Digital Self-Interference Cancellation under Nonideal RF Components: Advanced Algorithms and Measured Performance

Digital Self-Interference Cancellation under Nonideal RF Components: Advanced Algorithms and Measured Performance Dani Korpi, Timo Huusari, Yang-Seok Choi, Lauri Anttila, Shilpa Talwar, and Mikko Valkama Department of Electronics and Communications Engineering, Tampere University of Technology, Finland, e-mail: dani.korpi@tut.fi, timo.huusari@tut.fi, lauri.anttila@tut.fi, mikko.e.valkama@tut.fi Intel Corporation, Hillsboro, Oregon, USA, e-mail: yang-seok.choi@intel.com Intel Corporation, Santa Clara, California, USA, e-mail: shilpa.talwar@intel.com Abstract This paper addresses digital self-interference cancellation in a full-duplex radio under the distortion of practical RF components. Essential self-interference signal models under different RF imperfections are first presented, and then used to formulate widely linear, nonlinear and augmented nonlinear digital canceler structures. Furthermore, a general parameter estimation procedure based on least squares is laid out. Digital cancellation with actual measured self-interference signals is then performed using all the presented methods. To ensure a realistic scenario, the used transmitter has realistic levels of I/Q imbalance, and is also utilizing a highly nonlinear low-cost power. Furthermore, a realistic RF canceler is incorporated in the measurements, and both shared-antenna and dual-antenna based devices are measured and experimented. The obtained results indicate that only a digital canceler structure capable of modeling all the essential impairments is able to suppress the self-interference close to the receiver noise floor. Index Terms Full-duplex, self-interference, I/Q imbalance, nonlinear distortion, digital cancellation I. INTRODUCTION In-band full-duplex communications is a recent innovation in the field of wireless communications [1] [3]. In theory, it can double the spectral efficiency of the existing communications systems by utilizing all the spectral and temporal resources for both transmission and reception, i.e., transmitting and receiving at the same center-frequency at the same time. This makes fullduplex communications a very interesting prospect, as it can significantly help the future networks in obtaining the required throughputs. The potential of in-band full-duplex communications has already been demonstrated by actual prototypes [1], [2], [4], [5] as well as by a large amount of theoretical analysis, addressing various circuit impairments and deployment scenarios [6] [9]. The fundamental challenge behind in-band full-duplex communications is the problem of the own transmit signal coupling back to the receiver. This so-called self-interference (SI) must be heavily attenuated, as it will otherwise saturate the receiver chain, or in the very least make the detection of the received signal of interest very challenging. Typically, the SI signal is first attenuated at the input of the receiver chain by subtracting a properly delayed and attenuated version of the own transmit signal from the total received signal [1], [2]. This cancellation stage is referred to as RF cancellation, and it decreases the power of the total receiver input signal to a suitable level so that the receiver chain components will not be completely saturated. Usually, additional SI cancellation is still performed in the digital domain, referred to as digital cancellation [1], [10]. Ideally, after both of these cancellation stages the SI signal has been attenuated sufficiently low to achieve an adequate signal-to-interferenceplus-noise ratio (SINR) for detecting the received signal of interest. The previous research has, among other things, shown that the different circuit nonidealities are a significant issue in in-band full-duplex transceivers. This is caused by the fact that the SI signal is extremely powerful when it reaches the receiver chain, which means that even a relatively mild distortion can turn out to be significant with respect to the weak received signal of interest. I/Q imbalance and the nonlinear distortion induced by the transmitter power (PA) have been shown to be particularly prominent [7], [10]. These impairments are especially harmful to the digital canceler, assuming that it utilizes only classical linear processing [7], [8], [10]. Under such circumstances, neither the nonlinear distortion nor the I/Q imbalance can be suppressed, resulting in an unacceptably high residual SI power [11]. In this paper, we present different widely linear and nonlinear digital cancellation solutions, building on the behavioral SI signal modeling under imperfect RF components, most notably I/Q imbalance and nonlinear PA. We also evaluate the performance of the algorithms with actual RF measurements. The most advanced algorithm is capable of modeling both the I/Q imbalance and transmitter PA induced nonlinear distortion, thereby making such digital canceler resistant to these circuit impairments [11]. Its performance will also be directly compared to other solutions, which illustrates the gains that can be achieved by utilizing more elaborate digital processing. The parameter learning for all algorithms is done with a straight-forward block least squares approach. The rest of this paper is organized as follows. The system model for the considered full-duplex radio transceiver, alongside with the digital canceler structures, are described in Section II. After this, the parameter estimation procedure is discussed in detail in Section III. The measurement results are then presented and analyzed in Section IV, after which the conclusions are drawn in Section V.

Transmitter chain Power Variable gain I/Q Mixer IQ Mixer Low-pass Digital-to-analog converter Transmit data OR Wideband RF cancellation circuit Local oscillator Receiver chain Self-interference regeneration + Σ Band-pass Low-noise I/Q Mixer Low-pass Variable gain Analog-todigital converter Σ + Digital cancellation To detector Fig. 1. A block diagram of the considered full-duplex transceiver, showing both the circulator and dual antenna based layouts. II. SELF-INTERFERENCE MODELS AND CANCELER STRUCTURES The modeling of the in-band full-duplex transceiver is done based on the block diagram in Fig. 1, which depicts a typical structure for a full-duplex transceiver. There, two different layouts for the antenna interface are shown. The upper option shows a layout where the transmitter and receiver are separated by a circulator, which provides a certain level of passive isolation, while allowing for the use of only a single antenna [12, Chapter 9]. In the lower layout, a dual antenna setup is shown, where the transmitter and receiver have their own separate antennas, and the passive isolation is provided by the path loss occurring between them. Typically, a significant amount of additional SI cancellation is required in addition to the passive isolation, regardless of the number of antennas, and thus the full-duplex transceiver model includes an active RF cancellation stage, followed by an active digital canceler after the analog-todigital conversion. Together, all the cancellation stages must be able to suppress the SI below the receiver noise floor. As already discussed, the different RF impairments occurring in the full-duplex transceiver are crucial in terms of achieving the required level of SI cancellation. If the models used in generating the digital cancellation signal are not capable of reproducing an accurate copy of the observed SI signal, the performance of the full-duplex transceiver will be insufficient. Typically, this is the case when using a linear signal model for the SI [7], [8], [10]. In fact, recent results indicate that joint modeling of several sources of impairments is required to facilitate the use of the higher transmit powers [7]. Thus, the emphasis in this paper is on practical scenarios where the effects of both I/Q imbalance and transmitter PA nonlinearities are included in the SI signal model as well as in the corresponding digital canceler. Referring to Fig. 1, this means that the full-duplex transceiver is assumed to be otherwise linear, apart from the transmitter PA and the I/Q mixers. Following the derivations in [11], the observed SI signal in the digital domain can then be written as P p r(n) = h p (q,p q) (m)x(n m) q x (n m) p q p=1 + z(n), (1) where P is the highest considered nonlinearity order, M is the total memory length, h p (q,p q) (m) contains the unknown true coefficients of the signal model, x(n) is the original digital transmit signal, and z(n) represents the modeling error. Note that the signal model in (1) is here written for a SISO transceiver, unlike in [11], because the used measurement setup only supports a single transmitter and a single receiver. Also, the essential signal model is unaffected by the chosen antenna layout, i.e., it is the same for both circulator and dual antenna based setups. In general, (1) forms a robust basis for digital SI cancellation, with basis functions of the form x(n m) q x (n m) p q. Different cancellation solutions correspond then to different approximations of this model, where only different subsets of the basis functions are eventually deployed, leading to different levels of modeling accuracy and computational complexity. These are elaborated below. A. Linear Digital Canceler The crudest approximation of all is made by the linear digital canceler. Now, only the linear component is considered in the SI signal model and all the other basis functions are ignored. In other words, corresponding to the notation used in (1), the values for P and q are fixed to 1. The resulting SI signal estimate can be written as m=0 ĥ (1,0) 1 (m)x(n m), (2) where ĥ(1,0) 1 (m) is the estimate of the linear SI channel. The benefit of the linear canceler is that it is enough to estimate the coefficients of only the linear basis function, which corresponds to the original transmit signal. However, as already discussed, in most cases this is not sufficient to achieve the required cancellation accuracy. B. Widely Linear Digital Canceler Due to the severity of the I/Q imbalance in most low-cost radio transceivers nowadays, considering it in the SI modeling is typically highly beneficial [7]. The complexity of the SI signal model will slightly increase with respect to the linear canceler but the potential improvement in the cancellation capability is also significant. Referring to (1), the widely linear canceler merely

means that the value for P is set to 1, which results in two basis functions: the linear SI component and its complex conjugate. Thus, the SI signal estimate is 1 ĥ (q,1 q) 1 (m)x(n m) q x (n m) 1 q, (3) where ĥ(q,1 q) 1 (m) contains the channel estimates for the linear SI (q = 1) and its I/Q mirror image (q = 0) [7]. Assuming the same memory length for both estimates, the number of parameters is doubled with respect to the linear canceler since there are now two basis functions instead of only one. C. Nonlinear Digital Canceler The next step in increasing the complexity of the SI signal model is the nonlinear digital canceler, which takes into account the nonlinear distortion produced by the transmitter PA. Typically, it is not necessary to model the nonlinearities produced by the other components since usually the transmitter PA produces most of the nonlinear distortion [8]. The nonlinear signal model, first proposed in [10], can be obtained from (1) by setting q = (p + 1)/2 and p q = (p 1)/2. The corresponding estimate for the SI signal is then as follows. P p=1 m=0 ĥ ( p+1 2, p 1 2 ) p (m)x(n m) p+1 2 x (n m) p 1 where, again, p (m) contains the SI channel estimates for the different basis functions. It can be easily calculated that the number of basis functions, whose respective channel coefficients must be estimated, is now (P + 1)/2, which means that the nonlinear canceler is bound to be somewhat more computationally demanding than the linear or widely linear canceler. p+1 2 ĥ(, p 1 2 ) D. Augmented Nonlinear Digital Canceler It has been shown that under typical levels of I/Q imbalance and PA nonlinearity, modeling only one of these impairments might not be sufficient to achieve reasonable SINR levels [11]. For this reason, this paper provides measurement results with a full augmented nonlinear digital canceler, which is capable of modeling transmitter and receiver I/Q imbalance, alongside with a heavily nonlinear transmitter PA. This type of a solution can be expected to provide a significant improvement in performance with the higher transmit powers [7], [11]. In this case, the SI signal model used in the digital canceler consists of (1) without any approximations. The corresponding estimate of the SI signal is written as P p ĥ (q,p q) p (m)x(n m) q x (n m) p q, p=1 with ĥ(q,p q) p (m) again containing the SI channel estimates. Using the full augmented nonlinear SI signal model in the digital canceler will obviously result in an increase in the number 2, (4) (5) of basis functions, for which the channel coefficients must be estimated. It can be shown that this particular signal model contains ( ) ( P +1 P +1 2 2 + 1 ) basis functions. Thus, the computational complexity of the augmented nonlinear canceler can be rather high, but the cancellation performance is also likely to be significantly better compared to previous solutions. III. PARAMETER LEARNING To lay out the parameter learning procedure, let us resort to vector-matrix notation. The SI signal observed over a period of length N can easily be expressed as r = Ψh + n, (6) where r = [ r(n) r(n + 1) r(n + N 1) ] T, h contains the true parameters of the used signal model, n is the noise signal that contains also the error introduced by the possible mismatch in the signal model, and Ψ is a (horizontal) concatenation of the matrices Ψ q,p = ψ q,p(n+l) ψ q,p(n+l 1) ψ q,p(n k+1) ψ q,p(n+l+1) ψ q,p(n+l) ψ q,p(n k+2)........ ψ q,p(n+l+n 1) ψ q,p(n+l+n 2) ψ q,p(n k+n) Here, l and k are the numbers of pre- and post-cursor taps such that l + k = M, and ψ q,p (n) = x(n) q x (n) p q is a single basis function. The pre-cursor taps are required to be able to sufficiently model all the practical memory effects in an in-band full-duplex transceiver [7]. Hence, they are introduced here even though the theoretical signal model in (1) utilizes only post-cursor taps. Note that the order in which the matrices Ψ q,p are concatenated in Ψ does not matter, as long as all the necessary values of p and q are considered. The number of basis functions, or, in other words, the set of values for p and q, are defined by the signal model used by the digital canceler. Thus, for the linear digital canceler described in (2), the only basis function can be written as ψ 1,1 (n) = x(n). The widely linear canceler in (3) has an additional basis function ψ 0,1 (x(n)) = x (n), in addition to the linear one. In a similar fashion, as shown in (4), the nonlinear canceler utilizes the basis functions corresponding to p = 1, 3, 5,..., P and q = (p + 1)/2. Finally, the augmented nonlinear canceler has the largest number of basis functions, which correspond to the values p = 1, 3, 5,..., P and q = 1, 2, 3,..., p, according to (5). The most important task of the digital canceler is to estimate the vector h, which is a (vertical) concatenation of the vectors h (q,p q) p = [ h (q,p q) p (0) h (q,p q) (1) h (q,p q) p,ij (7) p (M 1) ] T, (8) where the first l taps of each h p (q,p q) correspond to the precursor part of the SI channel estimate. The well-known least squares solution to the parameter vector h can then be calculated as ĥ = (Ψ H Ψ) 1 Ψ H r, (9) assuming full column rank in Ψ. It should be noted, however, that if there is a model mismatch between the observed SI signal and the signal model utilized by the digital canceler, n will not

Spectrum analyzer Vector signal generator Power supply Local oscillator Canceler PA Circulator and antenna Fig. 2. The measurement setup with the circulator case. A similar setup was also used in the dual antenna case. necessarily be Gaussian distributed and, as a result, ĥ will be a biased estimate. Nevertheless, with sufficient modeling accuracy, least squares provides a very good estimate of the true SI channel coefficients, as will be shown below. IV. MEASUREMENT RESULTS To obtain realistic results regarding the performance of the different digital cancelers, real-life measurements are performed, including also a prototype RF canceler. They reveal whether the digital cancelers are capable of coping with the challenges posed by a real world environment and modeling accurately actual circuit imperfections. The whole measurement setup in a single-antenna case is shown in Fig. 2. There, Rohde & Schwarz (R&S) SMJ100A vector signal generator is used to generate a wideband OFDM waveform at 2.44 GHz center-frequency with an average power of 5 dbm and a bandwidth of 18 MHz. To model a typical low-cost transmitter, the image rejection ratio (IRR) of the signal generator is set to 25 db, according to LTE specifications [13]. The output is then connected directly to a Texas Instruments CC2595 PA, which has a gain of 23 db with the used input power. This particular PA is a commercial low-cost chip intended to be used in low-cost battery-powered devices, and thereby it produces significant levels of nonlinear distortion. The measurements are carried out for two different setups: a circulator-based setup and a dual antenna based setup. In the former, only one antenna is required by the whole system, as the transmitter and receiver can use the same antenna due to the isolation provided by the circulator [12, Chapter 9]. The deployed circulator and the low-cost shared-antenna yield an overall isolation only in the order of 20 db between the transmitter and receiver chains, mostly because of the powerful reflection from the antenna. In the latter setup, both the transmitter and the receiver have their own separate antennas, and the isolation between them is provided simply by the path loss. With a compact antenna separation of 20 cm, the isolation is in the order of 20 db also in the dual antenna case. In both setups, the PA output signal is divided between the RF canceler and the transmit antenna, which will decrease the effective transmit power by approximately 1.5 db. Thus, the actual transmit power is in the order of 16 dbm in all these experiments. The overall received signal is then routed back to the prototype RF canceler, which performs the analog cancellation. The RF cancellation procedure simply involves subtracting a modified copy of the PA output signal from the received signal and is described in more detail in, e.g., [14]. Finally, the processed signal is routed to the receiver (R&S FSG-8) and captured as digital I- and Q-samples, which are post processed offline to implement digital baseband cancellation. In the forthcoming results, linear, nonlinear, and augmented nonlinear digital cancelers are used to perform the final SI suppression. The widely linear canceler is excluded from the results for clarity, as its performance was observed to be largely similar to that achieved by the linear canceler, due to the heavily nonlinear PA. In all the experiments, the highest nonlinearity order of the models (P ) is set to 7, and the numbers of pre-cursor (l) and post-cursor taps (k) are set to 10 and 20, respectively. The length of the observation period is 15000 samples. A. Circulator-Based Setup The measured power spectral densities (PSD) with the circulator-based setup, where the transmitter and receiver use the same antenna, are shown in Fig. 3. It can be observed that the SI signal model used by the digital canceler has a rather significant effect on the achieved performance. The linear digital canceler can attenuate the SI signal only by 20 db after the RF canceler, while the nonlinear canceler achieves over 25 db of SI cancellation in the digital domain. The best performance, however, is obtained with the augmented nonlinear canceler, which attenuates the SI signal by 30 db, almost reaching the receiver noise floor. Its performance gain is due to the significance of both the PA-induced nonlinear distortion as well as the I/Q imbalance of the transmitter, since both of these impairments have a tangible effect on the waveform of the observed SI signal. Thus, even though the more comprehensive augmented nonlinear signal model will result in increased computational complexity in the digital canceler, it also provides a real improvement in the cancellation capability. B. Dual Antenna Based Setup The corresponding power spectral densities for the dual antenna setup are shown in Fig. 4, with a separation of 20 cm between the antennas. As already mentioned, this separation provides nearly the same overall passive attenuation for the SI signal as the circulator. The relative performances of the different digital cancelers are also largely similar to the circulator-based setup. Now, the augmented nonlinear canceler is able to improve the SI cancellation by approximately 3 db with respect to the next best solution, with the overall SI cancellation performance being almost the same as in the circulator-based setup. All in all, the augmented nonlinear signal model proves to be a good match for the observed SI signal, and it provides an improvement in performance in both the circulator and dual antenna based setups, the highest overall SI attenuation being

40 40 PSD [dbm/1 MHz] 20 0-20 -40 PA output RF canceller input RF canceller output Linear digital cancellation Nonlinear digital cancellation Augmented digital cancellation Receiver noise floor PSD [dbm/1 MHz] 20 0-20 -40 PA output RF canceller input RF canceller output Linear digital cancellation Nonlinear digital cancellation Augmented digital cancellation Receiver noise floor -60-60 -80-80 -100-15 -10-5 0 5 10 15 Frequency (MHz) -100-15 -10-5 0 5 10 15 Frequency (MHz) Fig. 3. The obtained power spectral densities with the circulator-based setup. Fig. 4. setup. The obtained power spectral densities with the dual antenna based in the order of 87 db. This implies that using a simple linear signal model in the digital canceler is not always sufficient to perfectly cancel the SI signal, which is an important requirement in potential commercial applications. Thus, use of the augmented nonlinear digital canceler, discussed also in [11], is most likely required if the performance of in-band full-duplex transceivers is to be utilized to the fullest extent. V. CONCLUSION In this paper, we have presented different advanced digital self-interference cancellation algorithms and analyzed their performance with real-life RF measurements. The results are highly representative of a practical scenario due to the real RF cancellation procedure and the most prominent impairments being included in the measurement setup. The findings showed that only the augmented nonlinear digital canceler, which is capable of modeling both the I/Q imbalance and the nonlinearity of the transmitter power, is able to suppress the selfinterference signal close to the receiver noise floor. The only drawback of this digital canceler is its high complexity, and thus simplifying it is an important future work item. ACKNOWLEDGMENT The research work leading to these results was funded by the Academy of Finland (under the project #259915), the Finnish Funding Agency for Technology and Innovation (Tekes, under the project Full-Duplex Cognitive Radio ), and the Linz Center of Mechatronics (LCM) in the framework of the Austrian COMET-K2 programme. The research was also supported by the Internet of Things program of DIGILE, funded by Tekes. REFERENCES [1] M. Jain, J. I. Choi, T. Kim, D. Bharadia, S. Seth, K. Srinivasan, P. Levis, S. Katti, and P. Sinha, Practical, real-time, full duplex wireless, in Proc. 17th Annual International Conference on Mobile computing and Networking, Sep. 2011, pp. 301 312. [2] M. Duarte and A. Sabharwal, Full-duplex wireless communications using off-the-shelf radios: Feasibility and first results, in Proc. 44th Asilomar Conference on Signals, Systems, and Computers, Nov. 2010, pp. 1558 1562. [3] M. Duarte, C. Dick, and A. 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