When two signals having overlapping frequency content are received at the same time, they interfere to obstruct detection of the information carried by each individual signal. We introduce here a new nonlinear optoelectronic filtering technique that enables the ability to individually detect two concurrent and spectrally overlapping signals, even when the amplitude ratio between the signals is as high as 100,000. We demonstrate our system for application in steganography where we unveil the information carried by a hidden desired RF signal, while a dominant interferer signal is intentionally transmitted nearby and at the same frequency. Our signal recovery technique, which operates assuming no a priori knowledge of either signal, presents an additional pathway that can be used to control how information can be processed and communicated.
© 2017 Optical Society of America
The problem of detecting a desired weak signal obstructed by a multitude of larger interfering signals remains today one of the fundamental challenges in communications. The solution to this problem would enable the ability to (1) enhance the bandwidth of communication systems through spectral reuse , (2) simultaneously transmit and receive (STAR) signals without interference , (3) uncover signals that would otherwise be jammed by a malicious interferer, (4) strategically hide entire communication channels beneath a fake transmitted interferer , and (5) enhance the detection sensitivity of radar systems. Additionally, in the realm of basic and applied science, many applications fundamentally depend on precision measurements of miniscule signals such as the detection of weak magnetic signatures over the earth’s magnetic field  and the detection of weak cosmic radiation in radio astronomy .
The main challenge to realizing this functionality in traditional systems stems from the need to preserve the information stored on the desired signal and to simultaneously remove the interferer along with its modulated information. In many cases, the spectral content of the desired and interferer signals overlap, and the separation of the two can no longer be performed by a conventional filter. Using principles derived from microwave-photonics [6–15], we report here a new nonlinear filter technique that accomplishes the goal of separating and detecting a desired RF signal buried beneath a dominant interferer. In contrast to the many other methods of signal cancellation that currently exist [16–21], our technique is powerful as it requires no a priori knowledge of the individual signals and thus acts to filter the unwanted interferer and recover the desired signal using only the combined signal available as input. The basis of our technique rests upon a nonlinear optoelectronic filter [22–25] that acts to discriminate between various signals based on signal amplitude, rather than on frequency. This critical distinction enables the unique ability to extract a desired signal, even when other interfering signals are located in close or overlapping frequency proximity. We demonstrate here the suppression of a large signal interferer by >50 dB, which not only enables conventional receivers having 80-dB dynamic range to operate with an effective dynamic range of >130 dB but also enables the recovery of RF signals that would otherwise be challenging to detect due to signal interference. We apply our technique to steganography [3, 26–32], in which we intentionally impose a large-signal interferer spectrally nearby a hidden desired signal such that the interferer masks the signature of the underlying signal. We then use the nonlinear optoelectronic filter as the sole means to uncover the information that was once hidden.
2. Nonlinear Optoelectronic Filter System and Operation
Figure 1 illustrates our concept, which consists of two independent transmitters of asymmetric amplitude representing the desired signal and the interferer. Both signals are broadcast simultaneously and combine to form a superimposed signal with the interferer masking the presence of the desired signal. For an eavesdropper listening in on the communication channel, only the interferer signal appears to be present as the hidden desired signal is too small to be observed. On the other hand, after passing both signals through the nonlinear optoelectronic filter, the interferer signal is suppressed leaving the desired signal visible for detection.
Our experimental system is shown in Fig. 2(a), which depicts a transceiver board consisting of two transmitter channels along with two receiver channels. Transmitter 1 (Tx 1), which represents the interferer, is amplified by 50 dB and reaches a signal amplitude of 20 dBm, while transmitter 2 (Tx 2), which represents the hidden desired signal, is instead output at varying amplitude in the range of −15 dBm to −5 dBm. The two channels are combined using a directional coupler with 10 dB additional insertion loss provided to Tx 2 such that the ratio of amplitudes between the interferer and the desired signal ranges between−35 dB to −45 dB. After passing through the communications channel, ten percent of the combined output is split off and sent to receiver 1 (Rx 1), while the remainder is directed to the nonlinear optoelectronic filter. The output of the optoelectronic filter is passed through a conventional RF filter (5 MHz bandwidth) to remove higher-order nonlinearities and then to receiver 2 (Rx 2) for processing.
The nonlinear optoelectronic filter, which consists of a continuous-wave (CW) laser, Mach-Zehnder (MZ) modulator, and photodiode, first takes in RF information comprising the desired and interferer signals and imprints it as modulation on the laser’s output power. The filtering step occurs when the RF signals are recovered via photodetection of the intensity-modulated laser signal with the voltage output governed by22, 33, 34]. Using a Bessel expansion, the nonlinearity of Eq. (1) is found to contain components at the interferer and desired signal frequencies with the form22]. Moreover, any and all phase or frequency modulated information stored on the interferer does not prevent the interferer from maintaining this critical amplitude and thus also becomes filtered out along with the interferer by the action of the nonlinear optoelectronic filter. This filtering is independent of the frequency of both signals, and therefore the nonlinear optoelectronic filter importantly allows the interferer to be removed independent of frequency separation or total bandwidth. However, for bandwidths that are comparable to the modulator bandwidth, the condition of constant modulation amplitude becomes difficult to maintain, and the attenuation of the interferer becomes reduced.
In our experimental demonstrations of covert communications, the desired signal and interferer channels are independently modulated with a unique pseudorandom quadrature phase-shift keyed (QPSK) sequence, and their carrier frequencies are upconverted to 2.5 GHz prior to transmission. We emphasize that only the combined input of the desired and interferer signals are processed by Rx 1 and by the nonlinear optoelectronic filter, and thus no knowledge of each of the individual signals is known or required. Figures 2(b) and 2(c) depict the measured signals at the two receiver inputs and highlight the powerful effect of the nonlinear optoelectronic filter on suppressing the large-signal interferer. In this example, the desired and interferer signals are intentionally separated in frequency by 1 MHz here to better illustrate the nonlinear filtering effect. Figure 2(b), which corresponds to the signal input to receiver Rx1, shows the combined desired signal and interferer channel without passing through the nonlinear optoelectronic filter. The ratio of signal power is 34 dB, and thus it becomes challenging to recover the desired signal without additional filtering. Figure 2(c) corresponds to the input as seen by receiver Rx 2 and shows the combined signal after passing through the nonlinear optoelectronic filter. From Fig. 2(c), we observe the ratio in signal power to now be 13 dB in favor of the hidden desired signal, which indicates a relative interferer suppression of 47 dB. A nonlinear intermodulation signal is also generated at −1 MHz frequency offset on the opposite side of the removed interferer signal due to the nonlinearity of the filter. This intermodulation signal is lower in amplitude than the original interferer by 34 dB but still can obstruct the detection of the desired signal. We will discuss its implications and removal next.
When the nonlinear intermodulation signal of Fig. 2(c) is well separated in frequency, it can be readily removed by conventional filtering techniques, and the desired signal can be subsequently recovered. However, for our purposes where the desired signal is intentionally positioned in close frequency proximity to an interferer, the resulting intermodulation signal will be too close in frequency to be isolated from the desired signal using conventional techniques of spectral filtering. An additional step is needed to separate the desired signal from the intermodulation signal with the constraint that no previously unavailable information can be used to perform this separation. To achieve this, we developed a signal processing technique for circumventing the intermodulation signal using only the total combined signal available as input. A block diagram of this signal processing technique is illustrated in Fig. 2(d).
In the first step, we multiply the output of the nonlinear optoelectronic filter by the receiver channel that bypasses the filter (Rx 1). The purpose of this step is to use the interferer of the bypass channel to downconvert both the desired signal and intermodulation spur of the filtered channel to baseband. The residual desired signal on the bypass channel is treated as noise in this downconversion. Furthermore, the byproducts of the multiplication arising from sum-frequency generation are subsequently removed using a low-pass filter. The result (see Fig. 2(e)) is a spectrum centered at zero frequency with the desired signal offset to the positive frequency side and the intermodulation spur offset by the same amount in negative frequency. At this point, the individual desired and intermodulation signals coherently combine together to form a single real-valued mixed signal comprising the modulated information of both the desired signal and the interferer. This mixed signal has the following function form
Since the angular frequencies of the desired signal and the interferer can be determined from the output of the nonlinear optoelectronic filter (i.e., Figs. 2(c) and 2(e)), once the modulated information of the interferer is determined, the information stored within the hidden desired signal can be extracted from Eq. (3). Therefore, in parallel to the previous step, we perform demodulation on the bypass channel (Rx 1) to extract the phase modulation stored on the interferer  making use of the fact that the interferer is much larger in amplitude than the desired signal. Afterward, we combine the information of the interferer with that of the mixed signal in Eq. (3) to determine the phase modulation stored in the hidden desired signal. This extraction process is unique except for the case when and are exactly equal. For this case, owing to the fact that cosine is even, an ambiguity arises if is symmetric for its possible positive and negative outcomes. As will be demonstrated later, we circumvent this ambiguity by adding a fixed phase offset to rotate the outcomes away from this symmetry point.
3. Nonlinear Optoelectronic Filter Demonstration – Continuous Wave
Here, we use the previously developed nonlinear optoelectronic filtering process to demonstrate the suppression of a dominant interferer at arbitrary frequencies. Our application critically requires signal recovery for frequency separations between the desired and interferer signals approaching zero. We choose a frequency separation of 4.75 Hz here for ease of visualization; however, we later will demonstrate the nonlinear optoelectronic filter even for cases where the offset is identically zero. The desired and interferer signals are shown in Fig. 3 and are centered at 2.5 GHz separated by 4.75 Hz. For clarity, no phase modulated information is applied to either signal. Initially, the desired signal is 64 dB lower in power compared to the interferer and is completely masked by the interferer’s noise. Upon passing the combined signal through the nonlinear optoelectronic filter, the amplitude difference diminishes to 13 dB, thus signifying that the interferer has been suppressed by 51 dB. The hidden desired signal becomes unmasked through this filtering process, and consequently, the dynamic range requirements of the subsequent receiver also become relaxed by 51 dB. Furthermore, the equivalent Q of a single-pole microwave filter would be ~1011, which is 5−6orders of magnitude larger than the highest quality factor microwave filters available . As before, the intermodulation spur generated at −4.75 Hz offset is an unwanted byproduct of the nonlinear optoelectronic filter but is now located much closer in frequency proximity to the desired signal compared to Fig. 2(c). On top of the 4.75 Hz frequency separation, if modulated information were now introduced onto the signals, the spectral content of the desired signal and intermodulation spur would overlap to obscure the detection of the desired signal. This highlights the need for our signal processing technique introduced earlier for dealing with the problem of the intermodulation signal.
4. Nonlinear Optoelectronic Filter Demonstration – QPSK Modulation
We now experimentally show the use of the nonlinear optoelectronic filter for information-carrying signals by enabling the recovery of a QPSK-modulated desired signal intentionally hidden in the background of an interferer. We also simultaneously investigate the limit to how small the amplitude of the desired signal can be for the signal to still be recovered by our technique. In contrast to the previous cases tested, the signals here are transmitted at 2.5 GHz but separated by zero frequency and also are phase modulated each with a pseudorandom QPSK sequence at a rate of 30 Kbaud. This rate is comparable to the subcarrier channel bandwidth used in typical cellular phone systems .
The left panel of Fig. 4(a) shows the normalized spectrum of the two signals with the interferer 35 dB larger than the desired signal. The resulting signal combining both the desired signal and interferer is directly demodulated, and the recovered phase of the interferer signal obtained through the direct demodulation is shown in the middle panel. From the recovered phase, we find the QPSK phase of the interferer to be nearly identical to the phase ideally transmitted. Thus, the reconstruction of the interferer is nearly perfect here owing to the fact that the extraneous 35-dB lower amplitude desired signal is too small to be seen. A fraction of the combined input is also sent through the nonlinear optoelectronic filter where the phase-modulated information of the desired signal is extracted. The results of this extraction are illustrated in the right panel of Fig. 4(a) where both the ideal QPSK phase and the recovered phase are shown. In this panel, each of the four QPSK levels are clearly definedand accompanied by a slight amount of additional noise that is inherent to our receiver. Even with this noise, no errors are present in the recovered phase after the effects of quantization are accounted for. As a comparison, Fig. 4(b) shows again the normalized input spectrum, demodulated interferer and recovered desired signal, but this time for a desired signal that is 40 dB lower than the interferer in amplitude. As expected, the demodulation of the interferer is nearly perfect. The recovered phase of the desired signal is illustrated in the right panel of Fig. 4(b) and indicates that no phase errors are present, although an increase in the noise from Fig. 4(a) is now observed. Continuing further to Fig. 4(c), the desired signal has decreased to now be 45 dB below the interferer. While the phase recovery of the interferer is again nearly ideal, the right panel of Fig. 4(c) shows that the noise in the desired signal phase has increased even further to now span a width nearing 90°. Despite this noise increase, the four individual levels of the QPSK phase are still clearly distinguishable, and no phase errors are observable in the desired signal.
In order to evaluate the phase error of our nonlinear optoelectronic filter technique, we graphically illustrate the recovered phase for both the interferer and desired signal and compare them to the ideally expected phase. This comparison is shown in Figs. 5(a) and 5(b) for the case when the power ratio between the interferer and desired signal is 35 dB. As is expected from Fig. 4(a), the interferer phase recovery is nearly ideal, and thus the depicted spread in phase is only on average ~1.1° off from the ideally transmitted phase. In comparison, the spread in the recovered desired signal phase is observed to be larger at 13.5° but is otherwise still clearly centered around the intended transmitted phase. With averaging, this RMS phase error can be improved, as will be shown next. We also note that the desiredsignal phases are rotated slightly (22.5°) from the interferer phases to prevent ambiguity in the phase recovery, as discussed previously.
Figure 5(c) compares the RMS phase error in the recovery of the desired signal for the case when the optoelectronic filter is used with the case when traditional demodulation is used. The phase error is plotted for three cases where the power ratio between the interferer and desired signal is varied between 35 dB and 45 dB. By utilizing the optoelectronic filter, the RMS phase error begins at 13.5° for 35 dB power ratio and increases to 26.4° and 63.8° for 40 dB and 45 dB power ratio, respectively. In comparison, without the optoelectronic filter, the direct demodulation of the desired signal instead unintentionally recovers the phase of the dominant interferer signal. Since the interferer is uncorrelated with the desired signal, its phase is on average 90° off from the ideal desired signal phase. Therefore, for all three trials of power ratio, the phase error is near 90° but is slightly off due to the finite number of samples in our trials. In order to improve on the quality of the recovered phase, we perform averaging (50 × ) on the phase points found within each symbol period (Fig. 5(c)). These data points illustrate that even though the phase error of the optoelectronic filter grows as the power ratio between the interferer and desired signal degrades, the recovered phase remains distributed around their ideal values. With an averaging of 50, the correct phase is found with errors of 0.9°, 1.7°, and 4.1° for the 35 dB, 40 dB, and 45 dB cases, respectively. In contrast, because the phase retrieved from direct demodulation is uncorrelated with the ideally transmitted phase, we observe that the RMS phase error remains the same even with averaging.
In order to demonstrate the versatility of the nonlinear optoelectronic filter, we once again intentionally hide the information of a desired signal within the message of an interferer. However, we now control the frequency offset between the two signals to be small but nonzero. Figure 6(a) depicts the spectrum of the desired signal and the interferer with the two signals 31.5 dB apart in amplitude and separated by 10 kHz. Both signals are QPSK modulated, where upon transmission, the individually chosen phase levels of each signal combine to create a pattern once decoded. In Fig. 6(b), the recovered phase of the dominant interferer signal, which would be the only information accessible to an eavesdropper, spells out the letters “MIT”. However, through the use of the nonlinear optoelectronic filter, the true underlying message is displayed, which in this case spells out the letters “LL”. We note that in this experiment, we averaged all the phase points within each symbol period to reduce the noise on the recovered phase.
We have demonstrated a powerful new technique that utilizes a nonlinear optoelectronic filter to remove the presence of a dominant interferer that would otherwise obstruct the detection of an underlying desired signal. We achieved a relative suppression of 51 dB between the interferer and desired signal when the two signals are separated by 4.75 Hz and centered at 2.5 GHz. When combined with a novel method we developed to mitigate the nonlinearities in the optoelectronic filtering process, we showed that the information of both the desired signal and interferer can be accurately detected despite having no a priori knowledge of the individual signals. This gives rise to new possibilities for covert channels of communications, in which we demonstrated the transmission and detection of a desired signal hidden 35 dB – 45 dB beneath an intentionally obstructing interferer located at the same frequency. An analysis of our phase errors showed that we are able to use the nonlinear optoelectronic filter to correctly recover the information stored within the hidden signal, while traditional demodulation methods are only able to successfully detect the hidden information at a rate no better than chance. We note that the restriction of the interferer amplitude to the value currently limits the use of the nonlinear optoelectronic filter to applications where the interferer amplitude is stationary, i.e. not modulated as otherwise would be in quadrature amplitude modulation (QAM). However, we expect that future algorithms could be developed to allow the nonlinear optoelectronic filter to become compatible with signals that are amplitude modulated. Additionally, with further research, we similarly anticipate the potential for the nonlinear optoelectronic filter to handle higher-order modulation formats with the possibility of multiple signals participating. With further improvement to the filter’s interferer suppression, the effective dynamic range available to a subsequent receiver could also be increased by 60 dB or more. Finally, through future advancements in the co-integration of photonics and electronics [37–39], the functionality of the nonlinear optoelectronic filter could be brought onto a semiconductor chip, which greatly reduces its size for implementation into portable devices.
We thank Prof. Rajeev J. Ram at the Massachusetts Institute of Technology and also Dr. Navid Yazdani and Dr. Keith Forsythe at MIT Lincoln Laboratory for helpful discussions. The opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Government.
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