### Multiple-antenna two-hop relaying for bi-directional transmission in wireless communication systems

In today’s wireless communication systems, usually the point-to-point transmission technique is used for the transmission between two nodes S1 and S2. If a point-to-point transmission between S1 and S2 is not possible, e.g., due to shadowing or limited transmit powers, two-hop relaying is a promising technique, in which the transmission between S1 and S2 is assisted by an intermediate relay station (RS). In this project, non-regenerative two-hop relaying is considered which means that the received signals at the RS are neither decoded nor re-encoded, but only linear signal processing (SP) is employed at the RS. Just recently, two-hop relaying has been investigated in conjunction with multiple-antenna techniques which promises significant performance gains in terms of achievable data rates. In this work, multiple antennas are used at S1, S2 and the RS in order to perform spatial multiplexing by adaptive beamforming (BF).

This project investigates two different two-hop relaying schemes for bi-directional transmission between S1 and S2, namely one-way and two-way relaying. In one-way relaying due to the half-duplex constraint, one time slot is required for the first hop transmission from S1 to the RS, and another time slot is required for the second hop transmission from the RS to S2. For bi-directional transmission, another two time slots are required for the transmission from S2 via the RS to S1 resulting in a requirement of four time slots in total. Thus, compared to a bi-directional point-to-point transmission between S1 and S2, which requires only one time slot for the transmission from S1 to S2 and another time slot for the transmission from S2 to S1, the number of required time slots is doubled in one-way relaying. In case of bi-directional transmission, the recently proposed two-way relaying scheme is a very promising scheme in terms of resource efficiency since it requires only two time slots. In two-way relaying, S1 and S2 transmit their signals simultaneously in the first time slot to the RS which retransmits a superposition of the signals of S1 and S2 in the second time slot. Thus, the received signal at each node contains the signal which has been transmitted by the respective receive node itself. If sufficient channel state information (CSI) is available at the receive node, it can determine the desired signal by subtracting the own transmitted signal. This subtraction is termed cancellation of duplex interference (CDI). In this project, a unified system model for one-way and two-way relaying is developed. For both relaying schemes, it is of particular interest how the sum rate of the system can be maximized by adaptive BF. The achievable sum rates depend considerably on the system capabilities, which are defined by the CSI availability and the SP capabilities at S1, S2 and the RS. Since the system capabilities influence the applicable adaptive BF algorithms, novel sum rate maximization problems are identified and classified by a framework consisting of four different cases of system capabilities:

• A system with full capabilities, in which S1 and S2 perform adaptive BF and CDI, and the RS, performs adaptive BF.

• A system with limited capabilities at the RS, in which only S1 and S2 perform adaptive BF and CDI.

• A system with limited capabilities at S1 and S2, in which only the RS performs adaptive BF.

• A system with local CSI at S1 and S2, in which S1 and S2 perform CDI, and only the RS performs adaptive BF.

The different cases are considered for one-way and two-way relaying, and the respective maximum sum rates are determined. In one-way relaying, an analytical BF algorithm for maximizing the sum rate in the system with full capabilities is reviewed.

For the other new cases of system capabilities in one-way and two-way relaying, numerical solutions to the sum rate maximization problems are given. For the systems with limited capabilities at the RS in one-way and two-way relaying, new sub-optimum analytical BF algorithms with close-to-optimum performances are proposed. It is shown that the maximum spatial multiplexing gain corresponds to the minimum of the number of antennas at the RS and the number of antennas at S1 and S2 in one-way relaying, and to the minimum of the number of antennas at the RS and twice the number of antennas at S1 and S2 in two-way relaying. Furthermore, it is demonstrated that the sum rate in two-way relaying is almost twice as high as the sum rate in one-way relaying.

Beside the adaptive BF algorithms maximizing the sum rate, other adaptive BF algorithms minimizing the mean square error (MSE), minimizing the MSE under the zero forcing constraint, and maximizing the signal-to-noise ratio are known to provide reasonable performance in point-to-point transmission. Since adaptive BF only performed at nodes S1 and S2 has already been investigated in several works regarding point-to-point transmission, in this project special attention is paid to the recent field of systems in which adaptive BF is only performed at the RS. For such systems in one-way as well as in two-way relaying, the aforementioned optimization problems, are newly formulated, solved, and analyzed. Promising performance results are especially obtained by the adaptive BF algorithm minimizing the MSE.

In order to obtain CSI in the different cases of system capabilities, novel pilot transmission schemes and the respective channel estimation algorithms are developed.

Furthermore, the impact of imperfect CSI on the performance of two-way relaying is considered. Finally, two scenarios with multiple nodes are introduced exemplarily in order to give a first insight into the problems arising from multiple access in two-way relaying.