Transmit Strategies for Full-Duplex Point-to-Point Systems with Residual Self-Interference Jianshu Zhang, Omid Taghizadeh, and Martin Haardt Communications Research Laboratory Ilmenau University of Technology P. O. Box 100565, D-98694 Ilmenau, Germany URL: www.tu-ilmenau.de/crl Abstract—In this paper, we study transmit strategies for a full- duplex (FD) point-to-point system with residual self-interference. Under the MISO and MIMO setup, finding optimal transmit strategies which maximize the system sum rate is a non-convex problem and in general NP-hard. Thus, we resort to a suboptimal solution which maximizes the signal-to-leakage-plus-noise ratio (SLNR). The SLNR based precoding design avoids the joint design of the precoders at the two transmitters. It also provides a closed-form solution. Noticing that properly adjusting the transmit power can also improve the performance of a FD system. We develop power adjustment schemes which maximize the system sum rate for SISO, MISO, and MIMO scenarios. The optimization problem is still non-convex. Nevertheless, by analyzing whether the constraints are active at the optimality, we are able to obtain a closed-form solution at the end. Due to the fact that the sum rate achievable power adjustment algorithms might violate the quality of service (QoS) requirements in the system, we also propose power adjustment schemes which consider the max-min fairness. Simulation results demonstrate that for our FD system the proposed schemes achieve a significant gain over traditional transmit strategies for half-duplex (HD) systems when they are applied to FD systems. Index Terms—full-duplex, MIMO, SLNR, convex optimization. I. I NTRODUCTION Full-duplex (FD) systems enable simultaneous transmission and reception on the same frequency at the same time. Thus they have the potential to double the spectral efficiency. The major difficulty of realizing a FD device lies in the cancellation of the loop-back self-interference. The strong self-interference can simply exceed the dynamic range of the receiver RF chain and causes it to work in its saturation stage which may damage the device. Recently, several RF self-interference cancellation techniques have been proposed in [1], [2], [3], [4], and [5]. When combined with self-interference subtraction in the complex baseband of the receiver, the self-interference can be further reduced and theoretically two independent half-duplex (HD) systems are obtained. Thereby, optimal transmit strategies for a HD point-to-point system can be applied, e.g., total power transmission for SISO, maximum ratio transmission (MRT) for MISO, and an SVD together with water-filling (WF) for MIMO. However, unlike a pure HD system, it is shown in [3] that in practice the residual self-interference is not zero. Furthermore, it influences the design of optimal transmit strategies of the two communicating devices. If the residual interference is not well handled, it can still prevent us from exploiting the benefits of full-duplex wireless communications. This motivates us to develop robust signal processing techniques to combat this residual self- interference. In this paper, we study a full-duplex point-to-point system with non-ignorable (insuppressible) residual self-interference. The problem of finding optimal transmit strategies which maximize the sum rate of the system yields a non-convex problem which might be intractable [3]. Thus, we resort to sub-optimal solutions. We first propose precoding techniques which take into account the trade-offs between increasing the achievable rate and reducing the residual interference power. To this end, we exploit the statistics of the residual interference and develop signal-to-leakage-plus-noise ratio (SLNR) based precoders which have closed-form solutions for both the MISO and the MIMO setup. On the other hand, properly controlling the transmit power can also improve the performance of a FD system. Thereby, given a fixed precoder we design optimal power scaling factors to achieve a better performance for the system. That is, power scaling factors which maximize the achievable sum rate are developed for SISO and MISO while power scaling factors which maximize the sum SINR are found for MIMO. Considering the fairness in the system, we also develop power adjustment schemes which maximize the minimum SINR in the system. The proposed power adjust- ment algorithms can be further combined with the proposed precoding algorithms to enhance the performance. Simulation results demonstrate that the proposed transmit strategies have achieved a significant gain over traditional half-duplex transmit strategies when applied to FD systems. Notation: Uppercase and lower case bold letters denote ma- trices and vectors, respectively. The expectation operator, trace of a matrix, transpose, conjugate, and Hermitian transpose are denoted by E{·}, Tr{·}, {·} T , {·} ∗ , and {·} H , respectively. The m × m identity matrix is I m . The Euclidean norm of a vector is denoted by ‖·‖. The Hadamard (element-wise) product is denoted by ⊙. diag{V } creates a column vector by aligning the elements of the main diagonal of the matrix V onto each entry of a column vector while diag{v} creates a diagonal matrix by aligning the elements of the vector v onto