**Interference Alignment**

Spectral efficiency is a key performance metric when it comes to the design of cellular systems. However, the users’ throughput capability in practical systems is greatly limited by interference from other co-channel users within the same cell or from neighbouring ones. It was traditionally thought that the best approach to deal with interference is to avoid it completely by allocating resources orthogonally.

However recent years have seen major advances in terms of understanding the information-theoretic capacity limits of interference limited networks. Results show that the maximum achievable capacity is much higher than what is currently obtained via conventional orthogonal methods. This has come along with the introduction of Interference Alignment (IA). IA involves a variety of techniques whose aim is to design beamformers that align unwanted signals into a restricted subspace that is smaller than the number of interferers themselves, thereby increasing overall capacity.

The initial promising results for IA were obtained under idealistic network settings where channel state information (CSI) is perfectly and immediately available at all nodes. This has made it difficult to translate theoretical gains into practical ones. Therefore IA research within our group focuses mainly on the management of interference in more realistic network scenarios under relaxed CSI conditions. Some of the CSI issues considered include:

However recent years have seen major advances in terms of understanding the information-theoretic capacity limits of interference limited networks. Results show that the maximum achievable capacity is much higher than what is currently obtained via conventional orthogonal methods. This has come along with the introduction of Interference Alignment (IA). IA involves a variety of techniques whose aim is to design beamformers that align unwanted signals into a restricted subspace that is smaller than the number of interferers themselves, thereby increasing overall capacity.

**Research****Members Involved : Paula Aquilina**The initial promising results for IA were obtained under idealistic network settings where channel state information (CSI) is perfectly and immediately available at all nodes. This has made it difficult to translate theoretical gains into practical ones. Therefore IA research within our group focuses mainly on the management of interference in more realistic network scenarios under relaxed CSI conditions. Some of the CSI issues considered include:

- Delay – depending on the system's coherence time and the nature of the acquisition process CSI may only be available after some delay.
- Uncertainty – errors made during the estimation and acquisition process result in the available CSI being only an imperfect estimate of the actual channel information.
- Reduced availability – to reduce the amount of overheads only part of the CSI data may be available.

**Publications**- P. Aquilina and T. Ratnarajah, "Linear Interference Alignment in Full-Duplex MIMO Networks with Imperfect CSI," IEEE Trans. on Communications, in press.
- P. Aquilina and T. Ratnarajah, "On the Degrees of Freedom of Interference Broadcast Channels with Topological Interference Management," IEEE Trans. Commun., in press.
- Y. Luo, T. Ratnarajah, J. Xue, and F. A. Khan, "Interference Alignment in Two-Tier Randomly Distributed Heterogeneous Wireless Networks Using Stochastic Geometry Approach," IEEE Systems Journal, in press.
- S. M. Razavi and T. Ratnarajah, "Channel Inversion and Regularization Revisited," Signal Processing, vol. 121, pp. 70–80, April 2016
- P. Aquilina and T. Ratnarajah, "Performance analysis of IA techniques in the MIMO IBC with imperfect CSI," IEEE Trans. Commun., vol. 63, no. 4, pp. 1259-1270, April 2015.
- S. M. Razavi and T. Ratnarajah, "Adaptive LS and MMSE based Beamformer Design for Multiuser MIMO Interference Channels," IEEE Trans. Veh.r Tech., vol. 65, no. 1, pp. 132-144, Jan. 2016
- Y. Luo and T. Ratnarajah, "Robust Stochastic Optimization For MISO Broadcasting Channel With Delayed CSIT and Limited Transmitting Antenna," IEEE Trans. on Veh. Tech., vol. 64, no. 8, pp. 3547-3559-Aug. 2015.
- S. M. Razavi and T. Ratnarajah, "Adaptively Regularized Phase Alignment Precoding for Multiuser Multiantenna Downlink," IEEE Trans. Veh. Tech., vol. 64, no. 10, pp. 4863-4869, Oct. 2015
- S. M. Razavi and T. Ratnarajah, "Performance Analysis of Interference Alignment Under CSI Mismatch," IEEE Trans. Veh. Tech., vol. 63, no. 9, pp. 4740-4748, Nov. 2014.
- S. M. Razavi, T. Ratnarajah and C. Masouros "Transmit-Power Efficient Linear Precoding Utilizing Known Interference for the Multiantenna Downlink," IEEE Trans. Veh. Tech., pp. 4383-4394, vol. 63, no. 9, Nov. 2014.
- S. M. Razavi and T. Ratnarajah, "Interference Alignment in K-User MIMO Interference Channels with Partially Coordinated Receivers,"
*IET Communications*, Vol. 8, no. 1, pp. 50-57, Jan. 2014. - Y. Luo, H. Du, J. Xue, T. Ratnarajah, and D. Wilcox, "On the Performance of Asynchronous Ad-hoc Networks Using Interference Alignment with Renewal Process,"
*IET Communications*, Vol. 7, no. 15, pp. 1628-1637, Oct. 2013. - H. Du, T. Ratnarajah, M. Sellathurai, and C. B. Papadias, "Reweighted Nuclear Norm Approach for Interference Alignment," IEEE Trans. Communications, vol. 61, no. 9, pp. 3754-3765, Sep. 2013.
- S. Ma, H. Du, T. Ratnarajah, and L.Dong, "Robust Joint Signal and Interference Alignment in Cognitive Radio Networks with Ellipsoidal CSI Uncertainties,"
*IET Communications*, Vol. 7, no. 13, pp. 1360-1366, Sep. 2013. - P. Aquilina and T. Ratnarajah, "Topological interference management for interference broadcast channels with alternating connectivity," in Proc. ISIT 2015, pp. 2426-2430.
- P. Aquilina and T. Ratnarajah, "Topological interference management for two cell interference broadcast channels with alternating connectivity," in Proc. ICASSP 2015, pp. 3043-3047.
- Yi Luo, Huiqin Du and T. Ratnarajah, "Robust beamforming for two-user MISO broadcasting channel with delayed CSIT," in Proc. SAM Workshop 2014, pp. 161-164.
- Y. Luo, H. Du, T. Ratnarajah and D. Wilcox, "Performance analysis of ad hoc networks with interference alignment," in Proc. ASILOMAR 2012
*,*pp. 1412-1416. - Y. Luo, A. Papazafeiropoulos and T. Ratnarajah, "Degrees of freedom region of MIMO interference channel with imperfect current and delayed CSIT," in Proc. WCNC 2014, pp. 863-868.
- S. M. Razavi and T. Ratnarajah, "Performance analysis of MAX-SINR algorithm under CSI mismatch," in Proc. ICASSP 2014, pp. 7729-7733.
- S. M. Razavi, T. Ratnarajah, C. Masouros and M. Sellathurai, "Regularized phase alignment precoding for the MISO downlink," in Proc. IWCMC 2014, pp. 201-206.
- S. M. Razavi and T. Ratnarajah, "Adaptive MMSE-based beamformer design for multiuser MIMO interference channels," in Proc. GLOBECOM 2014, pp. 3748-3753.
- S. M. Razavi and T. Ratnarajah, "Adaptive LS-based beamformer design for multiuser MIMO interference channels," in PIMRC 2014, pp. 633-637.
- Y. Luo and T. Ratnarajah, "Throughput of two-tier heterogeneous wireless networks with interference coordination," in PIMRC 2014, pp. 618-622.
- S. M. Razavi and T. Ratnarajah, "Asymptotic performance analysis of interference alignment under imperfect CSI," in WCNC 2014, pp. 352-537.
- A. Papazafeiropoulos and T. Ratnarajah, "Optimal degrees of freedom for the K user MIMO interference channel even with delayed CSIT," in Proc. WCNC 2014, pp. 543-547.
- P. Aquilina, T. Ratnarajah and A. Papazafeiropoulos, "DoF region and sum rate analysis for the K user MIMO IC with limited CSI feedback," in Proc. PIMRC 2014, pp. 832-836.
- Y. Luo, H. Du, T. Ratnarajah and D. Wilcox, "Performance of homogeneous and asynchronous ad hoc network with interference alignment," in Proc. ICC 2013, pp. 1805-1809.