Multi-domain blind source separation in-band full-duplex technique considering RF impairments

In-band full-duplex (IBFD) technology can potentially improve spectrum efficiency compared to half-duplex technology. The cancellation of the self-interference (SI) signal is the key to implementing the IBFD system to achieve accurate detection of the signal of interest. In this work, we fully account for the effect of IQ imbalance, phase noise (PN), additional Gaussian white noise (AWGN), and the nonlinear caused by the RF impairments of power amplifier, and adopt the method of canceling SI signal combined with the propagation, analog, and digital domain to cancel the SI signal, but the residual SI signal is still mixed with the signal of interest in the same time and frequency domain. In addition, a novel multi-domain blind source separation (MDBSS) self-interference cancellation method implemented by using the off-the-shelf components is proposed in this paper, which can realize the separation of residual self-interference signals from the signal of interest (SOI). Additionally, the multi-domain blind source separation (MDBSS) self-interference cancellation technique is used to achieve 75 dB of self-interference cancellation performance, which is proven through numerical simulation analysis, and the SOI is successfully separated in the receiver. Moreover, the multi-domain blind source separation (MDBSS) method in this paper can be applied to radar, jammer, and communication systems in the future.


INTRODUCTION
In-band full duplex (IBFD) technology has been widely studied in scientific research and the industry community for its potential and reliable double-spectrum efficiency [1][2][3] .As the Internet of Things, wireless communication devices are growing explosively and spectrum resources are being depleted.IBFD technology is the key technology to solve this problem.However, since the strong SI signal can obscure the SOI, conventional wisdom holds that two approaches can be used to solve the problem of self-interference [4][5][6] .For the first method, frequency-division duplex bidirectional communication is used, but this method wastes spectrum resources.The other is a time division duplex that can be used, but this method increases the latency.IBFD technology has emerged as an alternative to 5G or 6G, which can reduce latency.
For the practice transceiver system, however, it's hard to model the frequency response of the large bandwidth channel with traditional techniques.Therefore, the SI cancellation (SIC) performance of IBFD schemes will be inhibited as the bandwidth is increased.The SI problem can be solved in one of two ways.Firstly, the traditional route is to make the power of SI in the receiver below the receiver's noise floor by conventional SI cancellation techniques.The second route is to use the blind source separation (BSS) method for SOI.
IBFD technology can be used in WIFI, relay systems, satellite communication, and wearable intelligent terminals [7][8][9] .However, due to the portability of smart terminals, the sizes of hardware devices are strictly limited, which presents challenges to the system design and implementation of IBFD systems.Two major problems in realizing IBFD systems are the technology of SI cancellation and the construction of a full-duplex system.In addition, SI cancellation techniques can be divided into two categories, including active cancellation and passive suppression.Moreover, SI cancellation techniques can be implemented in the propagation domain, analog domain, and digital domain classified according to the different cancellation positions.Furthermore, the SI signal can be divided into three parts: the linear part, the nonlinear part, and the random noise of the transmitter.If the SI cancellation capability of the propagation domain is limited, the random signal with sufficient power of the transmitter will leak into the receiver, which cannot be modeled to cancel out.However, in the analog domain, there is a multi-tap method for canceling the SI signal, and the input signal contains real-time random noise of the transmitter.Thus, if the number of taps and the accuracy of the tap weight algorithm is reasonable, random noise from the transmitter can be effectively suppressed.Due to the complexity of the indoor environment, however, the reasonable number of taps is the subject of ongoing research.
Because of imperfections in the RF components, nonlinear components such as the mirror signal introduced by IQ imbalanced, odd order harmonics introduced by power amplifier nonlinearity, Gaussian white noise introduced by transceiver thermal effect, and phase noise introduced by local oscillator impairments are introduced into the transceiver system, as well as the multipath effect for reflection from the environment, which further increases the complexity of the model.When the model is solved by an algorithm, particularly, the AWGN is often ignored during model solving since it cannot be modeled and estimated.Moreover, the signals of interest are also unknown in signal modeling, so it is often ignored in modeling.However, this will make the reconstructed SI cancellation signal suppress the SOI in the SI cancellation stage if the SOI were to be introduced in the estimation stage.
BSS is often considered to be an effective interference suppression technique because of its strong ability to separate the mixed signals of two independent non-Gaussian signals [10][11] .SI belongs to one kind of interference, so SI cancellation technology belongs to one kind of anti-interference technology.Luo et al. proposed a full-duplex method based on GICA [12] , which has been shown to successfully improve the detection probability of radar systems.The FICA algorithm proposed by M.E.Fouda et al. [6] solves the problem of SI suppression.Experiments results show that the SNR of the receiver is successfully reduced by 6 dB as compared to the least square SI cancellation method.This paper combines multi-domain SI cancellation and BSS to realize SI suppression and extraction of the SOI.
The key innovations of this paper can be summarized: 1) First, a mathematical model is given to the system architecture and the signal model of the multi-domain blind source separation (MDBSS) method proposed in this paper takes full account of RF component imperfections.Furthermore, the method proposed in this article can be implemented using commercial components.2) Second, a theoretical derivation and a numerical simulation are performed for the SI performance limit of the proposed multi-domain blind source separation (MDBSS) method.3) The proposed method ultimately achieves extraction of the SOI in the digital domain.In addition, non-uniform frequency attenuation of the broadband linear frequency modulation (LFM) wireless signal channel is found to be one of the possible reasons affecting the performance of SI cancellation.
The remainder is organized as follows: Section 2 outlines the architecture of IBFD and the signal model of the multi-domain blind source separation (MDBSS) method; Section 3 presents the main content of MDBSS and the performance limit analysis of SI cancellation.In Section 4, the numerical simulation results and analysis are presented.A conclusion of the full text is given in Section 5.

CHANNEL MODEL OF IN-BAND FULL DUPLEX TRANSCEIVER
Mathematical modeling of the signals in the IBFD transceiver will be performed for the RF impedance problem.The paper will begin with a brief introduction to the basic full-duplex transceiver architecture used.Mathematical modeling is then performed for LO phase noise, IQ imbalance, PA nonlinearity, the effect of multipath reflection, and additional Gaussian white noise (AWGN) from the receiver.Finally, the main content is pointed out in the next section.
The architecture of the IBFD system is shown in Figure 1.While the method of performance evaluation in this paper is carried out by numerical simulation, the specific system implementation may refer to the information in Figure 1.This system adopts digital-assisted SI cancellation in the analog domain.The shared local oscillator is adopted to suppress phase noise.

Main and Auxiliary Transmitter
1) Digital Domain: The transceiver transmits a linear frequency modulation (LFM) signal with bandwidth B , which can be defined as x t e   (1) Then, the sampled digital signal presents (2) Figure 1.Design and implementation of IBFD system.
2) IQ Mixer: Due to the imbalance between the I and Q branches, the IQ mixer output signal model can be described as follows, which introduces the mirror component of the signal Where tx  is the imbalance coefficient,     is the complex-conjugate operation.We can use IRR to describe the quality of the IQ mixer, which can be presented as 2 , Because of the impairment of the common local oscillator, the phase noise is introduced, that is phase noise (PN), which can be presented as where 0 f denotes frequency, and ( )   denotes the PN, which can be described as where  denotes the 3 dB bandwidth of the PN Lorentz spectrum.
3) Power Amplifier: The introduction of a dramatically increasing nonlinear PA effect is referred to as intermodulation distortion.There are two models for RF impairments in power amplifiers, which are classified by whether they have memory.Using the memoryless model, the output signal of PA can be presented as Where ( ) PA f  can be modeled as the Rapp model, which is suitable for the solid-state power amplifier.

[ ] [ [ ]] ,
[ ] 1 where sat V , s , and g denotes the saturation voltage, smoothing factor, and signal gain respectively [7] .4) Propagation Domain: The SI signal of the main transmitter on the receiving antenna through the transmitter antenna considering the multi-path effect for the indoor scene can be represented as Where [ ] tx h l is the impulse response of the wireless channel considering a multipath effect, tx  denotes the propagation delay, and  presents convolution operation.
The auxiliary signal transmits from the transmitter to the receiver, which can be presented as where [ ] z n denotes the additional white Gaussian noise (AWGN), and , [ ] soi rx y n presents the SOI.2) Low Noise Amplifier: The SOI comes from a faraway terminal, which should be amplified by LNA.However, the residual SI signal simultaneously is amplified by LNA.SI suppression in the propagation domain and simulation domain is required to avoid low noise saturation, so at least 60 dB SI suppressing should be achieved.The output signal of LNA can be modeled as the Rapp model [7] .

 
The basic principles and performance limit will be discussed in Section 3.

BASIC PRINCIPLE AND PERFORMANCE LIMIT ANALYSIS OF MDBSS
For the method of multi-domain blind source separation (MDBSS), reflecting the gradual improvement of SI cancellation performance, we compare five SI suppression schemes combined with propagation, analog, and digital domain.The main contents are summarized in Table 1.Methods in the propagation domain and analog domain are to avoid receiver saturation, and at the same time to suppress SI to a reasonable level, and prepare for BSS in the digital domain.It is that we can change the power of the SOI by changing the direction of the beam.Likewise, the SI component of the mixed signal can be altered by changing the power of the transmitter.As the SOI passes through the IQ mixer, however, it is then down-converted to the baseband and mixed with the rest of the SI signal.

Analog
Low computational complexity Limited SIC

Basic principle analysis of MDBSS
Multi-domain blind source separation (MDBSS) method is the combination of the multi-domain SI cancellation method and the BSS method.The multi-domain SI cancellation is carried out by the three-domain joint method.The method of BSS obtains the SOI.This section details the basic algorithm and the principle of the method.1) Propagation Domain: The path loss of electromagnetic wave propagation in wireless space can be presented as The output signal of PA approximates the Hammerstein parallel model [7] , which can be described as where p  denotes the P-th nonlinear distortion parameter.
The parallel Hammerstein model can be presented as p p p q q PA tx p q p q p q p q p q p q p q where , q p q   denotes the coefficient of IQ imbalance coefficient and , [ ] p q n  denotes the characteristic matrix of the main transmitting channel.Since both PN and Gaussian white noise are random noises, which cannot be modeled and estimated, they are ignored in the modeling process.
The SI signal of the receiver digital domain can be modeled as where [ ] all z n denotes AWGN and higher nonlinear distortion components., [ ] p q d l denotes multipath, effect nonlinear effect, and IQ imbalance effect, which can be presented as , , ] q p q tx p q p q p q tx rx p .
To solve this model, we re-write this formula in matrix form and use the LS method, which is described as The results can be presented as [7]   1 2 ˆarg min .
The digital-assisted analog domain SI cancellation algorithm is performed through channel modeling and the estimation of the SI signal.The residual SI signal in the digital domain is also estimated and reconstructed by this method.Furthermore, since changes in the channel parameters IBFD system are thought to be slow, they can be estimated in advance and run for a considerable period to ensure acceptable performance degradation.
3) Principle of blind source separation method: The independent component analysis method adopted in this paper is one of the BSS methods, and its primary application condition is to separate two independent non-Gaussian sources.The received signal in the receiver can be presented after the cancellation of the three domains mentioned above x n denotes the SOI.It can be obtained by adjusting the transmitting power and rotating the beam direction, which can be presented as The matrix form can be presented as where To solve this problem, we need to solve the separation matrix, which can be presented as where W denotes the separation matrix.We can calculate the result by an iterative method, which can be presented as The final separation matrix is obtained by an iterative algorithm W  .Then the separation can be presented as X WY    .

Performance limit analysis of MDBSS
The ideal suppression state is equivalent to the ideal null error of all channel parameters, and the receiver antenna SI signal then can be presented as The energy of SI entirely due to RF impairments can be presented as Where the received SI signal after random phase rotation can be presented as EEICE-2023 Journal of Physics: Conference Series 2625 (2023) 012060 Then, due to the independence of each quantity, its energy can be presented as [ ] 2 2 .
Where the former term is much larger than the latter depending on the degree of isolation of the propagation domain, PN and channel delay mismatch will severely affect the degree of SI isolation.In contrast, changes in PN can hardly affect the degree of isolation.

PERFORMANCE EVALUATION OF MDBSS
We first presented the numerical simulation parameters and environment, then gave the results of the numerical simulation, and continued the analysis and discussion in this part.The direct components of the SI signal, which is the strong line-of-sight (LOS) component of the SI channel, can be modeled as Rician distribution, while the multipath channel is modeled as the Rayleigh fading model.Furthermore, Ω is the total power.Moreover, the model length of the wireless channel is 4, and the ratio of the amplitudes of three multipath channels is [1, 0.1, 0.01].Briefly, we simulated the multi-path indoor scene, and the simulation parameters will be detailed in Table 2.

Results and Discussions
Using the multi-domain blind source separation (MDBSS) method proposed in this work, we achieve 75 dB of SI cancellation performance.Finally, through independent component analysis, the residual SI signal and the SOI are separated in the digital domain of the receiver.
1) Power Spectral Density of Different Signals and the effect of 3 dB bandwidth of phase noise: IOP Publishing doi:10.1088/1742-6596/2625/1/01206010 cancellation is gradually optimized.Lastly, the factors that limit the SI cancellation performance of Cancellation 1, Cancellation 2, and Cancellation 5 are the IQ imbalance of the IQ mixer, the nonlinear effect of the power amplifier, and the multipath effect of reflection of the environment.The SI cancellation performance of Cancellations 3 and 4 are limited by path loss frequency inconsistencies and estimation errors of the SI channel model.Moreover, the opposite trend of the two graphs shows that the deterioration of thermal noise and white Gaussian noise of the system deteriorates as the increase of AWGN, and the performance of SI cancellation will decrease linearly.In this case, the main limiting factor of the SI suppression performance is the Gaussian random noise of the system.3) Effect of Varying -PSOI and K: Figure 4 shows the SIC influence of the power of the SOI and the multipath effect.The SI suppression performance of the proposed method is fundamentally stable, regardless of the signal strength of interest.Because of the definition of the parameter of K, the multipath effect becomes weaker as K increases.The SIC performance of the proposed Cancellation 2 and Cancellation 5 is optimized with the increase of K, while the SIC performance is stable when K is more than 28 dB.The main reason for the stable SI cancellation performance of Cancellation 3 and Cancellation 4 regardless of the varying multipath effect is that the parameter K is fully considered in the modeling and the model-solving accuracy is appropriate.Therefore, this method can be applied in indoor scenarios.5 presents the spectrum of the transmitter digital domain of the SOI and the spectral separation result in the digital domain by BSS.The results of the simulation show that if the power of the received SOI is sufficiently strong, such as -50 dBm, the interested signal and the self-interfering signal can be separated by the proposed method in the digital domain at the receiver.In summary, the multi-domain blind source separation (MDBSS) method can fundamentally achieve the goal of the full-duplex system.

CONCLUSION
In this paper, the multi-domain blind source separation (MDBSS) method is proposed, and the SI channel is modeled and its SI cancellation performance limit is analyzed.Numerical simulation verifies that the proposed method can realize the separation of residual SI signals and signals of interest.The frequency nonuniformity of the broadband channel and imperfections caused by RF components are proposed to be the possibility main limiting factors of full-duplex broadband systems.Simultaneously, the direct effect of increasing the temperature on the system is the improvement in the thermal noise power of the system.Furthermore, when the enemy jammer uses Gaussian white noise to realize blocking, the Gaussian thermal noise becomes the main reason limiting the SI cancellation performance.Moreover, as the presence of path loss, PN does not become the main limiting factor for the proposed scheme.In conclusion, the multi-domain blind source separation (MDBSS) method realizes the separation of residual self-interfering signal and the signal of interest (SOI) and can be applied to radar, jammer, and communication systems in the future.

Cancellation 2 and
d denotes the distance of antennas and  denotes the wavelength of electromagnetic wave.The definition of wavelength can be presented as , Cancellation 5 use the equation to estimate the path loss.2) Analog and Digital Domain:

Figure 2 .
(a) The power spectral density function of various signals related to the MDBSS method; (b) Self-interference cancellation performance function with varying the parameter of 3 dB bandwidth of phase noise 4.1 Simulation Environment

Figure 2 (Figure 3 .
a) shows the PSD of the digital domain signal of the main transmitting channel, the output signal of the power amplifier, the white Gaussian noise, and the receiver digital domain signal of the five multi-domain SI cancellation methods of multi-domain blind source separation (MDBSS).The SI cancellation performance reached approximately 75 dB by three-domain SI cancellation technology from the cancellation method 1 to 4. The change of frequency of the linear frequency modulation (LFM) signal causes the attenuation of the path loss at different frequencies to be different.Cancellation 2 fully considers this effect, while Cancellation 5 ignores it and uses only the path loss corresponding to the carrier frequency.As Cancellation 4 is an additional cancellation based on Cancellation 3 in the digital domain, Cancellation 4 has better SI cancellation performance than Cancellation 3. To put it another way, for the SI cancellation performance of wideband signals, how to solve the frequency nonuniformity problem of the wireless channel and incorporate it into the modeling is one of the possible factors for improving the performance of the SI cancellation.Furthermore, as can be presented in Figure2(b), the 3 dB bandwidth parameter of the PN has little influence on the performance of the SIC of the multi-domain blind source separation (MDBSS) method proposed in this work according to the results of the simulation.The self-interfering signal is converted to an RF signal in the X band by mixing the self-interfering signal.At the receiver, the received self-interfering signal and the SOI are converted to baseband signals by the IQ mixer.In Figure2, we can conclude that the performance of SI cancellation can be as high as nearly 75 dB.Self-interference cancellation performance function with varying the parameter of PAWGN and INR 2) Effect of Varying PAWGN and INR: Figure3shows the SI cancellation performance of five cancellation methods and the SI cancellation (SIC) limit with the change of white Gaussian noise power and INR.Firstly, the discrepancy in distance between the cancellation performance limit and Cancellation 4 may result from the incongruent SI channels at the broadband frequency, impairments to RF components, and SI channel error of estimation.Secondly, from Cancellation 1 to Cancellation 4, the performance of SI EEICE-2023 Journal of Physics: Conference Series 2625 (2023) 012060

Figure 4 .Figure 5 .
Self-interference cancellation performance function with varying the parameter of -PSOI and K.The power spectral density function of the digital domain signal of interest and the separation results of the MDBSS method.

4 )
Results of BSS: Figure The final SI signal in the digital domain in the receiver can be presented as 5