Rank-Constrained Semidefinite Programming for Beamforming and MIMO Radar

Semidefinite programming (SDP) is a class of convex optimization problems with a rich theory that can be efficiently solved in polynomial time. Many problems in wireless communications and radar systems can be formulated as SDPs with additional rank constraints. Unfortunately, rank-constrained SDPs are nonconvex and are hard to solve in general (some of them are in fact NP-hard, but not all of them). One important example is beamforming design in the downlink of a cellular network with multi-antenna base stations transmitting to single-antenna users. Such a problem can be formulated as a rank-constrained SDP. We have developed a framework to quantify exactly what low-rank solutions can be achieved, as well as algorithms to obtain such solutions. Another example is multiple-input multiple-output (MIMO) radar, which resembles the problem of MIMO communication systems. We have addressed the problem of design and optimization of the transmitted waveform for optimal performance.

Papers

• Maria Gregori, Miquel Payaró, and Daniel P. Palomar, “Sum-Rate Maximization for Energy Harvesting Nodes With a Generalized Power Consumption Model,” IEEE Trans. on Wireless Comm., vol. 15, no. 8, pp. 5341-5354, Aug. 2016.
• Ying Sun, Arnaud Breloy, Prabhu Babu, Daniel P. Palomar, Frédéric Pascal, and Guillaume Ginolhac, “Low-Complexity Algorithms for Low Rank Clutter Parameter Estimation in Radar Systems,” IEEE Trans. on Signal Processing, vol. 64, no. 8, pp. 1986-1998, April 2016.
• Yongwei Huang and Daniel P. Palomar, “Randomized Algorithms for Optimal Solutions of Double-Sided QCQP with Applications in Signal Processing,” IEEE Trans. on Signal Processing, vol. 62, no. 5, pp. 1093-1108, March 2014.
• Benjamín Béjar, Santiago Zazo, and Daniel P. Palomar, “Energy Efficient Collaborative Beamforming in Wireless Sensor Networks,” IEEE Trans. on Signal Processing, vol. 62, no. 2, pp. 496-510, Jan. 2014.
• Yongwei Huang and Daniel P. Palomar, “A Dual Perspective on Separable Semidefinite Programming with Applications to Optimal Downlink Beamforming,” IEEE Trans. on Signal Processing, vol. 58, no. 8, pp. 4254-4271, Aug. 2010.
• Yongwei Huang and Daniel P. Palomar, “Rank-Constrained Separable Semidefinite Programming With Applications to Optimal Beamforming,” IEEE Trans. on Signal Processing, vol. 58, no. 2, pp. 664-678, Feb. 2010.
• Antonio De Maio, Yongwei Huang, Daniel P. Palomar, Shuzhong Zhang, and Alfonso Farina, “Fractional QCQP with Applications in ML Steering Direction Estimation for Radar Detection,” IEEE Trans. on Signal Processing, vol. 59, no. 1, pp. 172-185, Jan. 2011.
• Antonio De Maio, Silvio De Nicola, Yongwei Huang, Daniel P. Palomar, Shuzhong Zhang, and Alfonso Farina, “Code Design for Radar STAP via Optimization Theory,” IEEE Trans. on Signal Processing, vol. 58, no. 2, pp. 679-694, Feb. 2010.