutions, both of which are linear operations and will not affect the power ratios between the received signals and the spurious signals, the dynamic range of the whole system is equal to that of each channel in the front-end.
3. Experiment and results
As shown in Fig. 1(c) and Fig. 1(d), in a single channel, only the upper sideband around a comb line of the optical signal and the corresponding comb line of the local OFC are selected by the demultiplexers and sent to the coherent optical receiver. Therefore, in a proof-of-concept experiment, a single channel in a dual-OFC-based channelizer can be equivalently implemented with the experiment setup shown in Fig. 2, in which the carrier OFC and the local OFC are substituted by a pair of coherent continuous-wave (CW) lights with a proper frequency difference. In the scheme, a CW light generated by a laser diode (RIO ORION) with a linewidth of 1 kHz is divided into two paths by a polarization-maintaining 3-dB beam splitter. In the upper path, the light is modulated by a sinusoidal signal with a frequency of m·Δ on an MZM (MZM1) biased at DSB-SC mode. The lower sideband is reserved by an OBPF (WaveShaper 4000S) and amplified as a “new carrier” fed into another null-biased MZM (MZM2), which is driven by the received wide-band RF signal. In the lower path, the light wave is fed into the coherent optical receiver as the optical LO, and mixed with the optical signal generated in the upper path. Then, by filtering and digitizing the quadrature down-converted signal, the output of a single channel is obtained. For other channels, the output signal can be obtained by adjusting the relative position of the RF signal and the carrier light wave in the optical frequency domain, which is determined by the frequency of the sinusoidal RF signal driving the MZM1.
In the experiment, a five-channel dual-OFC-based channelizer covering a frequency range from 10.1 GHz to 13.1 GHz is equivalently implemented as the front-end of the proposed RF receiver with the scheme shown in Fig. 2. The clocks of all RF sources and ADCs are locked to the same reference clock to synchronize the frequency of all channels. The channel spacing Δ and the channel bandwidth Bch are set to 500 MHz and 1 GHz respectively, corresponding to a channel overlap ratio of 50%. As indicated in Eq. (11), a higher channel overlap ratio η will lead to a better performance on channel estimation, while reducing the bandwidth efficiency of the receiver, which is defined as the maximum working bandwidth of the receiver divided by the sum of bandwidths of all channels. Define the RMS error introduced by secondary channel compensation as $\sigma ({2\pi {\kern 1pt} \delta \hat{\tau }{\kern 1pt} f + \delta \hat{\varphi }} )$, where σ(·) means the standard deviation. The 50% channel overlap ratio gives an compensation introduced RMS phase error as 1.5° under a low SNR as 15.83 dB, and consequently is an appropriate value in our experiment based on the trade-off between channel estimation performance and bandwidth efficiency. The frequency of the RF signal driving MZM1 is set to 10 GHz + mΔ (m = 0, 1, … 4) to match the center frequencies of the received RF signals. To estimate the frequently response Gm,I(f;n·Tpilot) and Gm,Q(f;n·Tpilot) of all channels, five SFCW pilot signals, each for a single channel, with frequency steps of 10 MHz and bandwidths of 1.1 GHz are fed into the front-end of the RF receiver in turn every 5 minutes.
A nonlinear frequency modulation (NLFM) signal and a band-limited random phase signal, are produced as wide-band RF signals to be received to demonstrate the performance of the receiver. Both signals have bandwidths of 3 GHz and center frequencies of 11.6 GHz. Beginning tags, which are identified by a period of zero-level signals, are added at the beginning of the signals to be received for temporal alignment.
In the back-end, the digitized signals of all channels are first aligned in time domain by aligning the beginning tags. Then the sliced signals of I path and the Q path obtained in each channels are compensated on the basis of the estimated Gm,I(f;n·Tpilot) and Gm,Q(f;n·Tpilot) of all channels. The frequency response of the I path of the third channel estimated with the pilot signals at the time of 0 min, 5 min, and 10 min are shown in Fig. 3 as a typical case. The zero-order and the first-order terms of the phase-frequency response are eliminated in Fig. 3 for a better observation. The response curves captured at the 0 min, 5 min, and 10 min are almost coincident in both the amplitude-frequency response and the phase-frequency response, which indicates the assumption discussed in section 2 is valid in the experiment.
After that, the compensated I path and the Q path signals of each channel are combined as a complex signal in digital domain. All sliced signals through the primary compensation are shown in Fig. 4. A typical image rejection ratio (IRR) and spurious free dynamic range (SFDR) are measured in the third channel (11.1 GHz∼12.1 GHz) as 45.83 dB and 40.04 dBc respectively.
The differences of residual terms of the transfer functions between adjacent channels are estimated in the secondary channel estimation based on Eq. (10). After the compensation of residual terms of the transfer functions, the sliced signals of all channels are stitched together to reconstruct the received wide-band RF signals. The reconstruction results of the NLFM signal and the band-limited random phase signal are shown in Fig. 5(a) and Fig. 5(c). It can be seen in Fig. 5(a) and Fig. 5(c), the reconstructed signals are exactly coincident with the original RF signals, which means both of the phase and the amplitude responses of all channels are well compensated. And as a comparison, the direct combination results, which are generated by filtering and combining the sliced signals of all channels without any compensation, are presented in Fig. 5(b) and Fig. 5(d).
The normalized mean squared error (NMSE) of the reconstructed NLFM signal and the reconstructed band-limited random phase signal are 7.9×10−3 (with an SNR of 22.03 dB at the output of the channelizer) and 4.08×10−2 (with an SNR of 15.83 dB at the output of the channelizer) respectively. The SNR losses caused by the stitching process are calculated as 1.01 dB for the NLFM signal and 1.93 dB for the band-limited random phase signal, which indicates the NMSE performance of the receiver would be significantly improved if the front-end of the receiver was replaced by a dual-OFC-based channelizer with a higher SNR (a dual-OFC-based channelizer with a SNR of 63 dB has been reported in the literature [6]).
To demonstrate the potential of the proposed wide-band RF receiver in practical applications, the performances on pulse compression and phase error are analyzed. As shown in Fig. 6(a) and Fig. 6(c) the pulse-compression curves of both reconstructed signals are consistent with the ideal pulse-compression curves and give compression ratios of 1.3946×105 for NLFM signal and 3.2830×105 for band-limited random phase signal respectively, which are close to the theoretical values as 1.3940×105 and 3.2616×105. The pulse-compression curves of the direct combination results are also shown in Fig. 6(b) and Fig. 6(d) as comparison. And the RMS phase error of the reconstructed signals are 4.44° and 11.35° respectively.
4. Conclusion
We proposed a novel wide-band RF receiver based on the dual-OFC-based photonic channelizer and the spectrum stitching technique. A dual-OFC-based photonic channelizer is utilized as the front-end to slice the wide-band RF signals in spectrum into different channels and convert them to the IF bands. After analog-to-digital conversion, the sliced signals in all channels are stitched together in the frequency domain with a three-step spectrum stitching processing to reconstruct the original wide-band RF signals. A proof-of-concept experiment is implemented to demonstrate the performance of the receiver. A NLFM signal and a band-limited random phase signal with bandwidths of 3 GHz and center frequencies of 11.6 GHz are sliced into five channels, then reconstructed with NMSEs of 7.9×10−3 and 4.08×10−2 respectively. The performances on pulse compression and phase error of the reconstructed signals are also analyzed, which show the potential of the proposed wide-band RF receiver in practical applications.
Funding
National Natural Science Foundation of China (61690191, 61701476); National Key R&D Program of China (2018YFA0701900, 2018YFA0701901).
Disclosures
The authors declare no conflicts of interest.
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