Achievable Transmission Rates and Self-interference Channel Estimation in Hybrid Full-Duplex/Half-Duplex MIMO Relaying Dani Korpi, Taneli Riihonen, Katsuyuki Haneda, Koji Yamamoto, and Mikko Valkama Department of Electronics and Communications Engineering, Tampere University of Technology, Finland Department of Signal Processing and Acoustics, Aalto University School of Electrical Engineering, Finland Department of Electrical Engineering, Columbia University in the City of New York, United States Department of Radio Science and Engineering, Aalto University School of Electrical Engineering, Finland Department of Communications and Computer Engineering, Graduate School of Informatics, Kyoto University, Japan e-mail: dani.korpi@tut.fi, taneli.riihonen@iki.fi Abstract This paper investigates the achievable throughput of a multi-antenna two-hop relay link under hybrid full/halfduplex operation. The analysis is facilitated by realistic waveform simulations, which explicitly model all the essential circuit impairments occurring in the relay transceiver together with degrading channel estimation and self-interference cancellation. The obtained results indicate that pure full-duplex operation does not ensure optimal performance but additional half-duplex are usually needed to maximize the endto-end throughput. Especially, it is shown that the estimation of the self-interference channel within the relay should be performed when the source is not transmitting anything while also the source should be allowed to transmit alone to avoid making the first hop a bottleneck. These findings form a solid basis for optimizing the full-duplex MIMO relay deployments in future mobile networks. I. INTRODUCTION Full-duplex radio technology is a novel paradigm in the field of wireless communications [1] [3]. Its basic premise is to transmit and receive data signals simultaneously on the same frequency band which, in theory, can as much as double the spectral efficiency of the current wireless communications systems. Simultaneous transmission and reception at the same center frequency is especially suitable for relaying applications, where a transceiver must extend the range between a source and a destination by forwarding the information it receives [], [5]. With an in-band full-duplex transceiver, relaying can potentially be performed without any additional resources, unlike with conventional half-duplex relays. However, the improved spectral efficiency comes at the cost of the need for elaborate interference cancellation. Namely, the relay s own transmit signal loops back to its receiver chain with very little attenuation due to the short distance between nearend antennas, and becomes an extremely strong distortion factor, typically referred to as self-interference (SI). To tackle the SI problem, a copy of the own transmit signal must be subtracted from the received signal [], [], [7]. By matching this cancellation signal to the actual propagation channel of the SI signal, it will ideally cancel out the interference. To ensure that the receiver chain is not completely saturated, the SI cancellation is usually done in two stages: first in the RF domain and then in the digital domain to suppress the residual SI below the noise floor [], [], [7]. Recently, an in-band full-duplex relay capable of suppressing the SI below the receiver noise floor has been implemented also in practice and thereby it has been shown to be a feasible concept []. When considering utilizing in-band full-duplex transceivers as relays, it is important to determine how to maximize the endto-end throughput from the source to the destination. Since it is known that it may be suboptimal for the relay to be constantly in full-duplex mode [], [9], in this study we will investigate the achievable source-to-destination throughput with an in-band fullduplex relay by assuming a flexible frame structure. That is, it will be determined how much of the time the relay should actually be in full-duplex mode to obtain the highest throughput between the source and the destination. In particular, we will analyze this while considering the effects of the different circuit impairments of the relay. To ensure that the obtained results are applicable to the real world, the SI channel estimation and digital cancellation are performed on the waveform level, instead of merely assuming a certain constant cancellation factor. This also means that the analysis takes into account the effect of the received signal on the SI channel estimation capability of the relay. Namely, if the full-duplex relay is receiving a signal from the source while it is also transmitting to the destination, it might have to partially estimate the SI channel during the reception, especially if the coherence time of the SI channel is short. This will increase the variance of the SI channel estimate, thereby affecting the digital cancellation performance [1]. Such a comprehensive analysis is currently missing from the literature, as the effect of the SI channel estimation has been so far ignored, alongside with the effects of the circuit impairments [9]. II. SYSTEM MODEL AND RATE EXPRESSIONS Let us consider the system illustrated in Fig. 1, where a halfduplex multi-antenna source and destination are communicating via a full-duplex-capable multiple-input multiple-output (MIMO) decode-and-forward relay with separate transmit and receive antennas. For simplicity, we assume that there is no direct link between the source and the destination, i.e., the destination only receives the signal of interest via the relay. Ideally, if the signalto-interference-plus-noise ratios (SINRs) of the source-to-relay and relay-to-destination links are balanced, the highest throughput from the source to the destination is achieved when the relay is operating as much as possible in full-duplex mode, that is, it is transmitting while simultaneously receiving a signal from the source. Under practical conditions, however, the two links are not identical and this is likely not the most efficient form of relaying [9]. In addition, in continuous full-duplex operation, the received signal from the source will interfere with the SI channel estimation procedure at the relay, especially in the digital canceller. This, on the other hand, will significantly decrease the reception SINR at the relay, thereby decreasing the overall throughput of the system.
Full-duplex relay BPF LNA IQ Mixer LPF VGA ADC Digital signal processing Destination Source RF signal processing IQ Mixer DAC LPF IQ Mixer VGA PA Fig. 1: A block diagram showing the considered system and the general structure of the simulated MIMO full-duplex relay. To investigate more optimal relaying procedures where the full-duplex capability of a MIMO relay can be utilized to the fullest extent, let us consider a transmission schedule illustrated in Fig.. There, the whole communication procedure has been divided into three periods: source-to-relay (SR) transmission, relayto-destination (RD) transmission, and simultaneous SR and RD transmission. To minimize the variance of the relay SI channel estimate, the estimation procedure will be performed such that it overlaps with the half-duplex RD transmission period. Also note that the SI channel estimate is only assumed to be valid for the duration of the SI channel coherence time, T coh, after which a new estimate is required. In the forthcoming analysis, the relative lengths of these different communication periods will be varied to investigate how they affect the overall throughput. The length of the RD transmission period is especially crucial, as it determines the interference level for the SI channel estimation procedure, and thereby defines the rate over the full-duplex period. Now, let τ SR denote the amount of time allocated for halfduplex (HD) SR transmission and τ RD the amount of time allocated for half-duplex RD transmission, which together comprise the half-duplex operation part of the hybrid operation mode. Defining the SI channel coherence time as T coh, it follows that during one repetition of the communication procedure the system spends a time period of T coh τ RD in the full-duplex (FD) mode where both (SR and RD) transmissions take place simultaneously. Using the above definitions to adapt the model of [9], the endto-end source-to-destination throughput for the considered two-hop hybrid full/half-duplex relay link can be written as {( ) ( ) τsr C = min CSR HD Tcoh τ + RD CSR F D, τ tot τ tot ( τrd τ tot ) C HD RD + ( ) Tcoh τ RD τ tot C F D RD } (1) where τ tot = T coh + τ SR is the duration of one repetition of the communication procedure and the per-hop achievable data rates for the SR and RD transmissions are given by N x ) Cx y = log (1 + sinr y i,x λ i,x i=1 where, when x {SR, RD} and y {HD, FD}, N x is the number () of spatial streams, sinr y i,x is the SINR of the ith spatial stream, and λ i,x is the ith singular value of the channel matrix. The SINRs in () depend on the level of the signal of interest, the noise floor, possibly the residual SI, and also on the channel characteristics. For the half-duplex spatial streams, the SINR (or, actually, just SNR without interference) is of the form sinr y i,x = snr y i,x = Lxpy i,x p n,x, (3) where L x is the pathloss in the corresponding hop, p y i,x is the power allocated to the ith spatial stream, and p n,x is the receiver noise floor. Now, x = {SR, RD} when y = HD and x = RD when y = FD. Thus, the SINR is also of this form for the RD signal in full-duplex mode because a decode-and-forward relay is considered. In a similar fashion, we can write the SINR for the SR signal in the full-duplex mode as follows. sinr F D i,sr = L SR p FD i,sr [ hi,r p n,sr + E ĥi,r ], () p i,rsi where p FD i,sr is again the power allocated to the ith spatial stream, h i,r is the effective channel of the residual SI signal before digital cancellation, ĥi,r is the corresponding estimate of this SI channel, and p i,rsi is the power of the residual SI before digital cancellation. As mentioned, a significant factor in terms of this analysis is the SI channel estimation procedure. In particular, whether the SI channel can be estimated during the half-duplex period, or whether it must be partially estimated also during the full-duplex communication slot. This will affect the optimal lengths of the half-duplex and full-duplex periods at the relay, as it is beneficial for the accuracy of the SI channel estimate to calculate it in halfduplex mode. Consequently, a complex interplay emerges between optimizing the cancellation performance and ensuring that enough time is actually spent in full-duplex mode. This trade-off can be controlled through varying the magnitude of τ RD under the constraint τ RD T coh.
Self-interference channel coherence time SR transmission without SI RD transmission Simultaneous SR and RD transmission with self-interference (SI) at the relay Half-duplex operation Self-interference channel estimation Full-duplex operation Fig. : A timeline of the proposed hybrid full-duplex/half-duplex communication procedure for a two-hop relay link. time III. SIMULATION RESULTS To evaluate the overall throughput of the considered system under realistic conditions, waveform simulations are performed. In the simulations, the relay is modeled according to the block diagram in Fig. 1 such that all the components have a basebandequivalent model in the simulator. This ensures that all the nonidealities produced in the transceiver chain are accounted for, resulting in a realistic SI waveform. More details on the actual simulator are provided in [3], while the models for the different nonidealities are discussed in more detail in, e.g., [11]. Table I lists the most relevant system-level parameters, which have been used in the simulations to generate the forthcoming results unless otherwise mentioned. Note that these specific parameter values do not represent any real-world commercial system but they have been merely chosen to represent a feasible example case. For instance, the amount of analog SI attenuation is chosen according to the measurement results obtained in []. The actual SI channel acquisition in the digital domain is performed using least-squares estimation, with the original own transmit signal acting as a reference pilot. To obtain a sufficiently accurate cancellation signal, the widely linear signal model presented in [1] is used in the digital canceller. Thus, all of the forthcoming results have been obtained by utilizing an actual digital SI cancellation procedure, instead of assuming some baseline performance. The results of the waveform simulations provide the SINRs to be used in evaluating the source-to-destination throughputs with (1), using various values for τ SR and τ RD. Also, since (1) represents an instantaneous case, the actual results have been determined by averaging the instantaneous rate over several independent channel realizations such that the singular values are calculated based on the corresponding channel matrices. The source-to-destination throughput for the flexible transmission scheme is shown in Fig. 3 for different SNR per receiver values at the destination. The horizontal axis shows the relative length of τ RD with respect to the SI channel coherence time, i.e., τ RD /T coh. In the figure, two alternative methods for choosing the value of τ SR have been used: setting τ SR such that the overall throughput is maximized, or simply setting τ SR. In the former, the maximization is done merely by determining the optimal value for τ SR with a grid search. In addition, the threshold of interferencefree SI channel estimation is also shown in the figure with a vertical line. If F s is the sampling frequency in the digital domain, then this means that τ RD = N/F s, where N = 5 is the example SI channel estimation sample size. Thus, the region on the lefthand side of the vertical line corresponds to a situation where the SI channel must be partially estimated while receiving a signal from the source. When observing the throughputs in Fig. 3, it can be seen that typically the best option is to select the length of the RD transmission period such that it is equal to the time required for TABLE I: Baseline simulation parameters for the considered system. Parameter Value Signal bandwidth 1.5 MHz Number of TX antennas at the source Number of RX/TX antennas at the relay / Number of RX antennas at the destination SNR per receiver at the relay 15 db SNR per receiver at the destination db Relay PA gain 7 db Relay PA IIP3 1 dbm IRR (RX and TX) at the relay 5 db ADC bits 1 Total transmit power of the relay dbm Analog SI attenuation at the relay 7 db SI channel estimation sample size at the relay 5 SI channel coherence time 1 ms interference-free SI channel estimation. This is especially crucial with higher SNR values at the destination, while with the lowest SNR value it is enough to limit τ RD to a certain range. This implies that, with a SNR of 5 db at the destination, the RD link is in fact mostly limiting the throughput, and thereby the SINR of the SR link is not crucial, rendering the SI channel estimate accuracy irrelevant. Another observation from Fig. 3 is that setting τ SR to zero maximizes the throughput when the SNR per receiver at the destination is low. This is again due to the fact that then the throughput of the RD link is limiting the source-to-destination throughput, and there is no reason to use any additional time for the SR transmission. This is also confirmed by the observation that setting τ SR to zero is not the optimal selection when the SNR at the destination is 5 db. Then, a dedicated SR transmission period is required to balance the throughputs between the two links. This conclusion differs from the one originally made in [9], where the relationship between the half-duplex RD transmission period and the SI channel estimation procedure is not considered; thus, in [9] the highest throughput is obtained by using only either the SR or RD halfduplex transmission period (but not both), in addition to the fullduplex period. In general, Fig. 3 implies that the lengths of the different communication periods have a significant effect on the sourceto-destination throughput. For this reason, the forthcoming results compare the highest achievable throughputs between different schemes for choosing these communication period lengths. The different schemes are as follows. Flexible hybrid scheme, which has no limitations on the lengths of the communication periods (except for τ RD T coh ). This corresponds to the case in Fig. 3 where the values of τ SR and τ RD are chosen such that the sourceto-destination throughput is maximized. In practice, the optimal values for τ SR and τ RD are determined by a simple grid search.
Source to destination throughput (bps/hz) 7 5 3 SNR = 5 db, τ is optimized D SR SNR D = 5 db, τ SR SNR = 15 db D SNR D = 5 db τ RD is equal to SI channel estimation time Source to destination throughput (bps/hz) 1 1 Flexible hybrid scheme SI channel estimation and optimized τ SR SI channel estimation and τ SR Full duplex scheme Half duplex scheme with optimal Half duplex scheme with equal 1.1..3..5..7..9 1 τ /T RD coh Fig. 3: The source-to-destination throughput for different SNR values at the destination (SNR D ) with respect to τ RD /T coh. 5 1 15 5 SNR per receiver at the relay (db) Fig. : The highest achievable source-to-destination throughputs with respect to the SNR at the relay. Fixed hybrid scheme with interference-free SI channel estimation, where the value of τ RD is chosen such that it is equal to the time required for estimating the SI channel. Thus, this scheme maximizes the time T coh τ RD the relay spends in full-duplex mode under the constraint of interference-free SI channel estimation. Furthermore, the forthcoming figures show the throughputs for two variations of this scheme: one where the value of τ SR is chosen with a grid search such that the throughput is maximized, and one where it is simply set to zero. Full-duplex scheme, where τ SR = τ RD. This means that all the communication between the source and the destination is performed such that the relay is in pure fullduplex mode. Half-duplex scheme, where the τ SR and τ RD are chosen optimally to maximize the end-to-end throughput. For more details, see, e.g., [5]. Half-duplex scheme with equal, where τ SR = τ RD. Thus, the transmission time has been divided equally between the source and the relay. Figure shows the resulting throughput values for the above schemes with respect to the SNR at the relay, with the other parameters being chosen according to Table I. Note that here the SNR does not include the effect of the residual SI but merely refers to the ratio between the powers of the desired signal and the noise, thereby reflecting the power level of the received signal. Also, all the curves in this figure have been calculated such that the throughput of each scheme is maximized within the specified boundaries for τ SR and τ RD. Firstly, Fig. indicates that the highest achievable sourceto-destination throughput is obtained using the flexible hybrid scheme, with the interference-free SI channel estimation scheme achieving practically identical performance. This corresponds well to the observations made from Fig. 3, where setting the value of τ RD equal to the SI channel estimation period seemed to produce the highest throughput. Thus, minimizing the interference during SI channel estimation while maximizing the time the relay spends in full-duplex mode seems likely to produce the highest source-todestination throughputs. Moreover, with a sufficiently high SNR at the relay, the optimal value of τ SR is close to zero, as the corresponding variation of the interference-free SI channel estimation scheme is capable of matching the throughput obtained by the flexible hybrid scheme. With a very low SNR at the relay, however, a half-duplex SR transmission period is required to maximize the throughput. In Fig., this is illustrated by the curve corresponding to τ SR not reaching the highest throughputs with the lower SNR range. When observing the throughputs of the other schemes, the next best option seems to be the full-duplex scheme, where the source and the relay are constantly transmitting. Even though the accuracy of the SI channel estimate is relatively low due to the interference from the source, the full-duplex scheme still outperforms the halfduplex scheme with a clear margin. This further confirms the earlier conclusion that it is beneficial for the source-to-destination throughput to maximize the time the relay is in full-duplex mode. Also, as expected, the lowest performance is achieved with the simple half-duplex scheme where the are divided equally between the source and the relay. The drawback of this scheme is that, if the channel conditions between the two links are different, there is no method of compensating for it and a lower throughput is achieved, assuming that the transmit powers cannot be adjusted. For this reason, in this case the half-duplex scheme with optimal transmission time division improves the throughput rather considerably, especially when the difference between the SNRs at the relay and destination is higher. This improvement is also clearly visible in Fig.. When considering a full-duplex relay, its transmit power is also an important factor. It will affect the S(I)NRs of both the SR link and the RD link, since a higher transmit power will increase the level of the residual SI after digital cancellation due to the different circuit impairments, while also increasing the SNR at the destination. To investigate these phenomena further, Fig. 5 shows the highest achievable throughputs for the different schemes with respect to the total transmit power of the relay. The SNR at the destination is also adjusted according to the transmit power. Again, the hybrid scheme provides the highest throughput, alongside with the scheme ensuring interference-free SI channel estimation and optimized τ SR.
Source to destination throughput (bps/hz) 7 5 3 Flexible hybrid scheme SI channel estimation and optimized τ SR SI channel estimation and τ SR Full duplex scheme Half duplex scheme with optimal 1 Half duplex scheme with equal 5 1 15 5 Total transmit power of the relay (dbm) Fig. 5: The highest achievable source-to-destination throughputs with respect to the total transmit power of the relay. The interference-free SI channel estimation scheme with τ SR can match the flexible hybrid scheme with the lower transmit powers but its performance drops drastically when the transmit power is increased beyond dbm. This is caused by the impairment-induced increase in the residual SI, which decreases the SINR of the SR link. Under these circumstances, a half-duplex SR transmission period would be required so that the throughput of the SR link could be improved to match the throughput of the RD link. However, under the constraint of τ SR, the SR link forms a bottleneck for the source-to-destination throughput. Moreover, with the lower transmit powers, also the full-duplex scheme is capable of obtaining throughputs comparable to the flexible hybrid scheme. However, with transmit powers above dbm, also the performance of the full-duplex scheme starts to drop due to excessive residual SI induced by the circuit impairments, resulting in a decreasing quality of the SR-link. Thus, with the highest transmit powers, continuous full-duplex transmission is not preferable, and, instead, a higher throughput will be achieved even with a half-duplex scheme. Overall, the results indicate that it is highly beneficial for the source-to-destination throughput to utilize half-duplex transmission periods, in addition to full-duplex periods, as has already been observed before [], [9]. However, unlike the previous works, this analysis also shows the relationship between the half-duplex and the SI cancellation capability of the relay, the central observation being that it is important to have an interference-free SI channel estimation period. Another novel conclusion is that, under some circumstances, both types of halfduplex are needed to obtain the highest source-to-destination throughput. In general, by maximizing the time the relay spends in full-duplex mode, while also ensuring interference-free SI channel estimation, a hybrid relaying scheme can be expected to outperform pure half- and full-duplex operation. IV. CONCLUSION This article investigated the achievable source-to-destina-tion throughputs when utilizing a MIMO full-duplex relay with a hybrid of full-duplex and half-duplex operation modes. The throughputs were obtained with realistic waveform simulations, which incorporated the most prominent circuit impairments into the full-duplex relay model. The digital self-interference cancellation procedure was also performed on the waveform level using an actual channel estimate. The obtained results indicate that it is beneficial for the total throughput to have also half-duplex included in the relaying procedure and, to maximize the throughput, the relay should estimate its self-interference channel such that the source is not transmitting simultaneously. These findings help in optimizing the deployment of full-duplex MIMO relays in future mobile networks. ACKNOWLEDGMENT The research work leading to these results was funded by the Academy of Finland (under the projects #59915, #53 In-band Full-Duplex MIMO Transmission: A Breakthrough to High-Speed Low-Latency Mobile Networks ), the Finnish Funding Agency for Technology and Innovation (Tekes, under the project Full-Duplex Cognitive Radio ), and the Linz Center of Mechatronics (LCM) in the framework of the Austrian COMET-K programme. The research was also supported by the Internet of Things program of DIGILE (Finnish Strategic Centre for Science, Technology and Innovation in the field of ICT), funded by Tekes. The second author s on-going research visit to Columbia University is supported by personal grants from the Walter Ahlström Foundation (through the Tutkijat maailmalle -program) and the Foundation for Aalto University Science and Technology. REFERENCES [1] B. Day, A. Margetts, D. Bliss, and P. Schniter, Full-duplex bidirectional MIMO: Achievable rates under limited dynamic range, IEEE Trans. Signal Process., vol., no. 7, pp. 37 3713, Jul. 1. [] M. Jain, J. I. Choi, T. Kim, D. Bharadia, S. Seth, K. Srinivasan, P. Levis, S. Katti, and P. Sinha, Practical, real-time, full duplex wireless, in Proc. 17th Annual International Conference on Mobile computing and Networking, Sep. 11, pp. 31 31. [3] D. Korpi, T. Riihonen, V. Syrjälä, L. Anttila, M. Valkama, and R. Wichman, Full-duplex transceiver system calculations: Analysis of ADC and linearity challenges, IEEE Trans. Wireless Commun., vol. 13, no. 7, pp. 31 33, Jul. 1. [] T. Riihonen, S. Werner, and R. Wichman, Hybrid full-duplex/halfduplex relaying with transmit power adaptation, IEEE Trans. Wireless Commun., vol. 1, no. 9, pp. 37 35, Sep. 11. [5], Transmit power optimization for multiantenna decode-andforward relays with loopback self-interference from full-duplex operation, in Proc. 5th Asilomar Conference on Signals, Systems and Computers, Nov. 11, pp. 1 11. [] M. Duarte, C. Dick, and A. Sabharwal, Experiment-driven characterization of full-duplex wireless systems, IEEE Trans. Wireless Commun., vol. 11, no. 1, pp. 9 37, Dec. 1. [7] D. Bharadia, E. McMilin, and S. Katti, Full duplex radios, in Proc. SIGCOMM 13, Aug. 13, pp. 375 3. [] M. Heino, D. Korpi, T. Huusari, E. Antonio-Rodríguez, S. Venkatasubramanian, T. Riihonen, L. Anttila, C. Icheln, K. Haneda, R. Wichman, and M. Valkama, Recent advances in antenna design and interference cancellation algorithms for in-band full-duplex relays, IEEE Communications Magazine, vol. 53, no. 5, May 15. [9] K. Yamamoto, K. Haneda, H. Murata, and S. Yoshida, Optimal transmission scheduling for a hybrid of full- and half-duplex relaying, IEEE Commun. Lett., vol. 15, no. 3, pp. 35 37, Mar. 11. [1] D. Korpi, L. Anttila, and M. Valkama, Impact of received signal on self-interference channel estimation and achievable rates in in-band fullduplex transceivers, in Proc. th Asilomar Conference on Signals, Systems and Computers, Nov. 1, pp. 975 9. [11], Feasibility of in-band full-duplex radio transceivers with imperfect RF components: Analysis and enhanced cancellation algorithms, in Proc. 9th International Conference on Cognitive Radio Oriented Wireless Networks and Communications (CROWNCOM), Jun. 1, pp. 53 53. [1] D. Korpi, L. Anttila, V. Syrjälä, and M. Valkama, Widely linear digital self-interference cancellation in direct-conversion full-duplex transceiver, IEEE J. Sel. Areas Commun., vol. 3, no. 9, pp. 17 17, Oct. 1.