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Digital Self-Interference Cancellation underNonideal RF Components: Advanced Algorithms
and Measured PerformanceDani 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: [email protected], [email protected], [email protected], [email protected]
†Intel Corporation, Hillsboro, Oregon, USA, e-mail: [email protected]‡Intel Corporation, Santa Clara, California, USA, e-mail: [email protected]
Abstract—This paper addresses digital self-interference can-cellation in a full-duplex radio under the distortion of practicalRF components. Essential self-interference signal models underdifferent RF imperfections are first presented, and then usedto formulate widely linear, nonlinear and augmented nonlineardigital canceler structures. Furthermore, a general parameterestimation procedure based on least squares is laid out. Digitalcancellation with actual measured self-interference signals isthen performed using all the presented methods. To ensure arealistic scenario, the used transmitter has realistic levels of I/Qimbalance, and is also utilizing a highly nonlinear low-cost poweramplifier. Furthermore, a realistic RF canceler is incorporated inthe measurements, and both shared-antenna and dual-antennabased devices are measured and experimented. The obtainedresults indicate that only a digital canceler structure capableof modeling all the essential impairments is able to suppress theself-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 inthe field of wireless communications [1]–[3]. In theory, it candouble the spectral efficiency of the existing communicationssystems by utilizing all the spectral and temporal resources forboth transmission and reception, i.e., transmitting and receivingat the same center-frequency at the same time. This makes full-duplex communications a very interesting prospect, as it cansignificantly help the future networks in obtaining the requiredthroughputs. The potential of in-band full-duplex communica-tions has already been demonstrated by actual prototypes [1], [2],[4], [5] as well as by a large amount of theoretical analysis, ad-dressing various circuit impairments and deployment scenarios[6]–[9].
The fundamental challenge behind in-band full-duplex com-munications is the problem of the own transmit signal couplingback to the receiver. This so-called self-interference (SI) mustbe heavily attenuated, as it will otherwise saturate the receiverchain, or in the very least make the detection of the receivedsignal of interest very challenging. Typically, the SI signal isfirst attenuated at the input of the receiver chain by subtractinga properly delayed and attenuated version of the own transmitsignal from the total received signal [1], [2]. This cancellationstage is referred to as RF cancellation, and it decreases the
power of the total receiver input signal to a suitable level so thatthe receiver chain components will not be completely saturated.Usually, additional SI cancellation is still performed in the digitaldomain, referred to as digital cancellation [1], [10]. Ideally, afterboth of these cancellation stages the SI signal has been attenuatedsufficiently low to achieve an adequate signal-to-interference-plus-noise ratio (SINR) for detecting the received signal ofinterest.
The previous research has, among other things, shown that thedifferent circuit nonidealities are a significant issue in in-bandfull-duplex transceivers. This is caused by the fact that the SIsignal is extremely powerful when it reaches the receiver chain,which means that even a relatively mild distortion can turn out tobe significant with respect to the weak received signal of interest.I/Q imbalance and the nonlinear distortion induced by the trans-mitter power amplifier (PA) have been shown to be particularlyprominent [7], [10]. These impairments are especially harmful tothe digital canceler, assuming that it utilizes only classical linearprocessing [7], [8], [10]. Under such circumstances, neither thenonlinear 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 nonlineardigital cancellation solutions, building on the behavioral SI sig-nal modeling under imperfect RF components, most notably I/Qimbalance and nonlinear PA. We also evaluate the performanceof the algorithms with actual RF measurements. The most ad-vanced algorithm is capable of modeling both the I/Q imbalanceand transmitter PA induced nonlinear distortion, thereby makingsuch 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 utilizingmore elaborate digital processing. The parameter learning for allalgorithms is done with a straight-forward block least squaresapproach.
The rest of this paper is organized as follows. The systemmodel for the considered full-duplex radio transceiver, alongsidewith the digital canceler structures, are described in Section II.After this, the parameter estimation procedure is discussed indetail in Section III. The measurement results are then presentedand analyzed in Section IV, after which the conclusions aredrawn in Section V.
IQ Mixer
Band-pass
filter
Low-noise
amplifier
I/Q Mixer Low-pass
filter
Variable gain
amplifier
Analog-to-
digital converter
Low-pass
filter
I/Q
Mixer
Variable gain
amplifier
Power
amplifier
Digital-to-analog
converter
Digital
cancellation
To
de
tecto
r
Transmitter chain
Receiver chain
Σ+
−
Local
oscillator
+
− Σ
Tra
nsm
it d
ata
Wideband
RF cancel-
lation circuit
TX
RX
TX
RX
TX
RX
ORSelf-interference
regeneration
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 CANCELERSTRUCTURES
The modeling of the in-band full-duplex transceiver is donebased on the block diagram in Fig. 1, which depicts a typi-cal structure for a full-duplex transceiver. There, two differentlayouts for the antenna interface are shown. The upper optionshows a layout where the transmitter and receiver are sepa-rated by a circulator, which provides a certain level of passiveisolation, while allowing for the use of only a single antenna[12, Chapter 9]. In the lower layout, a dual antenna setup isshown, where the transmitter and receiver have their own sep-arate antennas, and the passive isolation is provided by the pathloss occurring between them. Typically, a significant amount ofadditional SI cancellation is required in addition to the passiveisolation, regardless of the number of antennas, and thus thefull-duplex transceiver model includes an active RF cancellationstage, followed by an active digital canceler after the analog-to-digital conversion. Together, all the cancellation stages must beable to suppress the SI below the receiver noise floor.
As already discussed, the different RF impairments occurringin the full-duplex transceiver are crucial in terms of achieving therequired level of SI cancellation. If the models used in generatingthe digital cancellation signal are not capable of reproducingan accurate copy of the observed SI signal, the performance ofthe full-duplex transceiver will be insufficient. Typically, this isthe case when using a linear signal model for the SI [7], [8],[10]. In fact, recent results indicate that joint modeling of severalsources of impairments is required to facilitate the use of thehigher transmit powers [7]. Thus, the emphasis in this paper ison practical scenarios where the effects of both I/Q imbalanceand transmitter PA nonlinearities are included in the SI signalmodel as well as in the corresponding digital canceler.
Referring to Fig. 1, this means that the full-duplex transceiveris assumed to be otherwise linear, apart from the transmitterPA and the I/Q mixers. Following the derivations in [11], theobserved SI signal in the digital domain can then be written as
r(n) =
P∑p=1p odd
p∑q=0
M∑m=0
h(q,p−q)p (m)x(n−m)qx∗(n−m)
p−q
+ z(n), (1)
where P is the highest considered nonlinearity order, M is thetotal memory length, h(q,p−q)p (m) contains the unknown truecoefficients of the signal model, x(n) is the original digital trans-mit signal, and z(n) represents the modeling error. Note that thesignal model in (1) is here written for a SISO transceiver, unlikein [11], because the used measurement setup only supports asingle transmitter and a single receiver. Also, the essential signalmodel is unaffected by the chosen antenna layout, i.e., it is thesame 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)
qx∗(n−m)p−q . Dif-
ferent cancellation solutions correspond then to different approx-imations of this model, where only different subsets of the basisfunctions are eventually deployed, leading to different levelsof modeling accuracy and computational complexity. These areelaborated below.
A. Linear Digital CancelerThe crudest approximation of all is made by the linear digital
canceler. Now, only the linear component is considered in theSI signal model and all the other basis functions are ignored. Inother words, corresponding to the notation used in (1), the valuesfor P and q are fixed to 1. The resulting SI signal estimate canbe written as
r(n) =
M∑m=0
h(1,0)1 (m)x(n−m), (2)
where h(1,0)1 (m) is the estimate of the linear SI channel. Thebenefit of the linear canceler is that it is enough to estimate thecoefficients of only the linear basis function, which correspondsto the original transmit signal. However, as already discussed, inmost cases this is not sufficient to achieve the required cancella-tion accuracy.
B. Widely Linear Digital CancelerDue to the severity of the I/Q imbalance in most low-cost
radio transceivers nowadays, considering it in the SI modelingis typically highly beneficial [7]. The complexity of the SI signalmodel will slightly increase with respect to the linear canceler butthe potential improvement in the cancellation capability is alsosignificant. Referring to (1), the widely linear canceler merely
means that the value for P is set to 1, which results in two basisfunctions: the linear SI component and its complex conjugate.Thus, the SI signal estimate is
r(n) =
1∑q=0
M∑m=0
h(q,1−q)1 (m)x(n−m)
qx∗(n−m)
1−q , (3)
where h(q,1−q)1 (m) contains the channel estimates for the linearSI (q = 1) and its I/Q mirror image (q = 0) [7]. Assumingthe same memory length for both estimates, the number ofparameters is doubled with respect to the linear canceler sincethere are now two basis functions instead of only one.
C. Nonlinear Digital Canceler
The next step in increasing the complexity of the SI signalmodel is the nonlinear digital canceler, which takes into accountthe nonlinear distortion produced by the transmitter PA. Typi-cally, it is not necessary to model the nonlinearities produced bythe other components since usually the transmitter PA producesmost of the nonlinear distortion [8]. The nonlinear signal model,first proposed in [10], can be obtained from (1) by settingq = (p + 1)/2 and p − q = (p − 1)/2. The correspondingestimate for the SI signal is then as follows.
r(n) =
P∑p=1p odd
M∑m=0
h( p+1
2 , p−12 )
p (m)x(n−m)p+12 x∗(n−m)
p−12 ,
(4)
where, again, h(p+12 , p−1
2 )p (m) contains the SI channel estimates
for the different basis functions. It can be easily calculatedthat the number of basis functions, whose respective channelcoefficients must be estimated, is now (P + 1)/2, which meansthat the nonlinear canceler is bound to be somewhat more com-putationally demanding than the linear or widely linear canceler.
D. Augmented Nonlinear Digital Canceler
It has been shown that under typical levels of I/Q imbalanceand PA nonlinearity, modeling only one of these impairmentsmight not be sufficient to achieve reasonable SINR levels [11].For this reason, this paper provides measurement results with afull augmented nonlinear digital canceler, which is capable ofmodeling transmitter and receiver I/Q imbalance, alongside witha heavily nonlinear transmitter PA. This type of a solution can beexpected to provide a significant improvement in performancewith the higher transmit powers [7], [11]. In this case, the SIsignal model used in the digital canceler consists of (1) withoutany approximations. The corresponding estimate of the SI signalis written as
r(n) =
P∑p=1p odd
p∑q=0
M∑m=0
h(q,p−q)p (m)x(n−m)qx∗(n−m)
p−q ,
(5)
with h(q,p−q)p (m) again containing the SI channel estimates.
Using the full augmented nonlinear SI signal model in the digitalcanceler will obviously result in an increase in the number
of basis functions, for which the channel coefficients must beestimated. It can be shown that this particular signal modelcontains
(P+12
) (P+12 + 1
)basis functions. Thus, the compu-
tational complexity of the augmented nonlinear canceler can berather high, but the cancellation performance is also likely to besignificantly better compared to previous solutions.
III. PARAMETER LEARNING
To lay out the parameter learning procedure, let us resort tovector-matrix notation. The SI signal observed over a period oflength N can easily be expressed as
r = Ψh + n, (6)
where r =[r(n) r(n+ 1) · · · r(n+N − 1)
]T, h con-
tains the true parameters of the used signal model, n is the noisesignal that contains also the error introduced by the possible mis-match in the signal model, and Ψ is a (horizontal) concatenationof the matrices
Ψq,p =
ψq,p(n+l) ψq,p(n+l−1) ··· ψq,p(n−k+1)ψq,p(n+l+1) ψq,p(n+l) ··· ψq,p(n−k+2)
......
. . ....
ψq,p(n+l+N−1) ψq,p(n+l+N−2) ··· ψq,p(n−k+N)
(7)
Here, l and k are the numbers of pre- and post-cursor filtertaps such that l + k = M , and ψq,p(n) = x(n)qx∗(n)p−q isa single basis function. The pre-cursor taps are required to beable to sufficiently model all the practical memory effects in anin-band full-duplex transceiver [7]. Hence, they are introducedhere even though the theoretical signal model in (1) utilizes onlypost-cursor filter taps. Note that the order in which the matricesΨq,p are concatenated in Ψ does not matter, as long as all thenecessary values of p and q are considered.
The number of basis functions, or, in other words, the set ofvalues for p and q, are defined by the signal model used by thedigital canceler. Thus, for the linear digital canceler describedin (2), the only basis function can be written as ψ1,1(n) = x(n).The widely linear canceler in (3) has an additional basis functionψ0,1(x(n)) = x∗(n), in addition to the linear one. In a similarfashion, as shown in (4), the nonlinear canceler utilizes the basisfunctions corresponding to p = 1, 3, 5, . . . , P and q = (p +1)/2. Finally, the augmented nonlinear canceler has the largestnumber 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 estimatethe 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)p,ij
(1) ··· h(q,p−q)p (M−1) ]
T , (8)
where the first l taps of each h(q,p−q)p correspond to the pre-
cursor part of the SI channel estimate. The well-known leastsquares solution to the parameter vector h can then be calculatedas
h = (ΨHΨ)−1ΨHr, (9)
assuming full column rank in Ψ. It should be noted, however,that if there is a model mismatch between the observed SI signaland the signal model utilized by the digital canceler, n will not
Vector sig
nal generator
Vector sig
nal generator
Spectrum analyzer
Spectrum analyzer
CancelerCanceler
Circulator and antennaCirculator and antenna
Power supplyPower supply
Local oscillatorLocal oscillator
PAPA
Fig. 2. The measurement setup with the circulator case. A similar setup wasalso used in the dual antenna case.
necessarily be Gaussian distributed and, as a result, h will be abiased estimate. Nevertheless, with sufficient modeling accuracy,least squares provides a very good estimate of the true SI channelcoefficients, as will be shown below.
IV. MEASUREMENT RESULTS
To obtain realistic results regarding the performance of thedifferent digital cancelers, real-life measurements are performed,including also a prototype RF canceler. They reveal whetherthe digital cancelers are capable of coping with the challengesposed by a real world environment and modeling accuratelyactual circuit imperfections. The whole measurement setup in asingle-antenna case is shown in Fig. 2. There, Rohde & Schwarz(R&S) SMJ100A vector signal generator is used to generate awideband OFDM waveform at 2.44 GHz center-frequency withan average power of −5 dBm and a bandwidth of 18 MHz. Tomodel a typical low-cost transmitter, the image rejection ratio(IRR) of the signal generator is set to 25 dB, according toLTE specifications [13]. The output is then connected directlyto a Texas Instruments CC2595 PA, which has a gain of 23 dBwith the used input power. This particular PA is a commerciallow-cost chip intended to be used in low-cost battery-powereddevices, and thereby it produces significant levels of nonlineardistortion.
The measurements are carried out for two different setups:a circulator-based setup and a dual antenna based setup. In theformer, only one antenna is required by the whole system, asthe transmitter and receiver can use the same antenna due tothe isolation provided by the circulator [12, Chapter 9]. Thedeployed circulator and the low-cost shared-antenna yield anoverall isolation only in the order of 20 dB between the transmit-ter and receiver chains, mostly because of the powerful reflectionfrom the antenna. In the latter setup, both the transmitter andthe receiver have their own separate antennas, and the isolationbetween them is provided simply by the path loss. With acompact antenna separation of 20 cm, the isolation is in the orderof 20 dB also in the dual antenna case. In both setups, the PA
output signal is divided between the RF canceler and the transmitantenna, which will decrease the effective transmit power byapproximately 1.5 dB. Thus, the actual transmit power is in theorder of 16 dBm in all these experiments.
The overall received signal is then routed back to the prototypeRF canceler, which performs the analog cancellation. The RFcancellation procedure simply involves subtracting a modifiedcopy of the PA output signal from the received signal and is de-scribed in more detail in, e.g., [14]. Finally, the processed signalis routed to the receiver (R&S FSG-8) and captured as digital I-and Q-samples, which are post processed offline to implementdigital baseband cancellation. In the forthcoming results, linear,nonlinear, and augmented nonlinear digital cancelers are usedto perform the final SI suppression. The widely linear canceleris excluded from the results for clarity, as its performance wasobserved to be largely similar to that achieved by the linearcanceler, due to the heavily nonlinear PA. In all the experiments,the highest nonlinearity order of the models (P ) is set to 7, andthe numbers of pre-cursor (l) and post-cursor taps (k) are set to10 and 20, respectively. The length of the observation period is15000 samples.
A. Circulator-Based Setup
The measured power spectral densities (PSD) with thecirculator-based setup, where the transmitter and receiver usethe same antenna, are shown in Fig. 3. It can be observed thatthe SI signal model used by the digital canceler has a rathersignificant effect on the achieved performance. The linear digitalcanceler can attenuate the SI signal only by 20 dB after theRF canceler, while the nonlinear canceler achieves over 25 dBof 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 thereceiver noise floor. Its performance gain is due to the signifi-cance of both the PA-induced nonlinear distortion as well as theI/Q imbalance of the transmitter, since both of these impairmentshave a tangible effect on the waveform of the observed SI signal.Thus, even though the more comprehensive augmented nonlinearsignal model will result in increased computational complexityin the digital canceler, it also provides a real improvement in thecancellation capability.
B. Dual Antenna Based Setup
The corresponding power spectral densities for the dual an-tenna setup are shown in Fig. 4, with a separation of 20 cmbetween the antennas. As already mentioned, this separationprovides nearly the same overall passive attenuation for the SIsignal as the circulator. The relative performances of the differentdigital cancelers are also largely similar to the circulator-basedsetup. Now, the augmented nonlinear canceler is able to improvethe SI cancellation by approximately 3 dB with respect to thenext best solution, with the overall SI cancellation performancebeing almost the same as in the circulator-based setup.
All in all, the augmented nonlinear signal model proves tobe a good match for the observed SI signal, and it providesan improvement in performance in both the circulator and dualantenna based setups, the highest overall SI attenuation being
Frequency (MHz)
-15 -10 -5 0 5 10 15
PS
D [
dB
m/1
MH
z]
-100
-80
-60
-40
-20
0
20
40
PA output
RF canceller input
RF canceller output
Linear digital cancellation
Nonlinear digital cancellation
Augmented digital cancellation
Receiver noise floor
Fig. 3. The obtained power spectral densities with the circulator-based setup.
in the order of 87 dB. This implies that using a simple linearsignal model in the digital canceler is not always sufficient toperfectly cancel the SI signal, which is an important requirementin potential commercial applications. Thus, use of the augmentednonlinear digital canceler, discussed also in [11], is most likelyrequired if the performance of in-band full-duplex transceivers isto be utilized to the fullest extent.
V. CONCLUSION
In this paper, we have presented different advanced digi-tal self-interference cancellation algorithms and analyzed theirperformance with real-life RF measurements. The results arehighly representative of a practical scenario due to the realRF cancellation procedure and the most prominent impairmentsbeing included in the measurement setup. The findings showedthat only the augmented nonlinear digital canceler, which iscapable of modeling both the I/Q imbalance and the nonlinearityof the transmitter power amplifier, is able to suppress the self-interference signal close to the receiver noise floor. The onlydrawback of this digital canceler is its high complexity, and thussimplifying it is an important future work item.
ACKNOWLEDGMENT
The research work leading to these results was funded by theAcademy of Finland (under the project #259915), the FinnishFunding Agency for Technology and Innovation (Tekes, underthe project ”Full-Duplex Cognitive Radio”), and the Linz Cen-ter of Mechatronics (LCM) in the framework of the AustrianCOMET-K2 programme. The research was also supported by theInternet of Things program of DIGILE, funded by Tekes.
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Frequency (MHz)
-15 -10 -5 0 5 10 15
PS
D [
dB
m/1
MH
z]
-100
-80
-60
-40
-20
0
20
40
PA output
RF canceller input
RF canceller output
Linear digital cancellation
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Receiver noise floor
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