Abstract
In this work, we study the self-interference cancellation (SIC) capability of two basic radio frequency (RF) SIC schemes: auxiliary antenna cancellation and multireconstruction-path (MRP) cancellation (including particular two-reconstruction-path balun cancellation), and derive their cancellation capability in detail. Theoretical results show that auxiliary antenna cancellation capability and balun cancellation capability are related to the ratio of bandwidth to carrier frequency, the latter is further related to an angle ratio; that is, the ratio of the angle between the self-interference vector and the first fixed delay vector to the angle between the two fixed delay vectors, and common MRP cancellation capability is essentially related to the channel response of self-interference and the canceller frequency response. Numerical results confirm a perhaps obvious intuition: MRP cancellation outplays auxiliary antenna cancellation to cancel self-interference, especially when multiple self-interference paths exist, and MRP cancellation with more reconstruction paths achieves higher cancellation capability.
1. Introduction
In full-duplex wireless communication, a transceiver may simultaneously transmit one signal and receive another signal on the same frequency band; therefore, the full-duplex spectral efficiency, in theory, would be twice as high as the half-duplex one [1, 2]. However, the signal one transceiver has transmitted will inevitably reach the receiving chain on the same transceiver to cause self-interference. Due to the common short distance between transmission and reception of a transceiver, the self-interference signal in the receiving chain is usually strong enough to stop the useful signal form another transceiver to pass through the receiving chain for decoding. Therefore, there is a fundamental issue, i.e., self-interference cancellation, in full-duplex wireless communication. Recent studies have shown that a strong self-interference should be cancelled first in the RF domain to ensure the useful signal to pass through RF front end [3–14]. The commonly used RF-SIC schemes may be divided into two kinds.
The first one is antenna cancellation. It may be further divided into two subtypes. The first subtype is auxiliary antenna cancellation, as shown in Figure 1. On a single transceiver of this scheme, two transmitting antennas are used, where the second one is placed half carrier wavelength further from the receiving antenna than the first one. This antenna setting causes signals received from the two transmitting antennas to get a phase delay difference of π at the carrier frequency and thus add destructively. In practice, this scheme gives a cancellation of about 20 dB for 20 MHz bandwidth [3]. The second subtype is antenna-self-cancellation, which is based on advanced antenna design to improve isolation between the transmitting and receiving antenna ports. Here, isolation is approximately equivalent to cancellation. High isolation causes weak self-interference to enter the receiving chain. Reference [4] reports an antenna design that uses wavetraps to provide 70 dB isolation even with instantaneous bandwidths of 80 MHz.
The second scheme is multireconstruction-path (MRP) cancellation, as shown in Figure 2. In this scheme, multiple reconstruction paths with fixed time delay, variable attenuation, and optional variable phase shift are used to reconstruct the self-interference for cancellation. If a negative copy is reconstructed, the copy is added with the received signal; otherwise, it is subtracted from the received signal. The reconstruction may be done in the RF domain, where the RF transmit signal is tapped to multiple physical paths to accomplish reconstruction [5–8]. Bharadia et al. [5] report that their MRP scheme of this form cancels up to 60 dB for 80 MHz bandwidth. The balun cancellation in [9, 10] is a particular two-reconstruction-path cancellation case without phase shifters. Hong et al. [10] report that their scheme of this form cancels up to 33 dB for 40 MHz bandwidth. The reconstruction may also be done equivalently in the digital domain, where the digital baseband signal is filtered and then converted to the RF signal by an auxiliary transmit chain. Kiayani et al. [11] report that their MRP scheme of this form cancels up to 54 dB for 20 MHz bandwidth.
These two kinds of RF-SIC schemes, as shown in experimental results of previous studies, have reduced self-interference significantly; however, their theoretical cancellation capability has not been presented yet. The cancellation capability is defined as the ratio of the uncancelled self-interference signal power before cancellation to the residual interference signal power after cancellation in the interested signal band, which is a key performance indicator to the SIC scheme and determines whether the scheme is suitable or not. In this paper, we will study the theoretical cancellation capability of auxiliary antenna cancellation and MRP cancellation, considering that the antenna-self cancellation is quite related to antenna design; we will not study it here. The theoretical cancellation capability of the studied RF-SIC schemes will be derived in detail, and some closed-form expressions of cancellation capability will also be presented.
2. Auxiliary Antenna Cancellation Capability Analysis
2.1. System Model
The system model of auxiliary antenna cancellation is shown in Figure 1. This scheme, which aims at cancelling the line-of-sight (LOS) self-interference, is based on the principle that transmissions from two antennas with phase delay difference of π will add destructively at a receiving antenna [3]. The RF signal in this scheme is split into two parts in a constant ratio by a power splitter. The two parts are attenuated, respectively, by variable attenuators and and then sent, respectively, by antennas TX1 and TX2. TX1 and TX2, as well as receiving antenna RX, are placed elaborately to make TX2 further away from RX than TX1, where is the wavelength of the carrier. and are adjusted to make the two parts arrive at RX with the same gain, which is denoted as A.
2.2. Cancellation Capability Analysis
In order to obtain cancellation capability when only LOS self-interference path exists, we need to know the residual self-interference power and the original uncancelled total power. Here, we derive the residual self-interference power first.
The transmitted RF signal may be written aswhere denotes the sending complex baseband signal and is the carrier frequency. Its Fourier transform is [15]where is the Fourier transform of and denotes the complex conjugate of .
The received interference signal , which contains two parts, respectively, from TX1 and TX2 with corresponding delay, may then be expressed aswhere d is the distance between TX1 and TX2 and c is the speed of light. Its Fourier transform is
According to Parseval’s theorem and the symmetry of magnitude spectra of the real-valued signal, the residual interference signal power is given bywhere B is the signal bandwidth.
Equation (5) shows that the shape of , i.e., the amplitude-frequency characteristics of the sending complex baseband signal, affects the residual interference signal power . In order to fairly compare cancellation capability of each cancellation scheme, we take no account of the characteristics of sending signal and assume that has a rectangular shape, i.e., having a const value across the whole bandwidth B. Now, the residual interference signal power is
In order to obtain the cancellation capability, we also need to know the original uncancelled total power. The power of self-interference signal from TX1 is
And the power of self-interference signal from TX2 is
Therefore, the cancellation capability of auxiliary antenna cancellation scheme is
3. MRP Cancellation Capability Analysis
Figure 2 illustrates the system model of MRP cancellation. This scheme uses multiple reconstruction paths to reconstruct self-interference and then cancels it from the received signal. We first analyze the balun cancellation [9, 10], which is a particular two-reconstruction-path cancellation using a balun as a subtractor, and then we analyze the common MRP cancellation [5, 6].
3.1. Two-Reconstruction-Path Balun Cancellation
In balun cancellation, the two reconstruction paths have fixed time delays (, ) and variable attenuations (, ), but no phase shifter. This scheme aims at cancelling LOS self-interference or circulator leakage self-interference when a circulator is used.
In this scheme, settings of the two paths influence the residual self-interference power and the cancellation capability. The first one is the two fixed time delays. We denote the angle between and as β the angle between and as , i.e., and . x is the ratio of the angle between the self-interference vector and one fixed delay vector to the angle between the two fixed delay vectors, as shown in Figure 3. β is empirically set to , which is used in our following analysis. The second setting is the two variable attenuations. Our goal is to find and to cancel maximum and leave minimum self-interference power across the whole signal bandwidth.
Set the transmitted RF signal to be the same as equation (1) and the Fourier transform of transmitted RF signal thus to be the same as equation (2). The received residual interference signal is
And the Fourier transform of is
According to Parseval’s theorem and the symmetry of magnitude spectra for real-valued signal, the residual interference signal power is given by equation (12). In order to fairly compare cancellation capability, we presume that has a const value across the bandwidth B too. Now, the residual interference signal power is given by equations (13) and (14).
To find and that minimize , we examine the first derivative of with respect to and and set them to zero:
From equation (15), a set of and is obtained:
It may be verified that this set of and minimizes . Substituting this set of and (equation (16)) in equation (14) gives the lowest residual interference signal power , such that
The uncancelled self-interference signal power is as follows:
According to equations (17) and (18), when only the LOS or circulator leakage self-interference path exists, the cancellation capability of balun cancellation scheme is shown in the following equation:
3.2. Common MRP Cancellation
The common MRP cancellation, which is usually with more than two reconstruction paths, aims at cancelling multipath self-interference. It is worth noting that some MRP cancellations use phase shifters [6], while some do not [5]. Only the MRP cancellation using the phase shifter in [6] has shown a novel convex reformulation for tuning the attenuation and phase shifting parameters. Therefore, we focus on the cancellation capability of this scheme.
We denote the attenuation and phase shifting parameters as . McMichael and Kolodziej [6] have addressed by minimizing the average complex error power between the sampled versions of the measured channel response (when a canceller and signal-of-interest are absent) and the canceller frequency response . Here, and , whereas is the angular frequency sampling interval over the bandwidth of interest. Such a is obtained as follows:where
It contains sampled complex exponentials with frequencies dependent on fixed delays.
When is known, can be determined:
The residual self-interference power is
And the original uncancelled total power is
We assume that has a const value and thus has a const value across the bandwidth B too. Therefore, the cancellation capability is
There is no closed-form expression of common MRP cancellation capability. Numerical computation may be used to obtain an approximate value.
4. Results and Analysis
Through the analysis above, the cancellation capability about the whole signal bandwidth in different cancellation schemes is obtained, as shown in equations (9), (19), and (25). Equation (9) shows that the cancellation capability of the auxiliary antenna cancellation scheme is related to the signal’s fractional bandwidth (i.e., ). Equation (19) shows that the cancellation capability of the balun cancellation scheme is related to the signal’s fractional bandwidth and the angle ratio coefficient x. Equation (25) shows that the cancellation capability of common MRP cancellation is related to the channel response of self-interference and the canceller frequency response, the latter of which is further related to the tap delay setting and the sampling interval over the bandwidth of interest.
Figure 4 shows cancellation capability vs. signal bandwidth of these cancellation schemes when the carrier frequency is 2450 MHz [9] and only the LOS or circulator leakage self-interference path (as shown in Table 1) exists. For the MRP cancellation, the canceller consists of 6 taps (as shown in Table 2). The frequency sampling interval is .
From Figure 4, the following can be seen:(1)The results of auxiliary antenna cancellation and balun cancellation, which are aiming at cancelling LOS or circulator leakage self-interference, consist with the measurements reported. Figure 4 shows that the upper bound of antenna cancellation at 20 MHz is 35.7 dB, consistent with 20 dB measured in [3], and the upper bound of the worst balun cancellation setting () at 40 MHz is 38.7 dB, consistent with 33 dB measured in [10].(2)The order of cancellation capability from high to low is MRP cancellation, balun cancellation, and auxiliary antenna cancellation. The cancellation capability of all evaluated schemes increases when the signal bandwidth decreases. More reconstruction paths, or narrower bandwidth, may provide subtler canceller frequency response tuning, and thus the canceller frequency response closer to the self-interference channel response may be obtained; therefore, higher cancellation capability may be achieved.(3)Balun cancellation achieves higher cancellation capability when and lower cancellation capability when . It is easy to know that when the self-interference vector matches one of the fixed delay vectors ( or ), i.e., the self-interference and one of the reconstruction paths have the same time delay, self-interference may be completely cancelled by only this reconstruction path via turning its attenuation the same as the self-interference. When x varies towards 0.5, i.e., the self-interference vector comes to the middle of the two fixed delay vectors, vector reconstruction relationship is more easily broken by the frequency variation away from the carrier frequency in the bandwidth so that lower cancellation capability is achieved.
When multiple self-interference paths exist, equations (9) and (19) are no longer applicable for auxiliary antenna cancellation and balun cancellation, while equation (25) may also be used to take a numerical computation to obtain an approximate value. Figure 5 shows the cancellation capability when the specific case of multiple self-interference paths (as shown in Table 3) exists.
From Figure 5, the following can be seen:(1)The results of MRP cancellation consist with the measurements reported. Figure 5 shows that the MRP cancellation at 80 MHz is 60.9 dB, consistent with 60 dB measured in [5].(2)Multiple self-interference paths, which lead to a complicated self-interference channel response, will undermine the canceller frequency response matching rate and thus undermine the cancellation capability.(3)Similar to Figure 4, MRP cancellation with more reconstruction paths serves well to cancel multipath self-interference, and cancellation capability increases when the decrease in signal bandwidth.
5. Conclusion
In this paper, we derived in detail cancellation capabilities of auxiliary antenna cancellation and MRP cancellation, including particular two-reconstruction-path balun cancellation, and presented cancellation capability closed-form expressions under given conditions. Theoretical results show that auxiliary antenna cancellation capability and balun cancellation capability are related to the ratio of bandwidth to carrier frequency, the latter is further related to an angle ratio, i.e., the ratio of the angle between the self-interference vector and the first fixed delay vector to the angle between the two fixed delay vectors, and common MRP cancellation capability is essentially related to the channel response of self-interference and the canceller frequency response. Furthermore, numerical results confirm a perhaps obvious intuition: MRP cancellation outplays auxiliary antenna cancellation to cancel self-interference, especially when multiple self-interference paths exist, and MRP cancellation with more reconstruction paths achieves higher cancellation capability. Our work may be applied to evaluate the performance of an RF cancellation scheme and help the designer to select a suitable RF cancellation scheme in a full-duplex system design.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was supported by the young innovative talent project of Department of Education of Guangdong Province under Grant 2017GkQNCX107 and by the scientific research project of Qingyuan Polytechnic under Grant ZK18007.