The work in [22] presents yet another different approach for implementing an IBFD device. Namely, there an auxiliary TX chain–based RF canceller is used to regenerate and cancel the SI in the RF domain, but such that both the actual and auxiliary TX chains are linearized by means of digital predistortion. This means that the PA-induced nonlinear distortion can be omitted in the digital cancellation stage. With separate TX and RX antennas placed 30 cm apart, the prototype is shown to suppress the SI by 70 dB in total when transmitting a 5-MHz signal with a 20-dBm average transmit power. Of this, the amount of RF cancellation is roughly 40 dB, while the digital canceller, utilizing the signal model presented in [26] that incorporates the effects of DAC nonlinearities and I/Q imbalance, suppresses the SI by 11 dB.
The above prototypes represent the current state of the art in the literature, and thereby constitute the proper context for the SI cancellation performance achieved using the digital cancellation solutions presented in this thesis and reported in [P4, P5]. Table 5.1 presents also the key performance figures of these prototype implementations, while further details are provided below in Sections 5.3 and 5.4.
5.2
Simulated Self-interference Cancellation Perfor-
mance
Let us first verify the different digital cancellation solutions with a realistic waveform simulator that models all the significant analog impairments within a 2 × 2 MIMO IBFD transceiver, reported in detail in [P6]. The waveform simulator is implemented in Matlab and it follows the architecture in Fig. 2.5a, extended to a 2 × 2 MIMO scenario, to produce a realistic residual SI signal for the digital canceller. The used transmit signals are 20 MHz orthogonal frequency-division multiplexing (OFDM) waveforms following the specifications of LTE DL signals, the transmit power being defined as the combined power of these individual transmit signals after the PAs. Moreover, the same system parameters that were used in Section 3.2, listed in Tables 3.1 and 3.2, are used also in the waveform simulations, complemented with the additional parameters listed in Table 5.2. The only exception is the phase noise model, whose characteristics are now as shown in Fig. 5.1. The adopted phase noise model corresponds to a real-life charge-pump-type PLL–based oscillator to ensure as realistic results as possible [165]. Furthermore, no received signal of interest is present in the simulations to focus on the overall SI cancellation performance.
The MIMO SI coupling channel used in the simulations is randomly generated for each realization, although it is always set to have the desired K value, adopted from the measurement results reported in [59]. Similarly, the RF cancellation signals are generated using a random error component, and consequently the amount of RF cancellation varies from one realization to the next. Nevertheless, the average amount of RF cancellation is as specified in Table 3.1. The forthcoming results are generated by running 20 independent realizations for a given set of parameter values and then measuring the average residual SI power of these realizations. The only exception are the power spectral densities (PSDs), which represent only the outcome of a typical realization within an individual receiver for illustrative purposes. Hence, no major conclusions should be drawn from the PSDs alone, as they include no averaging, although they still represent a rather accurate scenario in terms of the true cancellation performance.
EVALUATING THE SELF-INTERFERENCE CANCELLATION PERFORMANCE
Table 5.2: The additional default parameters used in the waveform simulations.
Parameter Value
Number of TX/RX chains (Nt/Nr) 2/2
Sampling frequency 122.88 MHz
Level of TX crosstalk before the PAs −15 dB
Level of TX crosstalk after the PAs −15 dB
Transmit waveform OFDM
SI channel length 20 taps
SI channel K value 35 dB
Parameter estimation sample size (N ) 30 000 Nonlinearity order of the cancellers (P ) 5
Number of pre-cursor taps (M1) 10
Number of post-cursor taps (M2) 20
100 102 104 106 108
Frequency offset from carrier (Hz)
-160 -140 -120 -100 -80 -60 -40 Phase noise (dBc/Hz)
Figure 5.1: The phase noise characteristics used in the waveform simulator, taken from [165].
Using the waveform simulator, the following digital cancellation solutions are evalu- ated:
• digital cancellation using the linear signal model, presented in Section 4.2.1; • digital cancellation using the widely linear signal model, presented in Section 4.2.2; • digital cancellation using the nonlinear signal model, presented in Section 4.2.3; • digital cancellation using the nonlinear signal model incorporating crosstalk and
I/Q imbalance, presented in Section 4.2.4, without model complexity reduction; • digital cancellation using the nonlinear signal model incorporating crosstalk and
I/Q imbalance, presented in Section 4.2.4, with the model complexity reduction scheme presented in Section 4.3.3.
5.2 Simulated Self-interference Cancellation Performance -15 -10 -5 0 5 10 15 Frequency (MHz) -120 -100 -80 -60 -40 -20 0 PSD (dBm/200 kHz)
Before digital cancellation (-52 dBm) Linear signal model (-73 dBm) Nonlinear signal model (-73 dBm) Widely linear signal model (-89 dBm)
Nonlin. signal model incorp. crosstalk and I/Q imb. (-93 dBm)
Nonlin. signal model incorp. crosstalk and I/Q imb., 35% of basis func. (-93 dBm) Receiver noise floor (-97 dBm)
Figure 5.2: The PSDs of the signal after the different SI cancellation stages in the waveform
simulator. Here, the RX input is used as the reference point for all the signal powers, meaning that they do not include the RX gain.
10 15 20 25
Total transmit power (dBm)
0 5 10 15 20 25 30
Increase in the noise floor (dB)
Linear signal model Nonlinear signal model Widely linear signal model
Nonlin. signal model incorp. crosstalk and I/Q imb.
Nonlin. signal model incorp. crosstalk and I/Q imb., 35% of basis func.
Figure 5.3: The residual SI–induced increase in the noise floor with respect to the total
transmit power.
In all the cases, the unknown signal model coefficients are learned using the LS-based parameter estimation scheme presented in Section 4.3.1. The estimation is done over the specified amount of samples (N ), while the cancellation performance itself is evaluated for a different set of signal samples. Note that in this case oversampling is not necessary when generating the nonlinear basis functions as the initial sampling frequency is high enough to capture also the higher-order nonlinearities.
First, Fig. 5.2 shows the PSDs of the signal after the different SI cancellation stages using the default system parameters. It confirms the observation made in Section 3.2 regarding the dominant nature of the I/Q imbalance, as neither the nonlinear nor the linear canceller perform very well. On the other hand, the digital canceller utilizing the widely linear signal model obtains significantly higher levels of SI cancellation, while the case where both the I/Q imbalance and the nonlinear distortion are modeled results in the lowest residual SI power, as can be expected. The 4 dB increase in the noise floor
EVALUATING THE SELF-INTERFERENCE CANCELLATION PERFORMANCE 20 25 30 35 40 45 50 TX & RX IRR (dB) 0 5 10 15 20 25 30
Increase in the noise floor (dB)
Linear signal model Nonlinear signal model Widely linear signal model
Nonlin. signal model incorp. crosstalk and I/Q imb.
Nonlin. signal model incorp. crosstalk and I/Q imb., 35% of basis func.
Figure 5.4: The residual SI–induced increase in the noise floor with respect to the IRR of the
TX and RX chains.
even with the best digital cancellers can be attributed to the RF canceller output noise, as concluded already in Section 3.2. It can also be observed that retaining only 35% of the basis functions of the nonlinear signal model incorporating crosstalk and I/Q imbalance still results in the same cancellation performance. This illustrates the benefits of the proposed PCA-based model complexity reduction scheme.
To investigate the effect of the transmit power in more detail, Fig. 5.3 shows the increase in the noise floor, caused by the IBFD operation, with respect to the total transmit power. Again, in accordance with the conclusions made in Section 3.2, the signal models omitting the I/Q imbalance perform rather poorly, even with the lowest transmit powers. As for the widely linear signal model, it is capable of accurately modeling the residual SI up to a transmit power of approximately 20 dBm, after which the PA-induced nonlinearities start to become a significant factor. Beyond this point, modeling of both the I/Q imbalance and the nonlinearities is required to efficiently suppress the residual SI. The exact transmit power level where this transition occurs depends on the characteristics of the TX PA; if the PA is highly nonlinear, modeling of the nonlinear distortion is required with lower transmit powers, whereas the opposite is true for a more linear PA. Also note that the PCA-based model complexity reduction scheme increases the cancellation performance with the lower transmit powers as the smaller number of coefficients improves the estimation accuracy. With the highest transmit powers, however, more than 35% of the basis functions are needed to achieve the full modeling accuracy, as can be observed in Fig. 5.3.
Considering then the effect of I/Q imbalance, Fig. 5.4 shows the increase in the noise floor with respect to the IRR of the TX/RX chains, assuming that both have the same IRR. As can be expected, with the higher IRRs, the nonlinear signal model is more accurate than the widely linear model as then the PA nonlinearity is the dominant form of distortion. However, if the IRR is less than 43 dB, the digital canceller utilizing the widely linear signal model is the better option of these two. Moreover, as can be expected, the signal model considering both the I/Q imbalance and the nonlinear distortion retains high accuracy regardless of the IRR value, the cancellation performance of the reduced version being again nearly identical to the one utilizing all the basis functions.
5.3 Measured Self-interference Cancellation Performance of a Generic Inband