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4794 IEEE TRA NSA CTI ON S ON WIR ELESS COMMUNICATIONS, VOL.13, NO. 9, SEPTEMBER 2014
An Investigation Into Baseband Techniques for
Single-Channel Full-Duplex Wireless
Communication Systems
Shenghong Li, Student Member, IEEE, and Ross D. Murch, Fellow, IEEE
Abstract—Full-duplex wireless communication is becoming an
important research area because of its potential for increasing
spectral efficiency. The challenge of such systems lies in cancelling
the self-interference. In this paper, we focus on the design of dig-
ital cancellation schemes and use them to supplement RF/analog
cancellation techniques. The performance of digital cancellation
is limited by the non-ideal characteristics of different subsystems
in the transceiver, such as analog/digital converter (ADC), power
amplifier (PA), and phase noise. It is first shown that given the pre-
cancellation achieved by existing RF/analog techniques, the effects
of ADC, phase noise, and sampling jitter are not the bottleneck
in the system. Instead, the performance of conventional digital
cancellation approaches are mainly limited by nonlinearity of the
PA and transmit I/Q imbalance. In addition, the output SINR
of the desired signal is limited because the estimation precision
of the self-interference channel is affected by the desired signal.
To overcome these issues, we propose a two-stage iterative self-
interference cancellation scheme based on the output signal of the
power amplifier. Analytical and simulation results reveal that the
proposed cancellation scheme substantially outperforms existing
digital cancellation schemes for full-duplex wireless communica-
tion systems.
Index Terms—Full-duplex, wireless communication, self-
interference cancelation.
I. INTRODUCTION
AKEY objective of future wireless communication systems
is to use spectrum efficiently to achieve high capacity and
data rates within a limited bandwidth. Various techniques have
been proposed over the past decades. A different approach to
increase spectrum efficiency that is attracting growing research
interest is to consider full-duplex (FD) techniques in wire-
less communication systems [1]–[10]. Currently, most wire-
less systems require two separate channels for simultaneous
uplink and downlink communication, and common techniques
that can be employed are Time Division Duplexing (TDD)
or Frequency Division Duplexing (FDD), which separate the
uplink and downlink channels in the time/frequency domain.
On the contrary, full-duplex allows users to transmit and receive
Manuscript received June 1, 2013; revised November 20, 2013 and April
9, 2014; accepted July 14, 2014. Date of publication July 22, 2014; date of
current version September 8, 2014. This work was supported by Hong Kong
RGC under Grant GRF 618209. The associate editor coordinating the review
of this paper and approving it for publication was N. C. Sagias.
The authors are with Department of Electronic & Computer Engineering,
The Hong Kong University of Science and Technology, Kowloon, Hong Kong
(e-mail: eelsh@connect.ust.hk; eermurch@ee.ust.hk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TWC.2014.2341569
signals simultaneously in the same frequency band and time
slot, therefore the same channel can be used for the uplink
and downlink communications. The motivation for developing
full-duplex communication in wireless systems is to increase
the overall capacity [11]. In addition, existing wireless com-
munication systems can be redesigned dramatically to exploit
the benefits of full-duplex communications. For example, full-
duplex can be applied in Cognitive Radio and Relay Systems
[12], [13], and significant changes can be made to the current
Medium Access Control (MAC) layer protocols to improve the
network throughput [2], [14].
The main challenge of full-duplex wireless communication
is caused by the existence of self-interference, which needs to
be cancelled from the received signal for the detection of the
desired signal (signal of interest). Existing research on this topic
can be found in [1]–[10], [15]–[18]. In [1], the authors pro-
pose a Radio Frequency (RF) analog echo cancellation method
which provides 72 dB isolation for the self-interference signal.
In [2], antenna cancellation is combined with RF interference
cancellation to eliminate the self-interference, and a similar
antenna cancellation technique for multi-antenna systems is
presented in [7]. The authors of [3] present some experimental
results on the performance of narrow-band self-interference
cancellation, which is further characterized in [6]. A digitally
controlled near-field cancellation scheme is demonstrated in
[4], which provides up to 50 dB of isolation for the self-
interference. An inverse signal generated using a transformer is
utilized for cancellation in [5], which achieves 73 dB reduction
in self-interference when combined with digital cancellation.
The impact of phase noise on full-duplex wireless system is
considered in [8]. In addition, a digital cancellation scheme is
proposed in [10] which takes the effect of RF/analog impair-
ments into consideration and utilizes iterative signal process-
ing technique to improve the SINR performance; and similar
techniques have also been used in [19], [20] to cancel the inter-
subcarrier interference in subcarrier-based duplexing systems.
The effect of ADC on digital cancellation is studied in [15],
where a digital cancellation scheme based on the theory of
sparse signal recovery is also proposed. The trade-off between
ADC resolution, transmit power, physical isolation, and SNR is
studied in [16], with the benefit of combining digital and analog
cancellation highlighted. For systems with limited number of
antennas, the tradeoff between using the antennas for full-
duplex communication and using them for half-duplex MIMO
communication is analyzed in [9]. In addition, beamforming
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LI AND MURCH: BASEBAND TECHNIQUES FOR SINGLE-CHANNEL FULL-DUPLEX WIRELESS COMMUNICATION SYSTEMS 4795
has been used in [13], [17] to suppress self-interference and
it has been shown in [13] that receive beamforming can handle
self-interference due to the transmit signal noise.
A detailed classification of techniques for cancelling the self-
interference can be found in [21]. In this work, we catego-
rize different techniques roughly into ‘RF cancellation’ and
‘digital cancellation’, depending on where the cancellation is
carried out.1The advantage of RF cancellation is that the self-
interference is suppressed prior to the ADC, so that the impact
of various RF/analog impairments (quantization noise, nonlin-
earity, phase noise etc.) can be circumvented. In particular, RF
cancellation prevents the saturation of ADC and thus reduces
the requirement on the resolution of ADC. However, care needs
to be taken and it can be expensive to implement RF cancella-
tion techniques that are effective for wideband systems [16].
For example, the approach proposed in [2] is only effective for
narrowband system, while the scheme of [5] can only handle the
self-interference from a single signal path. The RF cancellation
scheme of [22] is based on multiple analog delay lines which
is expensive and difficult for adaptive adjusting. On the other
hand, by using finite-impulse-response (FIR) filter to model the
self-interference channel, digital cancellation can be applied in
wideband systems effectively. Compared with RF techniques,
digital cancellation is more flexible as the coefficients of FIR
can be adjusted conveniently. In addition, advanced digital
signal processing techniques can be employed to improve the
system performance. However, due to the presence of various
system impairments, it is impossible to use digital cancellation
alone to achieve full-duplex wireless communication. In par-
ticular, since the self-interference is significantly stronger than
the signal-of-interest, it is impossible to recover the signal-of-
interest due to the limitation of ADC resolution. Given the fact
that RF and digital cancellation can supplement each other,
one can combine RF and digital cancellation techniques in
wideband systems to improve the performance, as in [2], [3],
[5], [15]. Specifically, RF techniques can be used to cancel the
line-of-sight (LOS) component of the self-interference, so that
the effects of some RF/analog impairments (e.g., quantization
noise etc.) are reduced to a level that is not the bottleneck of the
system. Digital baseband cancellation can be used subsequently
to deal with the non-line-of-sight (NLOS) components.
While [1]–[7] has focused on RF techniques, no digital
cancellation approaches are employed in [1], [4], [7], and the
digital cancellation techniques used in [2], [3], [5], [6] are
straightforward. In this paper, we will mainly focus on digital
cancellation techniques and propose a novel scheme that can
be combined with RF techniques to improve the performance
of wideband full-duplex wireless communication systems. The
contributions of this paper are as follows:
1) After observing that the effects of ADC, phase noise,
and sampling jitter are not the bottleneck of WiFi-like
systems given the pre-cancellation achieved by existing
RF techniques, we show that PA nonlinearity and transmit
I/Q imbalance are the most prominent factors that limit
1We will not differentiate between RF-analog cancellation and baseband-
analog cancellation since most of the existing analog cancellation schemes are
based on RF techniques.
Fig. 1. Basic configuration of a full-duplex wireless device: transmission and
reception happens in the same frequency band and time slot. For the purpose
of exposition, here we assume that two different antennas are utilized for
transmission and reception, respectively.
the precision of digital self-interference cancellation. As
such, we propose to use the output signal of the power
amplifier for more accurate self-interference cancellation.
2) We show that the output SINR of the desired signal
using conventional digital cancellation schemes is limited
because the estimation precision of the self-interference
channel is affected by the desired signal. To address
this issue, we propose a two-stage iterative cancellation
scheme, which utilizes the detection result of the de-
sired signal to improve the accuracy of self-interference
cancellation.
The proposed digital cancellation scheme is evaluated by
analysis and simulation, and is shown to substantially outper-
form conventional digital cancellation schemes.
This paper is organized as follows. In Section II we describe
the implementation issues of full-duplex wireless communica-
tion systems and the impact of RF/analog impairments on the
system; in Section III, we describe the proposed digital cancel-
lation techniques, including self-interference cancellation based
on the output signal of power amplifier and two-stage iterative
cancellation scheme; the performance of the proposed scheme
is analyzed in Section IV, and verified by computer simulations
in Section V; finally, a conclusion is drawn in Section VI.
II. FULL-DUPLEX WIRELESS COMMUNICATION SYSTEMS
We consider a wireless communication device that transmits
and receives signals simultaneously in the same frequency
band, as shown in Fig. 1. The device is part of a communication
system and its role depends on the application scenario. For
example, it may be a full-duplex relay, or one of the two devices
in a point to point full duplex system. The signal picked up
by the device consists of three components: self-interference
due to its own transmission (also denoted as near-end signal
hereafter), desired signal transmitted from other device (also
denoted as far-end signal), and noise. To facilitate the detection
of the far-end signal, the self-interference is cancelled from the
received signal, which is shown as ‘Self-interference Cancel-
lation’ in Fig. 1, and may be carried out using RF techniques
and/or digital techniques.
4796 IEEE TRA NSA CTI ON S ON WIR ELESS COMMUNICATIONS, VOL.13, NO. 9, SEPTEMBER 2014
Since the near-end signal is significantly stronger than the
far-end signal, the cancellation ratio needs to be sufficiently
high to achieve satisfactory SINR for the desired signal. As a re-
sult, various aspects that limit the precision of self-interference
cancellation need to be considered. In particular, the RF/analog
impairments in wireless systems are important factors that
require investigation, including quantization error, PA nonlin-
earity, I/Q imbalance, phase noise of local oscillator (LO),
sampling jitter of ADC/DAC etc. In the following, we provide
a brief introduction of the impact of RF/analog impairments on
full-duplex wireless communication systems.
A. Impact of RF/Analog Impairments
Signals in wireless communication systems are distorted due
to RF/analog impairments in different subsystems. When a
complex baseband-equivalent signal x(t)passes through a sub-
system G, we write the resulting signal as G[x(t)], where G[·]
includes both the impairment effect and the linear characteristic
of the subsystem. More specifically, we write
x(t)=G[x(t)] = ax(t)+F[x(t)] ,(1)
where x(t)denotes the output signal of the subsystem, ax(t)
denotes the ideally linear signal component in which ais a
constant factor representing the signal gain, F[x(t)] denotes the
nonlinear spurious signal components caused by the RF/analog
impairment. Detailed mathematical models for G[·](and hence
F[·]) can be found in [23]–[25]. Note that the effects of G[·]
depends on both x(t)and the specific impairment. For example,
the effect of PA nonlinearity is determined not only by the type
of power amplifier used, but also by the relation between its
operating point and the power of x(t), i.e., the input/output
backoff (IBO/OBO). It is also useful to define the normal-
ized spurious signal as ˇx(t)Δ
=F[x(t)]/a (i.e., x(t)=a[x(t)+
ˇx(t)]). Then the impact of the impairment on the signal quality
can be characterized by ‘SNR limitation’ [24], which is defined
as the ratio between the power of x(t)and ˇx(t), i.e., SNRlmt =
Px/ˇ
Px, where Pxand ˇ
Pxdenote the power of x(t)and ˇx(t),
respectively. For ease of exposition, in this paper we will define
γas the inverse of SNR limitation, i.e.,
γ=1
SNRlmt
=ˇ
Px
Px
,(2)
which indicates the relative power of the spurious signal com-
ponents to the ideally linear signal component. We note again
that γdepends on both x(t)and the specific impairment. In
particular, for power amplifiers with fixed operating point, γis
dependant on Pxas it affects the IBO/OBO.
In this paper, we will consider the effects of quantization
error, PA nonlinearity, I/Q imbalance, phase noise of local
oscillator (LO), and sampling jitter of ADC/DAC, which are the
most important RF/analog impairments in the system, as have
been studied in [23], [24]. We first investigate the relative power
(γin (2)) of the spurious signal components caused by these im-
pairments. An example of these values are listed in Table I. The
result for PA nonlinearity is obtained from simulation based
on a 802.11a/g system, where the PA nonlinearity is modeled
TAB L E I
RELATIVE POWER (γ)OF THE SPURIOUS SIGNAL COMPONENTS
RESULTING FROM DIFFERENT RF/ANALOG IMPAIRMENTS
by Rapp Model [24], [25] with the parameter p=3 and an
input back-off (IBO) of 8 dB. The other results are obtained
by calculation according to [24]. The resolution of the ADC is
12 bits. The I/Q imbalance exhibits an amplitude mismatch of
0.5 dB and phase mismatch of 3 degrees. The power spectrum
density (PSD) of the LO phase noise has a constant value of
−110 dBc/Hz below 10 KHz, and decreases by 20 dB per
decade beyond that [26]. Finally, the root mean square (rms)
sampling jitter of the ADC/DAC is 2.5 ps (assuming 20 MHz
sampling rate and identical oscillator as for the case of phase
noise). Also note that the signal is assumed to be a single
10 MHz sinusoid wave for calculating the effects of quantiza-
tion noise and sampling jitter.
Since the received near-end signal is significantly stronger
than the far-end signal in full-duplex wireless communication
systems, it can be seen from Table I that the spurious com-
ponents of the near-end signal also have significant impact on
the far-end signal. For example, suppose the received near-end
signal is 60 dB stronger than the far-end signal, the nonlinear
signal components induced by PA nonlinearity would be 28 dB
stronger than the far-end signal, making the detection of far-end
signal impossible if not suppressed.
It is worth noting that there are also various other RF/analog
impairments in wireless communication systems. However, the
other impairments are much milder compared with those listed
in Table I. For example, since power efficiency is not critical for
the other amplifiers in the transceiver, they can be configured to
have very low nonlinearity, which can be neglected compared
with PA nonlinearity. In addition, by using one-stage down-
converter and digital demodulation, the receiver can be treated
as free of I/Q imbalance [27].2
B. Self-Interference Cancellation Using RF
and Digital Techniques
As is described in Section I, RF cancellation techniques are
immune to RF/analog impairments in the system, but care needs
to be taken and it can be expensive to implement RF cancel-
lation techniques that are effective for wideband systems. On
the other hand, digital cancellation can be applied effectively in
wideband systems, but is susceptible to RF/analog impairments
(in fact, as will be shown in Section III-A, the cancellation
ratio achieved by digital cancellation is limited by RF/analog
impairments). Therefore, one can combine RF and digital can-
cellation techniques to improve the performance of wideband
full-duplex wireless systems. Specifically, RF techniques can
be used to cancel the line-of-sight (LOS) component of the
2Although similar techniques may be used at the transmitter side to mitigate
transmit I/Q imbalance, we will not make such assumption in this paper because
this approach is not adopted in [27].
LI AND MURCH: BASEBAND TECHNIQUES FOR SINGLE-CHANNEL FULL-DUPLEX WIRELESS COMMUNICATION SYSTEMS 4797
self-interference, while digital baseband cancellation can be
used to deal with the non-line-of-sight (NLOS) components.
For the effects of RF/analog impairments to not limit the
system performance, it is desirable that the self-interference is
suppressed by RF techniques to such a level that the spurious
components of the self-interference is close to the noise floor.
As an example, we consider a system with 10 dBm transmit
power, 20 MHz bandwidth (corresponding to a noise floor of
−101 dBm), and the same levels of spurious signal components
as in Table I. It can be seen that about 40 dB attenuation is
required for the effects of quantization noise, phase noise, and
sampling jitter to reach the noise floor. However, to achieve the
same objective for PA nonlinearity and transmit I/Q imbalance,
the required attenuation is about 80 dB.
In this paper, unless otherwise stated, we will assume that
the isolation between the transmitter and receiver (denoted as
‘Tx-Rx isolation’ hereafter) is 40 dB, i.e., the LOS component
of near-end signal is attenuated by 40 dB using RF techniques.
Note that this is a reasonable assumption for the following
reasons:
1) The cancellation ratio achieved by RF techniques in [2],
[4], [5], [7] is between 40 dB and 50 dB.
2) As is reported in [5], [7], 40 dB Tx-Rx isolation can be
achieved when the antennas are separated by 15–20 cm.
In addition, since the NLOS components of the self-
interference travel over distances that are much longer than
15–20 cm and also undergo reflections/diffractions, they are
attenuated by more than 40 dB as well. Therefore the effects
of quantization error, phase noise, and sampling jitter are low
enough and are no longer the bottleneck of the system.
Nevertheless, as has been described in the previous example,
the spurious signal components caused by PA nonlinearity and
transmit I/Q imbalance are still much higher than the noise floor
when the Tx-Rx isolation is 40 dB. Therefore they are the most
prominent issues that limit the system performance. As such,
we will introduce a digital self-interference canceller based
on the output signal of the power amplifier in the following
section. In addition, a two-stage iterative cancellation scheme
is proposed to improve the output SINR of desired signal.
III. BASEBAND SELF-INTERFERENCE CANCELLATION FOR
FULL-DUPLEX WIRELESS COMMUNICATION SYSTEMS
In this section, we present two digital cancellation techniques
that can be applied in full-duplex wireless communication
systems to improve the performance, i.e., self-interference can-
cellation based on the output signal of power amplifier and two-
stage iterative cancellation.
We first consider a straightforward mathematical model of
full-duplex systems in which the receeived signal can be written a
r(n)=x(n)⊗h(l)+y(n)⊗g(l)+z(n),(3)
where x(n)and y(n)are the sample representations of the near-
end and far-end transmit signal, respectively; h(l)and g(l)(l=
1,...,L)denote the impulse response of near-end and far-end
channel, respectively; Lis the order of the channels; ⊗de-
notes the operation of convolution; z(n)is the received noise.
For ease of exposition, we assume that the signal samples and
channel responses are i.i.d.,3i.e., E[x(n)x∗(m)] = E[y(n)y∗
(m)]= δ(n−m),E[h(l)h∗(k)] = χnearδ(l−k),E[g(l)g∗(k)] =
χfarδ(l−k),E[z(n)z∗(m)] = σ2
zδ(n−m), where E[·]de-
notes expectation, δ(·)is the Kronecker delta function, χnear
and χfar represent the gain of the near-end and far-end channel
signal pathes, respectively, σ2
zis the power of received noise.
Therefore the power of the received self-interference and de-
sired signal are Pnear =χnearLand Pfar =χfar L, respectively.
Considering a frame of Nfsamples, (3) can be rewritten in
vector form as
r=Xh +Yg +z,(4)
where r=[r(1); ...;r(Nf)] is the vertical concatenation of
r(n),z=[z(1); ...;z(Nf)],h=[h(0); ...;h(L−1)],g=
[g(0); ...;g(L−1)].X=[x0,...,xL−1], where xl=[x(1 −
l); ...;x(Nf−l)].Yis defined similarly as Xfrom y(n).
During digital cancellation, the near-end channel h(l)is
estimated and used for generating estimates of the self-
interference, which are then subtracted from the received signal.
One approach of channel estimation is the least square method,
which estimates the near-end channel according to
h=(XHX)−1XHr.(5)
The self-interference cancellation is then carried out using
rc=r−X
h.(6)
By substituting (4) into (5), we get
h=h+(XHX)−1XH(Yg +z)
=h+Δh,(7)
where ΔhΔ
=(XHX)−1XH(Yg +z)is the channel estima-
tion error. The residual self-interference after cancellation is
then given by rnear,Δ=XΔh, whose power can be shown to
be (see Appendix A)
PΔ=L
NfPfar +σ2
z.(8)
Comparing PΔwith the power of received self-interference, it
is shown that the self-interference is suppressed by a factor of
η=Pnear
PΔ
=Nf
L(Pfar +σ2
z)Pnear.(9)
Furthermore, we can write the output SINR of the desired
signal as
SINR =Pfar
PΔ+σ2
z
=Pfar
L
Nf(Pfar +σ2
z)+σ2
z
<Nf
L.(10)
3Note that these assumptions do not compromise the insights of the analysis
that follows. The same conclusions can be reached if more complex models are
used.
4798 IEEE TRA NSA CTI ON S ON WIR ELESS COMMUNICATIONS, VOL.13, NO. 9, SEPTEMBER 2014
It can be seen from (9) and (10) that for an ideal full-duplex
system:
1) The suppression of self-interference increases with the
power of received self-interference (9).
2) The output SINR of the desired signal is limited by a
constant determined by the channel order Land frame
length Nf(10).
The reason is that the estimation precision of hincreases
with Pnear, but is affected by the existence of the desired signal
(cf. (7)). Note that the second property relies on the validity of
the first property. Suppose the suppression of self-interference
is fixed, when Pnear increases, the output SINR will decrease
due to increasing PΔ. Unfortunately, this situation will occur
when RF/analog impairments are present, as will be shown in
the following subsection.
A. Self-Interference Cancellation Based on the Output Signal
of Power Amplifier
In this subsection, we show that the cancellation of self-
interference is limited by RF/analog impairments, and propose
a digital cancellation scheme based on the output signal of
power amplifier to address this issue.
As is described in Section II-B, the effects of quantization
error, phase noise, and sampling jitter can be made low enough
given reasonable Tx-Rx isolation, while the spurious signals
caused by PA nonlinearity and transmit I/Q imbalance are much
stronger. Therefore we use the effect of PA nonlinearity and
transmit I/Q imbalance as an example to demonstrate the impact
of RF/analog impairments on digital cancellation. Note that the
effect of other impairments (e.g., quantization error) are similar,
but are omitted here for brevity (however, they are included in
Sections IV and V).
We use x(n)=x(n)+ ˇx(n)and y(n)=y(n)+ˇy(n)to
denote the near-end and far-end transmit signal, respectively,
where ˇx(n)and ˇy(n)represent the spurious signal components
caused by PA nonlinearity and/or I/Q imbalance (cf. (1), note
that ais assumed to be unity for simplicity). Then (3) becomes
r(n)=x(n)⊗h(l)+y(n)⊗g(l)+z(n)
=(x(n)+ˇx(n)) ⊗h(l)
+(y(n)+ˇy(n)) ⊗g(l)+z(n).(11)
Since the term ˇx(n)⊗h(l)in (11) cannot be removed by (6),
the cancellation of self-interference in (9) becomes
η≈Pnear
ˇ
Pnear +L
Nf(Pfar +σ2
z),(12)
where ˇ
Pnear denotes the power of the term ˇx(n)⊗h(l).Fol-
lowing (2), we can write the power of ˇx(t)as γ(note that the
power of x(n)is assumed to be unity in the above), then we
have ˇ
Pnear ≈γχnearL=γPnear. Therefore it can be seen from
(12) that η<P
near/ˇ
Pnear =1/γ, i.e., the cancellation ratio
achieved by digital cancellation is limited, as opposed to the
ideal case of (9) where the cancellation ratio increases with the
received power of self-interference. In addition, since Nf
L, the denominator of (12) is usually dominated by ˇ
Pnear.
Fig. 2. Digital cancellation. Left: conventional method such as those used in
[2], [3], [5], [6]. Right: proposed approach using the output signal of power
amplifier.
Therefore we have η≈1/γ, i.e., the cancellation ratio is a
constant value determined by PA nonlinearity and transmit I/Q
imbalance. This result is consistent with [5, Fig. 10]. Therefore
we conjecture the constant cancellation ratio of digital cancel-
lation in [5] is mainly caused by RF/analog impairments such
as PA nonlinearity and transmit I/Q imbalance.
To improve the cancellation ratio, we propose to carry out di-
gital cancellation using the output signal of the power amplifier,4
which is obtained by attaching a coupler to the transmit antenna
and use another RF front-end to convert the signal to digital
samples,5as shown in Fig. 2. Denoting the resulting samples
as x(n), the procedure of channel estimation and cancellation
as in (5) and (6) can be denoted as
h=(
XH
X)−1
XHrand
rc=r−
X
h, respectively, where
Xis constructed from x(n)
following the same structure as Xin (4). This way, the spurious
components of the self-interference caused by PA nonlinearity
and transmit I/Q imbalance can also be suppressed, achieving
higher cancellation ratio of the self-interference.
B. Two-Stage Decision Feedback Iterative Cancellation
As has been shown previously, due to the fact that the
estimation precision of the near-end channel is affected by
the desired signal, the output SINR of full-duplex systems is
limited. According to (10), to achieve higher SINR, one need to
increase the frame length Nf, i.e., to use more data samples
for channel estimation. However, since the channel impulse
response h(l)and g(l)are treated as static within each frame
in (3)–(6), increasing Nfwill decrease the cancellation ratio
due to channel variation.
To address this issue, we propose a two-stage iterative can-
cellation scheme, where the far-end signal is removed from
the received signal for more accurate channel estimation and
cancellation [31]. In the first stage, the self-interference can-
cellation is carried out according to (5) and (6). In the second
stage cancellation, the far-end signal is detected based on the
result of (6) and used for generating an estimate of the far-end
transmit signal y(n). An estimate of the received far-end signal
is subsequently generated and subtracted from the received
signal as follows
r=r−
Y
g,(13)
4An alternative approach is nonlinear echo cancellation. For example,
Volterra filter [28] can be employed to model the nonlinear signal path. We
choose the proposed approach due to the high complexity in identifying the
parameters of nonlinear models.
5Same approach has been used in [29], [30].
LI AND MURCH: BASEBAND TECHNIQUES FOR SINGLE-CHANNEL FULL-DUPLEX WIRELESS COMMUNICATION SYSTEMS 4799
Fig. 3. Structure of the proposed two-stage iterative cancellation scheme.
where
Yis constructed from y(n)following the same structure
as Yin (4),
gis an estimate of the far-end channel. ris then
used together with Xto estimate the near-end channel again
according to (5). By taking the far-end signal into account,
the near-end channel can be estimated more precisely, thus im-
proving the accuracy of cancellation. After the cancellation, the
far-end signal is detected again and used for a new iteration of
near-end channel estimation and self-interference cancellation.
This procedure is repeated until a satisfactory cancellation ratio
and output SINR is achieved.
Note that in addition to the pre-known training symbols, we
can also use y(n)to improve the accuracy in estimating the far-
end channel g, i.e., decision-feedback channel estimation [32].
Therefore, we can combine the procedure of far-end channel
estimation, far-end signal removing, and near-end channel esti-
mation into one step as follows
h
g=(AHA)−1AHr,(14)
where
hand
gare jointly estimated using AΔ
=[X
Y].
The proposed two-stage iterative cancellation scheme is de-
picted graphically in Fig. 3. Note that the fundamental prin-
ciple of this scheme is identical to that of multi-stage Parallel
Interference Cancellation (PIC) in Multiuser Detection (MUD)
[33]–[35], with each iteration in the second stage cancellation
corresponding to a stage of PIC. In particular, one can show that
the procedure of the proposed scheme is the same as that carried
out for a two-user system in [34], [35], with the exception that
in our case the near-end transmit signal is known. Therefore
the performance of the two-stage iterative canceller must be
as good or better than that of a two-user system in [34], [35].
In addition, by considering the near-end transmitter and far-
end transmitter as two transmit antennas in a Multiple Input
Multiple Output (MIMO) system, the system model of (4) is
identical to that of a wide band 2 ×1 MIMO system. Therefore
the proposed iterative cancellation scheme is the same as the
iterative channel estimation and data detection algorithm of
[36], though the soft decisions of data symbols are used for
channel estimation in [36] while we use hard decisions here.
We note that the decoding errors of the desired signal will
affect the precision of near-end channel estimation in the next
iteration, a phenomenon known as ‘error propagation’ in mul-
Fig. 4. Structure of the proposed transceiver for full-duplex wireless commu-
nication systems. RF cancellation is assumed to have been applied to cancel the
LOS self-interference, but not shown in the figure.
tiuser detection. To improve the resilience to error propagation,
one can employ the technique of soft decision as in [32], [36].
However, as is shown in [32], [37], the system performance can
be improved effectively using hard decision so long as the initial
detection error is moderate. In Section V, it will be shown by
simulation that the system performance in terms of SINR and
BER is substantially improved by introducing the second stage
cancellation.
C. Overall Structure of Proposed Full-Duplex
Wireless Transceiver
Combining the two digital cancellation approaches described
in Section III-A and B, we propose a transceiver structure for
full-duplex wireless communication systems as shown in Fig. 4.
We have considered a system based on 802.11a/g, an existing
wireless standard where full-duplex communication could be
applied because of its low transmitting power and low channel
variation rate. The transceiver is depicted in baseband equiv-
alent form, with the process of up/down-conversion omitted
for simplicity of illustration. Note that RF cancellation has
been applied in the system to suppress the LOS component of
self-interference, but is not shown in Fig. 4 because one may
also rely on antenna separation for the same purpose when the
device is not constrained by size, as described in Section II-B.
As is shown in Fig. 4, the OFDM symbols are passed
through a wave shaping filter and DAC, resulting in analog
baseband signal ξ(t), which is subsequently up-converted and
amplified into ξPA (t)for transmission. The block labeled “I/Q
error” represents the effect of I/Q imbalance introduced during
up-conversion; while “PA” represents the nonlinear effect of
the power amplifier. ξPA (t)is converted into digital samples
for estimating the near-end channel and canceling the self-
interference, and the detection of the far-end signal is carried
out subsequently, after the carrier frequency offset (CFO) and
transmitter I/Q imbalance of the far-end signal is estimated and
compensated.
Since wide-band frequency selective channels are converted
into multiple narrow-band sub-channels in OFDM systems.
4800 IEEE TRA NSA CTI ON S ON WIR ELESS COMMUNICATIONS, VOL.13, NO. 9, SEPTEMBER 2014
One may also consider carrying out self-interference cancel-
lation on each sub-channel, i.e., in the frequency domain. How-
ever, while the ideal linear components of the self-interference
can be cancelled, the nonlinear components arising from PA
nonlinearity and I/Q imbalance cannot be handled on a sub-
channel basis. The reason is that the orthogonality between
sub-channels provided by the feature of cyclic prefix etc. in
ideal OFDM systems does not apply to the nonlinear signal
components. Therefore the performance of frequency domain
cancellation will be limited by PA nonlinearity and transmit I/Q
imbalance as in Section III-A.
We denote the received signal as ρ(t)(cf. Fig. 4) and the far-
end transmit signal as ψPA (t).UsingξPA(k),ψPA (k), and ρ(k)
to denote the baseband equivalent samples of ξPA(t),ψPA (t),
and ρ(t), respectively, we have
ρ(k)≈
Λ−1
l=0
ηlξPA (k−l)+ej(ω0
+ωk)
Λ−1
l=0
ςlψPA (k−l)+ζ(k),
(15)
which is similar to the model of (3) or (11), with ηland ςl
representing the impulse response of the near-end and far-end
channel respectively, Λis the order of the channels and ζ(k)
represents the received noise. Note that the term ej(ω0+ωk)is
included to model the carrier frequency offset (CFO) between
the two communicating devices, where ω=2π(Δf/fs)with
Δfand fsrepresent the frequency offset and the sampling rate
of ρ(k)respectively, and ω0denotes the initial phase difference.
In addition, since the signals in real systems are not strictly
band-limited, the sampling rate fsis chosen as fs=RRx/T to
ensure the accuracy of signal representation and cancellation,
where Tis the sampling period of OFDM symbols (i.e., system
bandwidth), RRx is the oversampling ratio. We write (15) in
vector form for a frame of Nfsamples as follows
ρ≈Ξη+ejω0ΦΨς+ζ,(16)
where Φ=diag([1,e
jω,...,e
j(Nf−1)ω]), while ρ,Ξ,η,Ψ,
ς, and ζare constructed similar to the corresponding matri-
ces/vectors in (4). The two-stage iterative cancellation scheme
described in Section III-B can then be applied to (16), with Ξ,
ΦΨ,η, and ejω0ςcorresponding to X,Y,h, and gof (4),
respectively. In particular, the detection result of the far-end
signal and the estimation of CFO are used for constructing
Ψ
and
Φ(i.e., estimates of Ψand Φ), respectively. In addition, the
effect of transmit I/Q imbalance is also taken into consideration
to improve the accuracy in generating estimates of the far-
end signal. As is shown in Fig. 4, the detection result of
the far-end signal is modulated again and passed through a
pulse shaping filter to get
ψ(k).
Ψis then constructed from
ψIQ(k)=α
ψ(k)+
β
ψ∗(k), where αand
βare the parameters
characterizing the effect of I/Q imbalance [24].
IV. PERFORMANCE ANALYSIS OF THE
PROPOSED TRANSCEIVER
This section investigates the analytical performance of the
proposed full-duplex transceiver of Fig. 4 in terms of average
signal to interference and noise ratio (SINR), which is de-
fined as SINR =E[Pfar (t)]/(σ2
z+E[PI(t)]), where E[·]means
taking the expectation over time (i.e., over different channel
realizations). Pfar(t)and PI(t)denote the power of the received
far-end signal and that of the residual near-end interference at
time instant t, respectively. σ2
zrepresents the noise power.
To simplify the analysis, we consider a model similar to (11),
where x(n)and y(n)are OFDM symbols. We will denote γPA ,
γIQ,γPN , and γQN as the relative power of the spurious signal
components caused by PA nonlinearity, I/Q imbalance, phase
noise, and quantization, respectively (cf. Table I). The analysis
steps we follow are similar to those in (3)–(10). However, the
analysis in this section is more involved due to the incorporation
of signal distortions and the fact that the transmit signals x(n)
and y(n)are not i.i.d. as assumed in Section III.
To facilitate the analysis, we use uw=[uw
1;...;uw
N]to de-
note the vector of near-end transmit symbols in the frequency-
domain for the w-th OFDM symbol, where Nis the length
of the Inverse Fast Fourier Transform (IFFT), i.e., the total
number of subcarriers. uw
nis non-zero only if n∈S, which
denotes the set of subcarriers in use. The time-domain samples
xw
DT =[xw
1;...;xw
N]are obtained by applying IFFT to uw, i.e.,
xw
DT =FHuw, where the (m, n)-th entry of Fis
[F](m,n)=1
√Ne−j2π
N(m−1)(n−1) m, n =1,...,N (17)
Then the w-th OFDM symbol is given by xw=[xw
CP;xw
DT],
where xw
CP =[xw
N−M+1;...;xw
N]is the last Msamples of
xw
DT, i.e., the Cyclic Prefix (CP). Similarly, we can define
the w-th OFDM symbol of the far-end signal as yw=[yw
CP;
yw
DT], with the corresponding frequency-domain symbols vw=
[vw
1;...;vw
N]. We then write the received signal as
r=Xh +Yg +z+zq,Rx +zPN,(18)
where the dimension of ris W(M+N)×1since there are
WOFDM symbols in each frame, zq,Rx and zPN denote the
quantization noise and phase noise at the receiver side, re-
spectively. X=X+XPA +XIQ,Y=Y+YPA +YIQ .X
and Yare constructed from the xwand ywrespectively. XPA
and YPA represent the nonlinear signal components resulting
from PA nonlinearity, while XIQ and YIQ represent the signal
components resulting from Tx I/Q imbalance.
Note that different RF/analog impairments are coupled to-
gether in practical systems, and it is not rigorous to model the
joint effects of multiple impairments by independent additive
error terms (spurious signals). However, since the spurious sig-
nal caused by each impairment is much weaker than the ideally
linear signal (cf. Table I), we can use (18) as an approximation.
For example, when two RF/analog impairments are applied on
a signal x(t)sequentially, the resulting signal can be written as
(cf. (1), note that ais assumed to be unity for simplicity)
x(t)=G2{G1[x(t)]}
=G2{x(t)+F1[x(t)]}
=x(t)+F1[x(t)] + F2{x(t)+F1[x(t)]}(19)
LI AND MURCH: BASEBAND TECHNIQUES FOR SINGLE-CHANNEL FULL-DUPLEX WIRELESS COMMUNICATION SYSTEMS 4801
Since x(t)is much stronger than F1[x(t)],wehaveF2{x(t)+
F1
[x(t)]}≈F2
{x(t)}, therefore x(t)≈x(t)+F1[x(t)]+F2[x(t)],
and the same approximation can be made for the effect of
multiple impairments that are coupled together.
Because of the special structure of xwand yw, we can write
Xas X=[X1;...;XW], where Xw=[Xw
CP;Xw
DT]with
Xw
CP and Xw
DT defined as follows6
Xw
CP =⎡
⎢
⎢
⎣
xw
N−M+1 xw−1
N... x
w−1
N−L+2
xw
N−M+2 xw
N−M+1 ... x
w−1
N−L+3
... ... ...
xw
Nxw
N−1... x
w
N−L+1
⎤
⎥
⎥
⎦
Xw
DT =⎡
⎢
⎣
xw
1xw
N... x
w
N−L+2
xw
2xw
1... x
w
N−L+3
... ... ...
xw
Nxw
N−1... x
w
N−L+1
⎤
⎥
⎦
Similarly, we can write Yas Y=[Y1;...;YW].Ywmay be
written as Yw=[[Yw−1
DT ](N−q+1:N,1:L);Yw
CP;[Yw
DT](1:N−q,1:L)]
or Yw=[[Yw−1
CP ](N−q+1:N,1:L);Yw
DT;[Yw
CP](1:N−q,1:L)], where
Yw
CP and Yw
DT are defined similar to Xw
CP and Xw
DT
respectively, and qis an integer that depends on the time offset
between the near-end signal and the far-end signal. In addition,
the signal obtained from the power amplifier is written in
matrix form as
X=X+Xq+XPN
=X+XPA +XIQ +Xq+XPN.(20)
where XPN and Xqdenote the signal distortions caused by
phase noise and quantization error.
A. SINR of the First Stage of Cancellation
In the first stage of cancellation, the near-end channel is
estimated by
hs1 =(
XH
X)−1
XHr=h+Δhs1 ,(21)
where the channel estimation error is
Δhs1=(
XH
X)−1
XH(−Xqh−XPNh+Yg+z+zq,Rx +zPN).
(22)
Therefore the received signal after self-interference cancella-
tion is
ss1 =r−
X
hs1
=Yg −
XΔhs1 −Xqh−XPNh+z+zq,Rx +zPN ,
(23)
where
XΔhs1 represents the residual near-end signal. It can be
noticed that the achievable SINR of far-end signal is limited by
the last 6 terms of (23). In the following we will calculate the
power of these terms to obtain the SINR value.
6We assume that when the received samples are divided into frames, the
boundaries are chosen to be at the boundaries of transmit OFDM symbols.
We first look at the term
XΔhs1. Since in (22) the power
of the received far-end signal (Yg)is stronger than the other
terms (Xqh,XPNh,z,zq,Rx , and zPN), as explained in
Section II-B, Δhs1 can be written approximately as Δhs1 ≈
(
XH
X)−1
XHYg. By following similar steps as (38)–(40), we
can get the power of residual near-end signal as follows
PΔ,s1 =
Tr E(
XH
X)−1
XHYggHYH
X
(N+M)W,(24)
where the expectation can be firstly taken with respect to
channel realizations gand then with respect to the transmit
samples (Xand Y), which is valid if g,X, and Yare mutually
independent. As in Section III, we assume that the elements of
gare i.i.d., i.e., E[ggH]=χfarI, then (24) changes into
PΔ,s1 =
χfarTr E(
XH
X)−1
XHYYH
X
(N+M)W.(25)
The difficulty of obtaining PΔ,s1 then lies in the calculation of
E[(
XH
X)−1
XHYYH
X]in (25), and we will provide an ap-
proximate result as follows.
Since X=[X1;...;XW]as previously defined and
Xfea-
tures the same structure, we have
XH
X=W
w=1 (
Xw)H
Xw.
Since limW→∞(1/W )W
w=1 (
Xw)H
Xw=E[(
Xw)H
Xw],we
can approximate
XH
Xby WE[(
Xw)H
Xw]for large W.Using
a similar approach,
XHYYH
Xcan be written as
XHYYH
X=W
w=1
(
Xw)HYwW
w=1
(Yw)H
Xw(26)
=
W
w=1
(
Xw)HYw(Yw)H
Xw
+
W
w1=1,w2=1
w1=w2
(
Xw1)HYw1(Yw2)H
Xw2(27)
(a)
≈W×E(
Xw)HYw(Yw)H
Xw(28)
(b)
=W×E(
Xw)HEYw(Yw)H
Xw(29)
where (a)follows from the fact that
Xw1,
Xw2,Yw1, and Yw2
are independent with each other for w1=w2, thus the second
term of (27) can be approximated by zero for large W;(b)holds
if the expectation of (28) is taken firstly w.r.t. Ywand then
w.r.t.
Xw1.
Therefore, (25) can be rewritten as
PΔ,s1 ≈χfar
(N+M)W×Tr
R−1
XHX
RXHYYHX,(30)
where
RXHX
Δ
=E[(
Xw)H
Xw], and
RXHYYHX
Δ
=E[(
Xw)H
RYYH
Xw],RYYH
Δ
=E[(Yw)HYw].
According to (20), the signal distortions caused by RF/analog
impairments need to be considered in calculating
RXHX. Since
4802 IEEE TRA NSA CTI ON S ON WIR ELESS COMMUNICATIONS, VOL.13, NO. 9, SEPTEMBER 2014
γQN and γPN can be ignored compared with γPA and γIQ (cf.
Table I), we can write
RXHXas
RXHX≈E(Xw)HXw+γIQE(Xw)HXw∗+γPA I,
(31)
where the term γIQE[(Xw)HXw]∗is due to the fact that the
effect of I/Q imbalance on a signal x(t)is characterized by
xIQ(t)=αx(t)+βx∗(t), while the term γPA Iis due to the
assumption that the samples of the nonlinear signal components
resulting from PA nonlinearity are i.i.d. Similarly,
RXHYYHX
can be written as
RXHYYHX≈E(Xw)HRYYHXw
+γIQE(Xw)TRYYH(Xw)∗+γPA RYY H,(32)
where RYYH≈E[(Yw)HYw]+γIQE[(Yw)HYw]∗+γPA I.
Therefore we can calculate
RXHYYHXand
RXHXbased on
uw. We provide an example of calculating E[(Xw)HXw]in
Appendix B. The other terms are similar and are omitted here.
We next look into the effects of the term Xqhand zq,RX in
(23). Note that Xqdenotes the quantization error introduced
when digitizing the output signal of power amplifier (cf. (20)),
while zq,RX denotes the quantization error at the receiver side.
According to the definition at the beginning of Section IV, the
power of these two terms can be written as PQN,x=γQNPTx
and PQN,r=γQNPRx , where PTx and PRx denote the transmit
and received signal power, respectively. Since Xqhcan be
viewed as the quantization noise Xqgoing through the near-end
channel, we can approximate its power by P
QN,x=μPQN,x,
where μrepresents the near-end channel gain. Denoting the
power of received near-end signal as Pnear =μPTx ,wehave
P
QN,x=μγQNPTx =γQN Pnear. Also, since the received is
dominated by the near-end signal, PQN,r≈γQNPnear. There-
fore we can combine the power of Xqhand zq,RX into one
term as PQN =P
QN,x+PQN,r≈2γQNPnear . Similarly, we
can write the combined power of the term XPNhand zPN in
(23) as PPN ≈2γPNPnear .
Therefore the SINR after the first stage cancellation can be
obtained as follows
SINRs1 =Pfar
σ2
z+PPN +PQN +PΔ,s1
,(33)
where Pfar and σ2
zrepresent the power of the received far-end
signal and noise, respectively.
B. SINR of the Second Stage of Cancellation
Since the far-end signal is taken into consideration in the
second stage of cancellation, the estimation precision of the
near-end channel is improved over the first stage of cancella-
tion. However, as has been described in Section III-B, there
will be errors during the decoding of the desired signal, which
will propagate into the next iteration and affect the precision
of cancellation. Therefore it is very complicated to analyze the
performance of the second stage cancellation. In this paper,
we will give an analysis assuming that Yg and YIQgare
perfectly removed from the received signal of (18). Note that
similar assumption has been made in [38], [39] to analyze
the performance of SIC in MUD systems. In particular, the
estimation error of the near-end channel will be
Δhs2 ≈(
XH
X)−1
XH(YPA g+z+zq,Rx +zPN
−Xqh−XPNh).(34)
In the following, we will show that the terms Xqh,XPNh,
z,zq,RX, and zPN in (34) can be neglected in the analysis.
Take t h e t e r m zas an example, the estimation error of the
near-end channel due to the existence of zis given by Δhz≈
(
XH
X)−1
XHz, and the resulting residual near-end signal is
sr,z=
XΔhz=
X(
XH
X)−1
XHz. Since pre-multiplying zby
X(
XH
X)−1
XHmeans projecting zto the column space of
X, i.e., from a space with a dimension of (M+N)Wto a
subspace with a dimension of L(L(M+N)W), the norm
of sr,zis much smaller than that of z. Therefore, the power of
the residual near-end signal caused by the existence of the term
zis much smaller than that of z, and can be neglected in the
calculation of SINR since zalso affects SINR (cf. (23). The
same results apply to Xqh,XPNh,zq,RX , and zPN in (34), and
we only need to account for the term YPA g. Using a similar
approach as (24)–(30), we can write the power of the residual
near-end signal as follows
PΔ,s2 ≈χfar
(N+M)W×Tr
R−1
XHX
RXHYPA YH
PA X,(35)
where
RXHYPA YH
PA X
Δ
=E[(
Xw)HRYPA YH
PA
Xw],RYPA YH
PA =
E[Yw
PA (Yw
PA )H]. Using the assumption again that the samples
of the nonlinear signal components induced by PA nonlinearity
are i.i.d., we have RYPAYH
PA =L×γPA PTxI, therefore
RXHYPA YH
PA X=L×γPA PTx
RXHX, and (35) will be
PΔ,s2 ≈χfarγPA PTx L2
(N+M)W.(36)
Therefore the SINR in the second stage of cancellation is
SINRs2 =Pfar
σ2
z+PPN +PQN +PΔ,s2
.(37)
Note that SINRs1 in (33) reduces to (10) when there are no
RF/analog impairments and the transmit signals x(n)and y(n)
are i.i.d. as assumed in Section III. Specifically, PΔ,s1 reduces
to PΔ,s1 =(χfarL2/(N+M)W)=(Pfar L/Nf), which is
consistent with PΔin (42) (note that the noise is neglected
in calculating PΔ,s1). With the introduction of second stage
cancellation, the self-interference is cancelled more precisely. It
can be shown from (36) that PΔ,s2 ≈γPA PΔ,s1 if the transmit
signals x(n)and y(n)are i.i.d., therefore a higher SINR can be
achieved. In addition, there is a tradeoff in choosing Was has
been described in Section III-B: The precision of cancellation
can be improved by increasing Wsince more samples can be
used for estimating the near-end channel. On the other hand,
since the channels are treated as static within each frame,
increasing Wwill decrease the cancellation ratio due to channel
variation.
LI AND MURCH: BASEBAND TECHNIQUES FOR SINGLE-CHANNEL FULL-DUPLEX WIRELESS COMMUNICATION SYSTEMS 4803
V. S IMULATION RESULTS
The performance of the proposed digital cancellation scheme
is evaluated by computer simulation in this section. We consider
a system with two users communicating with each other and the
parameters used in the simulation are similar to those of IEEE
802.11a/g systems. The bandwidth of the system is 20 MHz.
The FFT size and CP (Cyclic Prefix) length are 64 and 16,
respectively. Fifty-two of the 64 subcarriers are occupied. The
transmit symbols on each subcarrier are QPSK modulated.
For simplicity, no coding or data scrambling are applied. The
pulse shaping filter is a Hanning windowed sinc function, with
oversampling factor RTx =16.
The far-end channel is modeled as multipath Rayleigh fading
with standard power delay profile (PDP) as specified in the
IEEE 802.11 standard [40]. Each signal path has a bell Doppler
spectrum shape with the maximum Doppler shift of 6 Hz. The
near-end channel is made up of two parts, i.e., line-of-sight and
non-line-of-sight. The NLOS channel is modeled similar to the
far-end channel with the same power delay profile and a path
loss of 60 dB.7The LOS channel is modeled as Rician fading
with a K-factor of 10, while the path loss depends on the Tx-Rx
isolation, which is determined by the performance of the RF
cancellation techniques applied. Unless otherwise stated, we
will assume the Tx-Rx isolation to be 40 dB, as is described
in Section II-B.
The transmit power is chosen to be 15 dBm. As in Table I,
the PA nonlinearity is modeled by Rapp Model [24], [25] with
the parameter p=3. In addition, the operating point of the PA
is adjusted so that the input back-off (IBO) is 8 dB. The I/Q
imbalance exhibits an amplitude mismatch of 0.5 dB and phase
mismatch of 3 degrees. The power spectrum density (PSD)
of the LO phase noise has a constant value of −110 dBc/Hz
below 10 KHz, and decreases by 20 dB per decade beyond that
[26]. The carrier frequency offset between the near-end and
far-end transmitter is set to 10 KHz. The resolution of ADCs
is chosen to be 14 bits. The oversampling factor RRx at the
receiver side is selected as 4, and a FIR filter with 40 taps is
used for self-interference cancellation. Unless otherwise stated,
3 iterations are performed in the second stage of cancellation.
The cancellation is carried out based on frames with length
Nf= 3200, which corresponds to a duration of 10 OFDM
symbols (note that the performance will be degraded if the
frame is too long due to channel variation, as described in
Section IV). The far-end channel state information for detection
and the carrier frequency offset are acquired from training
symbols. We notice that the time shift between the near-end
signal and far-end signal has no obvious effect on the output
SINR, therefore in the simulation we assume that the two users
start transmitting signal frames at the same time, i.e., the time
shift between the received near-end signal and far-end signal
equals the propagation delay between the two users.
7This corresponds to a propagation distance of 5 m in free space for 5 GHz
radio signal, which means that the nearest object that reflects the signal is 2.5 m
away from the device. In fact, as described in Section II-B, due to the power
loss in reflection/diffraction, the self-interference from NLOS pathes is much
lower compared with the LOS component.
Fig. 5. Cancellation achieved by the proposed digital cancellation scheme
under different levels of Tx-Rx isolation.
We use the conventional digital cancellation approach of
[5] as a baseline for comparison, which features the same
structure as the left hand side of Fig. 2 and cancels the self-
interference according to (6) using near-end channel estimated
in the frequency domain. The performance of our proposed
scheme is compared with the baseline scheme [5] under the
same Tx-Rx isolation and system parameters.
We first investigate the performance of the proposed scheme
in terms of cancellation ratio, which is defined as the ratio
between the power of the self-interference before and after
the digital cancellation (cf. (9)). Fig. 5 shows the cancellation
ratio for different levels of Tx-Rx isolation when the path loss
experienced by the far-end signal is 70 dB. We can see that the
proposed scheme achieves 46 dB cancellation in the first stage
when the Tx-Rx isolation is 40 dB. In addition, the cancellation
ratio increases as Tx-Rx isolation decreases, which is consistent
with what has been observed in [6], [21]. This is because the
power of the received self-interference increases as the Tx-Rx
isolation decreases, which will increase the precision of near-
end channel estimation, as described in Section III-A. The
cancellation ratio achieved by the proposed scheme increases to
60–70 dB when the second stage cancellation is also included.
On the other hand, the baseline digital cancellation scheme only
achieves about 28 dB cancellation for almost all the cases of
receive power, which is due to the effect of PA nonlinearity and
transmit I/Q imbalance as described in Section III-A. Note that
a similar phenomenon can be observed for the second stage
of the proposed scheme. The reason is the quantization error
and phase noise cannot be handled by digital cancellation. As
the power of received self-interference increases, the effects of
quantization error and phase noise become the bottleneck of the
performance.
Fig. 6 depicts the output SINR of the desired signal corre-
sponding to the result of Fig. 5. It can be seen that the SINR
achieved in the first stage of cancellation is almost a constant
value, while the introduction of second stage cancellation can
improve the SINR performance. The simulation results matches
well with the analysis. Moreover, the SINR values achieved by
the proposed scheme is much higher than that of the baseline
scheme. In fact, the performance of the proposed scheme is
4804 IEEE TRA NSA CTI ON S ON WIR ELESS COMMUNICATIONS, VOL.13, NO. 9, SEPTEMBER 2014
Fig. 6. SINR performance of the proposed scheme under different levels of
Tx-Rx isolation. SNR =46dB.
Fig. 7. SINR performance of the proposed full-duplex system for different
distances between the near-end user and far-end user. Tx-Rx isolation is
assumedtobe40dB.
limited by quantization error and phase noise; while the base-
line is limited by PA nonlinearity and I/Q imbalance, which
generates much more signal distortions as is shown in Table I.
As the Tx-Rx isolation increases, the receiver sees a decreased
power in the spurious signal components caused by distortions
(cf. ˇ
Pnear in (12), PPN and PQN in (33) and (37)), therefore
higher SINR values can be achieved. However, the SINR will
finally saturate as Tx-Rx isolation keeps increasing, since it is
bounded by the received far-end signal to noise ratio.
Fig. 7 shows the SINR performance of the proposed
transceiver for different path losses experienced by the far-end
signal. We define ESR and SNR as the received near-end signal
to far-end signal ratio and the received far-end signal to noise
ratio, respectively. The achieved SINR values achieved by the
proposed schemes is much higher than that achieved by the
baseline scheme, and is substantially increased by introduc-
ing the second stage of cancellation. In particular, the SINR
achieved in the first stage of the proposed scheme is substan-
Fig. 8. BER performance of the proposed transceiver for different distances
between the near-end user and far-end user.
tially lower than the SNR value when the path loss of far-end
signal is small, while in the second stage cancellation this gap
is reduced to about 8 dB. Note than this gap depends on the
quantization error and phase noise, i.e., PPN and PQN in (37).
Therefore the output SINR of the second stage cancellation can
be further increased with higher Tx-Rx isolation, as can be seen
in Fig. 6.
To further demonstrate the effectiveness of the second stage
cancellation, we show the bit error rate (BER) performance of
the proposed system in Fig. 8, using the same configuration as
for Fig. 7. It can be seen that the BER is decreased substantially
by introducing the second stage cancellation, especially when
the far-end path-loss is low. In addition, this improvement is
mainly achieved in the first 2 iterations of the second stage can-
cellation, and is negligible after 3 iterations. The reason is that
the near-end channel identification and far-end data detection
have reached the highest achievable accuracy in 3 iterations,
and the subsystem imperfections emerge as the bottleneck.
Since the far-end transmit signal used in the second stage
cancellation is generated based on the output of the decoder
(cf. Fig. 3), the system performance is affected by the decoding
errors. To investigate this effect, Fig. 8 also shows the BER
performance when perfect detection is used for generating far-
end transmit signals in the second stage cancellation (marked
as ‘perfect detection’). It can be seen that the BER performance
for perfect detection is only slightly better than for the proposed
scheme. The reason is that the effect of PA nonlinearity on
the far-end signal cannot be reproduced when generating the
estimate of the far-end transmit signal. Therefore the accuracy
of self-interference cancellation in the second stage is mainly
limited by the nonlinear components of the far-end signal, as
can be seen in (34)–(36). It is also worth noting that the BER
performance in Fig. 8 is different from that can be achieved
in ideal Rayleigh-fading channels with the SINR values in
Fig. 7. The reason for this is twofold: (1) the residual self-
interference is not Gaussian distributed; (2) we have taken
various RF/analog impairment effects into consideration in the
simulation, including PA nonlinearity, LO phase noise, and
CFO, each of which will degrade the BER performance.
LI AND MURCH: BASEBAND TECHNIQUES FOR SINGLE-CHANNEL FULL-DUPLEX WIRELESS COMMUNICATION SYSTEMS 4805
Fig. 9. Performance of the proposed cancellation scheme for different ADC
resolutions. SNR =46dB.
Fig. 9 shows the performance of the proposed system for
different ADC resolutions (Nbit1 and Nbit2 in Fig. 4). The far-
end path-loss is chosen to be 70 dB, and we have considered
two cases in which the Tx-Rx isolation is 40 dB and 60 dB,
respectively. It can be seen that the output SINR in dB scale
increases almost linearly with the resolution of ADC when the
ADC resolution is low, and saturates as the resolution keeps in-
creasing. This is because the quantization error is the major fac-
tor limiting the system performance when the ADC resolution
is low. As the precision of ADCs increases, the power of quan-
tization noise decreases and other effects will emerge as the
bottleneck. It is also shown that when Tx-Rx isolation increases
from 40 dB to 60 dB, the requirement on ADC resolution can be
decreased by 3 bits to achieve the same SINR value. The reason
is that the dynamic range of the received signal is decreased due
to the reduction in the power of the self-interference.
VI. CONCLUSION
We have focused on digital cancellation techniques in full-
duplex wireless communication systems. We show that the
effects of ADC, phase noise, and sampling jitter are not the
bottleneck of WiFi-like systems given the pre-cancellation
achieved by existing RF techniques. However, PA nonlinearity
and transmit I/Q imbalance are significant factors that limit
the precision of digital self-interference cancellation, and as
such we propose to use the signal at the output of the power
amplifier to carry out the cancellation. In addition, to improve
the output SINR, we propose a two-stage cancellation scheme
which iteratively refines the cancellation using the detection
result of the desired signal. The proposed approach is evaluated
analytically and by simulation, and is shown to substantially
outperform existing digital cancellation schemes.
APPENDIX A
The power of residual self-interference is given by
PΔ=1
Nf×Tr E[XΔhΔhHXH](38)
=1
Nf×ETr X(XHX)−1XH
×(YggHYH+zzH)X(XHX)−1XH (39)
=
Tr EX(XHX)−1XH(YggHYH+zzH)
Nf
.(40)
where the second equality is due to Tr(AB)=Tr(BA). Since
E[g(l)g∗(k)]= χfar δ(l−k)and E[z(n)z∗(m)] = σ2
zδ(n−m),
we get E[ggH]=χfarIand E[zzH]=σ2
zI. By taking the ex-
pectation with respect to gand zfirst, (40) is written as
PΔ=
Tr EX(XHX)−1XHYYHχfar +σ2
zI
Nf
.(41)
Moreover, since E[y(m)y∗(m)] = δ(n−m),E[YYH]=LI.
By taking the expectation in (41) with respect to y(n), we get
PΔ=
Tr EX(XHX)−1XHχfarL+σ2
zI
Nf
(42)
=Pfar +σ2
zTr E(XHX)−1XHX
Nf
(43)
=L
NfPfar +σ2
z.(44)
APPENDIX B
Since Xw=[Xw
CP;Xw
DT],E[(Xw)HXw]=E[(Xw
DT)HXw
DT]+
E[(Xw
CP)HXw
CP], we can then calculate E[(Xw
DT)HXw
DT]and
E[(Xw
CP)HXw
CP]separately. Noticing that each column of
Xw
DT contains the elements of xw
DT with different orders and
since xw
DT =FHuw, we can write the n-th column of Xw
DT
as [Xw
DT](:,n)=FH
nuw, where FH
n(n=1,...,L)is obtained
from IFFT matrix (cf. (17)) by changing the row orders accord-
ing to the structure of Xw
DT. Therefore the (i, j )-th element of
E[(Xw
DT)HXw
DT]can be written as
E(Xw
DT)HXw
DT(i,j )=E(uw)HFiFH
juw
=TrFiFH
jEuw(uw)H,
where E[uw(uw)H]can be calculated from the statistics of uw.
For example, assuming the nonzero elements of uware i.i.d.
with zero mean and variance of E[|uw|2], then E[uw(uw)H]=
E[|uw|2]diag([a1,,...,a
N]), where anequals 1 or 0 depend-
ing on whether the corresponding subcarrier is used or not.
E[(Xw
DT)HXw
DT](i,j )can then be obtained. E[(Xw
CP)HXw
CP]
can also be calculated similarly and therefore we can get
E[(Xw)HXw].
ACKNOWLEDGMENT
The authors would like to thank the anonymous reviewers
and the editors for helping improve this work. The authors also
gratefully acknowledge the support of the Hong Kong RGC.
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Shenghong Li (S’09) received the bachelor’s de-
gree in communication engineering from Nanjing
University, Nanjing, Jiangsu, China, in 2008, and
the Ph.D. degree in electronic and computer engi-
neering from Hong Kong University of Science and
Technology (HKUST), Hong Kong, in 2013, respec-
tively. He is now with the Commonwealth Scientific
and Industrial Research Organisation (CSIRO) of
Australia. His research interests include full-duplex
techniques wireless communication systems, coop-
erative communication and MIMO.
Ross D. Murch (M’84–SM’98–F’09) received the
bachelor’s and Ph.D. degrees in electrical and elec-
tronic engineering from the University of Canterbury,
New Zealand. He is a Chair Professor and Depart-
ment Head of Electronic and Computer Engineering
at the Hong Kong University of Science and Tech-
nology (HKUST). His research contributions include
more than 200 publications and 20 patents on wire-
less communication systems and antennas including
MIMO, OFDM, propagation, MIMO antennas, and
these have attracted over 9000 citations. His current
research interests include the Internet-of-Things, energy harvesting, recon-
figurable systems and autonomous systems. He is the founding and current
Director of the Center for Wireless Information Technology, HKUST and also
acts as a consultant for industry and government. He has been the publication
editor, area editor and associate editor for IEE E T RANSACTIONS ON WIRE-
LESS COMMUNICATIONS, is currently the Chair of the IEEE Communications
Society technical committee on wireless communications and is also a dis-
tinguished lecturer for IEEE Vehicular Technology Society. He has been the
David Bensted Fellow, Simon Fraser University, Canada, and was an HKTIIT
Fellow at Southampton University, U.K. He was the Technical Program Chair
for the IEEE Wireless Communications and Networking Conference in 2007,
Keynote Chair for IEEE International Conference on Communications in 2010,
and also the Advanced Wireless Communications Systems Symposium in IEEE
International Communications Conference in 2002. He was also a keynote
speaker at IEEE GCC 2007, IEEE WiCOM 2007, IEEE APWC 2008, and
IEEE ICCT 2011. He has a strong interest in education and enjoys sharing his
experiences with students. He is also a Fellow of IET and HKIE.
