Interference alignment aided by non-regenerative relays
Final Report Abstract
In this project, bi-directional communication between multiple node pairs has been considered. Multiple amplify and forward half duplex relays with multiple antennas aid in the communication. The relays have been used to manipulate the effective channels between the transmitters and the receivers to aid in the interference alignment (IA) process. Both one-way relaying and two-way relaying protocols have been investigated. In both relaying protocols, the numbers of antennas required at the relays and at the nodes have been derived. Also, a number of algorithms to design the transmit filters, the relay filters, and the receive filters have been developed. In case of one-way relaying, we started with a single antenna at the nodes. This made it possible to linearize the problem by considering a single variable per node which defines the transmit signature of the corresponding node. Furthermore, we generalized the linearization method to the case where each node has N antennas and transmits N = d data streams. The method we developed is optimum in the DoF sense, because each node has N antennas and transmits N data streams in two time slots, which is half of the DoF it could achieve in the absence of interferers. We have derived the number of antennas required at the relays to make IA feasible. Also, we have obtained a closed form solution to achieve IA. If the relays have more antennas than required to perform IA, several IA solutions exist. The algorithm we obtained in this project gives all the IA solutions. Among these IA solutions, we can choose the ones which optimize a given objective function. We investigated different objective functions, like the minimization of transmit power at the relay, the minimization of the sum mean squared error, and the maximization of the sum rate. The first two lead to convex problems and we have proposed closed form solutions. However, sum rate maximization is a non-convex problem. We proposed a new method to reformulate this into a multi-concave problem. Considering the aforementioned objective functions aids in improving the performance of the system especially in low and medium SNRs. Furthermore, when the nodes do not have transmit CSI, we fixed the precoders and IA is achieved through the design of the relay filters only. In case of two-way relaying, we started with a single relay. Since the two-way relay channel is a multiple key-hole channel, the number R of antennas at the relay limits the number Kd of DoF in the system. First we investigated R = Kd. IA is tri-linear problem. Using the fact that selfinterference can be cancelled, we developed the concepts of signal and channel alignment and decoupled IA into three linear problems, namely signal alignment, channel alignment and transceive zero forcing. We have derived the number of antennas required at the nodes to achieve IA. We have shown that with R = Kd, the same number of DoF as in a MIMO interference channel without a relay is achieved. However, with the help of the relay a closed form solution to the IA problem is obtained for any number of node pairs in the system. In addition, when the relay has more than the minimum required number of antennas, i.e., R > Kd holds, we have utilized the additional antennas either to increase the DoF in the system or to reduce the required number of antennas at the nodes. Furthermore, for the case when there are multiple IA solutions, we formulated an optimization problem to find an IA solution that maximizes the SNR. This optimization problem is non-convex and we have proposed a gradient based algorithm to find a local maximum. The properness condition derived and the algorithms developed for the single relay case have been generalized for multiple relays. In addition, to improve the performance at low and medium SNRs, we have proposed an MMSE based scheme. Minimization of the MSE is a non-convex problem. However, by fixing one of the three kinds of variables, namely, the transmit filters, the relay filters or the receive filters, the problem becomes convex. We have proposed an algorithm to iteratively minimize the MSE. All the above mentioned methods require global CSI. In this project, further scenarios where the nodes have no CSI or limited CSI have been investigated. IA algorithms and the corresponding properness conditions have been derived for the case of no or limited CSI.
Publications
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Cooperative zero forcing in multi-pair multi-relay networks. Proc. International Symposium on Personal, Indoor and Mobile Radio Communications, Sydney, Sep. 2012, pp. 1740–1745
R. S. Ganesan, H. Al-Shatri, T. Weber and A. Klein
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Interference alignment using a MIMO relay and partially-adapted transmit/receive filters. Proc. IEEE Wireless Communications & Networking Conference, Paris, Apr. 2012, pp. 459–464
H. Al-Shatri, R. S. Ganesan, A. Klein, and T. Weber
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Perfect versus imperfect interference alignment using multiple MIMO relays. Proc. IEEE International Symposium on Wireless Communication Systems, Paris, Aug. 2012, pp. 676–680
H. Al-Shatri, R. S. Ganesan, A. Klein and T. Weber
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Closed-form solutions for minimizing sum MSE in multiuser relay networks. Proc. IEEE 77th Vehicular Technology Conference, Dresden, June 2013, pp. 1–5
H. Al-Shatri, X. Li, R. S. Ganesan, A. Klein, and T. Weber:
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Iterative MMSE filter design for multi-pair two-way multi-relay networks. Proc. IEEE International Conference on Communications, Budapest, June 2013, pp. 5929–5933
R. S. Ganesan, H. Al-Shatri, T. Weber, and A. Klein
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Pair-aware interference alignment in multi-user two-way relay networks. IEEE Transactions on Wireless Communications, vol. 12, no. 8, 2013, pp. 3662–3671
R. S. Ganesan, H. Al-Shatri, A. Kühne, T. Weber, and A. Klein
