1.- INTRODUCTION
The exponential evolution in mobile data traffic demands a spectrum and power efficient wireless transceiver which is capable to keep out this growth [1]. One of the most promising techniques for these requirements is FD (full-duplex) communication, where transmission and reception can occur simultaneously in the same frequency band [2-6]. The FD technique can further improve the spectral efficiency of the next generation wireless systems, such as the 5G network [7]. It can also boost or double the throughput of the conventional HD (Half-Duplex) [4]. Doubling throughput is of course a desirable achievement, but the challenge lies in attaining FD communication within the same spectrum is challenging. Especially the challenge is managing the SI (Self-Interference) that occurs from the transmitter to the receiver [4,8-11]. Transmitter non-linearities, in particular those introduced by the RF PA (Power Amplifier), have a significant impact on the SI cancellation in full-duplex systems [2]. The nonlinear distortions introduced by non-ideal hardware components remain, and must be removed in the digital domain [2].The nonlinearities produced by the DAC (Digital to Analo Converter) and phase noise were omitted in the signal model in [7]. The phase noise must be considered in FD transceivers utilizing OFDM to minimize its effect on the SI cancellation performance [12]. Its effect can be reduced by sharing the same local oscillator between the transmitter and receiver chains [13,14].
To achieve the benefits of FD technique, each receiver needs to effectively cancel the SI from its own transmitted signal [15]. In literature, there are two main methods for SI mitigation: passive suppression and active cancellation [1,16]. In passive suppression technique, the SI is blocked before it passed through recover circuitry. In case of active cancellation technique, the unwanted signals are removed by using analog and digital cancellation [1]. Active cancellation methods use an extra transmitter to create the destructive SI cancellation [6]. Passive suppression can be implemented as an integrated part of the antenna sub-system to increase the transmitter-receiver isolation [10,17]. Active SI cancellation technique is categorized into two types: RF cancellation stage is introduced to suppress the strong SI before the LNA (Low Noise Amplifier) and the ADC (Analog to Digital Converter) in order to prevent possible LNA /ADC overlapping, the digital cancellation stage, after the ADC reduces further the residual SI to a sufficient low level required for proper signal detection [15].The recent development in the area of Massive MIMO allows deployment of hundreds of antennas at the eNodB [18]. It is necessary to model the crosstalk, between transmitter chains in MIMO configuration, otherwise the accuracy of the regenerated SI signal is not sufficiently high [7]. The practical implementation of the FD techniques requires the strong self-interference signal to be suppressed, ideally to the noise-floor, as any residual SI will reduce the signal-to-noise ratio of the incoming desired signal [2].The PA operating at higher transmission powers (outside the linear region of the power amplifiers) was observed to introduce a significant ‘non-cancellable’ residual component [2,19]. In general, for known I/Q imbalance and PA distortion characteristics, the efficient DPD (Digital Predistortion) can be obtained [20]. Applying DPD to the baseband signal, the resulting transmit signal should have significantly reduced nonlinear components, which in turn would allow simpler cancellation models to be used. The cancellation chain can also be predistorted to further compensate for any residual nonlinear components still present in the transmitted signal [2]. Predistorting for all transmitters RF components nonlinearities requires us to find the inverse of the signal model corresponding to theses nonlinearities. While the inverse of a memory polynomial is also a memory polynomial, explicitly inverting the model is challenging [2,20,21]. In the ideal case, when the predistorted signal is applied as an input to the nonlinear component, the output will be free of nonlinear distortion. The DPD requires finding a suitable model for the inverse of the signal model corresponding to the cascaded nonlinear RF components such as DAC (Digital to Analog Converter), IQ-mixer, PA and nonlinear crosstalk effect.
As the contributions in this paper, we propose a new SI cancellation method, called ‘’DPD cancellation’’, where digital predistortion and SI cancellation algorithm are jointly applied. We will first model the SI signal by taking into account the nonlinearities of all transmitter RF components, and nonlinear crosstalk between transmitter chains in MIMO-FD transceivers. Then this signal model will be used to obtain the DPD coefficients. Also, we will model the nonlinearities of the receiver RF components in order to apply digital cancellation using the obtained signal model to remove the residual SI.
We will finally test and analyze the performance of our SI cancellation method. The results will be compared with others methods in literature.
This paper is organized as follows: Section 1: Introduction, Section 2: System Model, Section3 : Signal Model, Section 4: Digital Predistortion for all Hardware Impairments, Section 5: Self-Interference Cancellation, Section 6: Numerical Results and Analysis, finally Section 7 presents the Conclusions.
2.- SYSTEM MODEL
In this paper, we will consider MIMO-FD system in Figure 1 where two transceivers can transmit and receive simultaneously in the same frequency band. Each transceiver must be capable to cancel out the SI signal produced by its own transmission. The SI must be attenuated below the noise floor. To this end, we will apply DPD to linearize the transmit signal, which can minimize the nonlinearities of the transmit signal. Furthermore, the cancellation chain itself also can introduce nonlinearities, which arise from the internal amplifiers in the RF front-end [2]. To take into account these nonlinearities, DPD is applied at both, transmit and cancellation chains as proposed in [2]. Particularly, in this paper, DPD is applied to all RF components such as DAC, IQ-mixer, and PA, so that the transmit signal will be linear. Also the Digital Predistortion coefficients take into account the effect of nonlinear crosstalk. In the cancellation chain we incorporate an RF cancellation circuitry to take into account (by sounding the transmit and cancellation chains) the attenuation, delay, and multipath fading effect that will experiment the transmit signal between the transmitter
At the receiver side, analog cancellation is first applied to prevent the receiver RF components saturation, such as LNA and ADC. After analog cancellation, digital cancellation is applied to further cancel the residual nonlinear SI components in the digital baseband domain. In this paper, to model the predistortion coefficients, we consider the DAC nonlinearities, the IQ imbalance between the direct and image component introduced by the mixers, the PA nonlinearities, and the crosstalk between transmitter chains before the PA. The phase noise is considered in the system architecture by using the same mixer for transmit, cancelation and receiver chains, which can reduce the effect of the phase noise [2,14,21]. The transmitter and cancellation predistortion coefficients are computed sequentially by sounding the channels using a randomly generated OFDM training signal [2].
3.- SIGNAL MODEL
The DAC nonlinearities can be modeled in the baseband representation of the baseband signal using Taylor’s series expansion as [21]
Where
In the baseband, the impact of the IQ imbalance can be modeled as an additional complex conjugate term as [21-23]
Where
Where
Where
The PA nonlinearities can be modeled as [1,7,20-22,24-26]
Where
Substituting (4) and (6) into (5) gives
Where
Then (7) can be rewritten as:
This is the signal model in (8) contents all RF components impairments and nonlinear crosstalk effects between the transmitter chains. It will be used to find the predistortion coefficients, to linearize the transmit signal, which can minimize the effect of these nonlinearities on the SI cancellation performance at the receiver.
4.- DIGITAL PREDISTORTION OF ALL HARDWARE IMPAIRMENTS
In this section we outline the application of the DPD to the signal model in (8) corresponding to all transmitters RF components nonlinearities and nonlinear crosstalk signal model. The basic idea behind DPD is to compensate for the nonlinear distortion introduced by the RF components by appropriately distorting the baseband signal as [2,25,27].
In this paper, we follow the approach outlined in [2], and [25]. Figure 2 shows how a baseband signal, u(n), is predistorted before passing through the RF components. In the ideal case, when the predistorted signal, x(n), is applied as an input, y(n) will simply be u(n), and free of nonlinear distortion. Predistorting for all RF components requires us to find the inverse of (8), since it contains all nonlinearities of transmitter RF components. Inverting the signal model in (8) is challenging. By applying (8) we can model the inverse of (8), the output, y(n) is used to predict the input, x(n) as depicted in Figure 2, where y(n) is the output signal of “All RF Components and Crosstalk” circuit, and x(n) is its input, also x(n) corresponds to the output signal of the predistortion circuit. As depicted in Figure 1 y(n) will be the input of DAC components. Furthermore Figure 2 shows how the predistortion coefficients are estimated from the inverse of all RF components model. Once the system has converged, the coefficients are copied into the predistortion stage, which can then be run in open loop [2,21].
The KM predistortion coefficients, w, are estimated by transmitting a frame (containing N samples) of training data,
The transmitter and cancellation predistortion coefficients are computed sequentially by sounding the channels using a randomly generated OFDM signal. First, the transmit chain coefficients,
5.- SELF-INTERFERENCE CANCELLATION
To prevent the receiver RF components saturation, we must first apply analog cancellation (RF cancellation). Digital cancellation will remove the residual SI which will experiment the nonlinearities introduced by the hardware impairments. As depicted in Figure 1, for RF cancellation the analog circuitry can adjust attenuation, delay and phase between the transmitter and cancellation chains. We will model the receiver nonlinearities before applying digital cancellation algorithm to cancel out the SI from the total received signal.
5.1.- ANALOG CANCELLATION
For analog SI cancellation in this paper, we present an hybrid RF canceller using auxiliary transmitter with linear processing as [7]. Due to the DPD of the baseband signal, the transmitted signal, and analog cancellation reference signal, can be assumed linear. Thus, linear processing in the RF canceller is reasonable, since the RF canceller must only attenuate the SI such that the receiver is not saturated. The hardware complexity of this type of RF cancellation scheme scales with
We denote the actual MIMO propagation channel impulse response from transmit antenna j to receive antenna i by
Note that
We assume active cancellation, where the canceller structure utilizes an extra transmitter chains to up convert and subtract (after suitable gain, phase, and delay adjustments) estimated replicas of SI signals from the received signal at RF. The RF canceller can be either single-tap or multi-tap. Also, it can be easily shown that the cancellation signal is of similar form as the actual received SI signal. Thus the output signal of the RF canceller chain can be written as
Where
The residual SI after RF cancellation can be expressed as
Note that the residual SI signal
Now, the nonlinearities introduced by the receiver RF components such as LNA, IQ-mixer, and ADC must be removed by the digital cancellation.
5.2.- DIGITAL CANCELLATION
Generally, digital SI cancellation is applied after analog cancellation to remove the nonlinearities introduced by hardware non-ideality. For digital cancellation in this paper, we will first estimate the residual SI channel, regenerate the residual SI signal, and then subtract it from the received signal.
We will consider the output signal of the RF canceller
The residual SI signal after the LNA can be written as
Where
Incorporating the effect of the IQ imbalance of the IQ-mixer, we can rewrite
Where
Where
After N observations,
Where
The nonlinear residual SI estimate
Where
Where
The vector
Applying Least Square (LS) solution to the parameter vector
Now, with the residual SI channel estimate, we can regenerate the residual SI signal and subtract it form the received signal.
The output of the digital SI canceller at receive antenna
Which corresponds to the detector input signal.
6.- NUMERICAL RESULTS AND ANALYSIS
In this section, we perform full waveform simulations of MIMO-FD transceiver with Matlab/Simulink to test and analyze our proposed method. The simulation parameters are given in Table 1, Table 2, and Table 3. The SI channel between transmit and receive antennas is modeled as a FIR filter. The power difference between the main component and the multipath components (K-factor) is 35.8 dB [29]. In the simulation, RF cancellation is implemented by subtracting the transmitted signal from the received signal with a small amplitude and phase mismatch such that the specified amount of total SI power reduction is obtained. For the simulation purpose in this paper, the PH model nonlinearity order is 5, and the filter lengths of the PH model are 10 for all the branches as [29].
The Figure-of-merit in this paper is the SINR (Signal-to-Interference plus Noise Ratio) of the detector input signal. As simulation results Figure 3 shows a comparison of SINR at input of the detector for different SI cancellation methods in literature. All the curves are plotted for the same passive suppression achieving 40 dB by antennas separation, and 30 dB achieved by RF cancellation. As depicted in Figure 3, for transmit power lower than 15 dBm, DPD Cancellation provides the best SINR when comparing to Nonlinear Cancellation method proposed in [29], Widely Cancellation method proposed in [30], Linear Cancellation and Joint Cancellation methods proposed in [22]. For high level of transmit power (more than 15 dBm), the PA will operate in its nonlinear region and some nonlinearities will be added to the signal of interest due to the non-ideality of the proposed Digital Predistorter, which can deteriorate the SINR. The SINR deterioration due to the high transmit power occurs with all existing digital cancellation methods. In this situation DPD Cancellation method is approximately comparable to Joint Cancellation method in terms of SINR, and is better than others methods in literature.
Component | Gain (dB) | IP2 (dBm) | IP3 (dBm) | NF |
---|---|---|---|---|
PA (Tx) | 27 | - | 13 | 5 |
LNA (Rx) | 25 | - | 5 | 4.1 |
Mixer (Rx) | 6 | 50 | 15 | 4 |
Parameter | value |
---|---|
SNR target | 10 dB |
Bandwidth | 12.5 MHz |
Rx noise Figure | 4.1 dB |
Rx sensitivity | -88.9 dBm |
Rx input power | -83.9 dBm |
Antenna separation | 40 dB |
RF cancellation | 30 dB |
PAPR | 10 dB |
IRR (Tx) | 25 dB |
IRR ( RX) | 50 dB |
7.- CONCLUSIONS
For practical implementation of FD transmission technique in future wireless systems, a robust SI cancellation algorithm must be investigated. To this end, several investigations have been done. However most of these works do not take into account the nonlinearities of the RF components at both transmitter and receiver sides, and the crosstalk between transmitter chains in MIMO FD devices, which can deteriorate SI cancellation performance.
Therefore, we proposed a method that considers simultaneously these nonlinearities and crosstalk effect in the signal model and algorithm based on predistortion of transmit baseband signal, to improve the SI cancellation performance. The simulation results show that, DPD cancellation provides better levels of SINR at the input of detector at the receiver, when compared to others methods in literature.
Our method allows simplification of SI signal model, which can be very challenging when considering jointly hardware nonlinearities and crosstalk effect in MIMO FD transceivers.
In this paper, we have considered MIMO FD 2x2 transceivers, further investigations are needed to apply the same algorithm to massive MIMO FD scenario where 5G network devices size would be considered.