8.1 Summary and Conclusions
In this thesis, various resource allocation and spatial multiplexing techniques have been investigated for wireless relay networks. In chapter 4, a spa- tial multiplexing technique has been proposed for a two way relay network using convex optimization techniques. The proposal considered multiple transmitter-receiver pairs and a MIMO relay transceiver has been optimized to satisfy a set of target SINRs for every users while minimizing the to- tal transmission power at the relays. The optimization in its original form has not been convex; however, the semidefinite relaxing has been applied for transforming the non-convex problem into convex problem. Accordingly, the non-convex rank-one constraint has been dropped to form the optimization problem using SDP. The proposed SDP technique has also been extended to a two way asynchronous relay network which utilized FIR filter-based relays to overcome intersymbol interference. The simulation results showed that the proposed two way relay technique has the ability to enhance spectrum efficiency and the filter based relays can effectively mitigate the interference from the various users and reduce BER.
In chapter 5, an MMSE based design criterion has been proposed for
Section 8.1. Summary and Conclusions 131
the design of two way relay network. The work considered both a single pair of users and multiple pair users. A new approach has been proposed to determine the optimum signal scaling factor required to use all avail- able transmission power at the relay though certain manipulation in the Lagrangian formulation. A bisection method has also been used to reduce the computational complexity.
Power allocation technique for an OFDM-based cognitive radio wireless relay network has been proposed in Chapter 6. The work considered asym- metric resource allocation between source to relay and relay to destination of a secondary wireless network while ensuring interference leakage to primary user receiver is below a threshold. The asymmetric resource allocation is to ensure that the capacity of the channel from source to relay and the relay to destination is matched in order to maximise the overall throughput.
Finally, a MIMO-OFDM relay network with multiple users has been considered in chapter 7. Accordingly, the base station and the relay employ multiple antennas forming a MIMO channel while the user terminals employ single antenna forming MISO channels between the relay and the user termi- nals. Singular value based channel decomposition and water filing algorithm has been proposed to optimise the transmission from source to relay while a set of beamformers and power allocation have been designed to optimise transmission from relays to destination. As in chapter 6, the throughputs of the channel from source to relay and relay to destination have been equated to maximise the overall capacity. The beamformers have been designed us- ing the principle of BC-MAC duality. The proposed algorithm in its dual form has been solved using bisection-based and GP.
Section 8.2. Future Work 132
8.2 Future Work
The potential areas for future research have been recognized. All the algo- rithms proposed in this thesis, were developed based on the assumption that the CSI is well known. However, in reality, CSI may have errors due to feed- back quantization, estimation error etc. Therefore, the resource allocation and beamforming techniques proposed in various chapters in this thesis can be extended to include possibility of imperfect or incomplete CSI and robust designs can be performed.
The work in Chapters 4 and 5 on two-way relay network can be extended to a cognitive radio network scenario where interference constraints have to be imposed in addition to the optimization of SINR or MMSE criterion in the design framework. Also, the work in these chapters considered single antenna based peer-to-peer users, and only the relays employed multiple antennas. This work has the potential for possible extension towards em- ploying multiple antennas at the transmitter and the receiver. In this case, the beamforming vectors at the transmitter and the receivers as well as the relay transceiver matrix have to be designed jointly. This problem is very likely to be non-convex; however, convex approximations or iterative design methods can be employed to solve this joint optimization problem.
Also, the works in Chapter 6 and 7 considered single antenna for the receiver terminals. These works can also be extended to multiple antennas based receiver terminals. Hence both the channels from the source to relay and relay to multiple destinations will be MIMO and joint optimization of source precoder, relay transceiver and receiver filters needs to be performed over all OFDM subcarriers. Finally the work in Chapter 7 considered only one channel in time slot 1 that is from source to relay. However, it is possible to have multiple relays as well as other user terminals in addition to relays in the first time slot. Hence, the optimization framework can be extended
Section 8.2. Future Work 133
to cater this requirement as part of the future work. It is also possible to consider multiple hops for all the relay designs considered in the thesis.
Appendix
A. Proof: Maximization of SINR
maximize w wHRdw wHR i+nw = maximize w wHRdw wHR1/2 i+nR 1/2 i+nw (9.2.1)
This maximization is equivalent to
maximize u u HR−1/2 i+n RdR −1/2 i+n u subject to uHu = 1, (9.2.2)
where u = R1/2i+nw and the solution of (9.2.2) will be the eigenvector corre-
sponding to the largest eigenvalue of R−1/2i+n RdR−1/2i+n .
R−1/2i+n RdR−1/2i+n u = λmaxu ⇒ R−1i+nRdR−1/2i+n u = λmaxR
−1/2 i+n u
⇒ R−1i+nRdw = λmaxw (9.2.3)
This completes the proof.