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27
Optimal resource allocation for MIMO ad hoc cognitive radio networks
 in Proc. 46th Annu. Allerton Conf. Commun., Control, Comput
, 2008
"... Abstract—Maximization of the weighted sumrate of secondary users (SUs) possibly equipped with multiantenna transmitters and receivers is considered in the context of cognitive radio (CR) networks with coexisting primary users (PUs). The total interference power received at the primary receiver is ..."
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Abstract—Maximization of the weighted sumrate of secondary users (SUs) possibly equipped with multiantenna transmitters and receivers is considered in the context of cognitive radio (CR) networks with coexisting primary users (PUs). The total interference power received at the primary receiver is constrained to maintain reliable communication for the PU. An interference channel configuration is considered for ad hoc networking, where the receivers treat the interference from undesired transmitters as noise. Without the CR constraint, a convergent distributed algorithm is developed to obtain (at least) a locally optimal solution. With the CR constraint, a semidistributed algorithm is introduced. An alternative centralized algorithm based on geometric programming and network duality is also developed. Numerical results show the efficacy of the proposed algorithms. The novel approach is flexible to accommodate modifications aiming at interference alignment. However, the standalone weighted sumrate optimal schemes proposed here have merits over interferencealignment alternatives especially for practical SNR values. Index Terms—Ad hoc network, cognitive radio, interference network, MIMO, optimization. I.
Linear precoding designs for amplifyandforward multiuser twoway relay systems
 IEEE Trans. Wireless Commun
, 2012
"... Abstract—Twoway relaying can improve spectral efficiency in twouser cooperative communications. It also has great potential in multiuser systems. A major problem of designing a multiuser twoway relay system (MUTWRS) is transceiver or precoding design to suppress cochannel interference. This pap ..."
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Abstract—Twoway relaying can improve spectral efficiency in twouser cooperative communications. It also has great potential in multiuser systems. A major problem of designing a multiuser twoway relay system (MUTWRS) is transceiver or precoding design to suppress cochannel interference. This paper aims to study linear precoding designs for a cellular MUTWRS where a multiantenna base station (BS) conducts bidirectional communications with multiple mobile stations (MSs) via a multiantenna relay station (RS) with amplifyandforward relay strategy. The design goal is to optimize uplink performance, including total meansquare error (TotalMSE) and sum rate, while maintaining individual signaltointerferenceplusnoise ratio (SINR) requirement for downlink signals. We show that the BS precoding design with the RS precoder fixed can be converted to a standard second order cone programming (SOCP) and the optimal solution is obtained efficiently. The RS precoding design with the BS precoder fixed, on the other hand, is nonconvex and we present an iterative algorithm to find a local optimal solution. Then, the joint BSRS precoding is obtained by solving the BS precoding and the RS precoding alternately. Comprehensive simulation is conducted to demonstrate the effectiveness of the proposed precoding designs. Index Terms—MIMO precoding, twoway relaying, nonregenerative relay, minimum meansquareerror (MMSE), convex optimization. I.
Geometry of the 3User MIMO interference channel
 in Proc. Allerton Conference on Communication, Control, and Computing (Allerton
, 2011
"... Abstract—This paper studies vector space interference alignment for the threeuser MIMO interference channel with no time or frequency diversity. The main result is a characterization of the feasibility of interference alignment in the symmetric case where all transmitters have M antennas and all ..."
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Abstract—This paper studies vector space interference alignment for the threeuser MIMO interference channel with no time or frequency diversity. The main result is a characterization of the feasibility of interference alignment in the symmetric case where all transmitters have M antennas and all receivers have N antennas. If N ≥M and all users desire d transmit dimensions, then alignment is feasible if and only if (2r+1)d ≤ max(rN, (r+1)M) for all nonnegative integers r. The analogous result holds with M and N switched if M ≥ N. It turns out that, just as for the 3user parallel interference channel [1], the length of alignment paths captures the essence of the problem. In fact, for each feasible value of M and N the maximum alignment path length dictates both the converse and achievability arguments. One of the implications of our feasibility criterion is that simply counting equations and comparing to the number of variables does not predict feasibility. Instead, a more careful investigation of the geometry of the alignment problem is required. The necessary condition obtained by counting equations is implied by our new feasibility criterion. I.
Giannakis, “Distributed optimal beamformers for cognitive radios robust to channel uncertainties
 IEEE Trans. Sig. Proc
, 2012
"... Abstract—Through spatial multiplexing and diversity, multiinput multioutput (MIMO) cognitive radio (CR) networks can markedly increase transmission rates and reliability, while controlling the interference inflicted to peer nodes and primary users (PUs) via beamforming. The present paper optimiz ..."
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Abstract—Through spatial multiplexing and diversity, multiinput multioutput (MIMO) cognitive radio (CR) networks can markedly increase transmission rates and reliability, while controlling the interference inflicted to peer nodes and primary users (PUs) via beamforming. The present paper optimizes the design of transmit and receivebeamformers for ad hoc CR networks when CRtoCR channels are known, but CRtoPU channels cannot be estimated accurately. Capitalizing on a normbounded channel uncertainty model, the optimal beamforming design is formulated to minimize the overall meansquare error (MSE) from all data streams, while enforcing protection of the PU system when the CRtoPU channels are uncertain. Even though the resultant optimization problem is nonconvex, algorithms with provable convergence to stationary points are developed by resorting to block coordinate ascent iterations, along with suitable convex approximation techniques. Enticingly, the novel schemes also lend themselves naturally to distributed implementations. Numerical tests are reported to corroborate the analytical findings. Index Terms—Beamforming, channel uncertainty, cognitive radios, distributed algorithms, MIMO wireless networks, robust optimization. I.
1A Feasibility Test for Linear Interference Alignment in MIMO Channels with Constant Coefficients
"... Abstract—In this paper, we consider the feasibility of linear interference alignment (IA) for multipleinput multipleoutput (MIMO) channels with constant coefficients for any number of users, antennas and streams per user; and propose a polynomialtime test for this problem. Combining algebraic geo ..."
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Abstract—In this paper, we consider the feasibility of linear interference alignment (IA) for multipleinput multipleoutput (MIMO) channels with constant coefficients for any number of users, antennas and streams per user; and propose a polynomialtime test for this problem. Combining algebraic geometry techniques with differential topology ones, we first prove a result that generalizes those previously published on this topic. Specifically, we consider the input set (complex projective space of MIMO interference channels), the output set (precoder and decoder Grassmannians) and the solution set (channels, decoders and precoders satisfying the IA polynomial equations), not only as algebraic sets but also as smooth compact manifolds. Using this mathematical framework, we prove that the linear alignment problem is feasible when the algebraic dimension of the solution variety is larger than or equal to the dimension of the input space and the linear mapping between the tangent spaces of both smooth manifolds given by the first projection is generically surjective. If that mapping is not surjective, then the solution variety projects into the input space in a singular way and the projection is a zeromeasure set. This result naturally yields a simple feasibility test, which amounts to checking the rank of a matrix. We also provide an exact arithmetic version of the test, which proves that testing the feasibility of IA for generic MIMO channels belongs to the boundederror probabilistic polynomial (BPP) complexity class. Index Terms—Interference alignment, MIMO interference channel, polynomial equations, algebraic geometry, differential topology. I.
Distributed MIMO Interference Cancellation for Interfering Wireless Networks: Protocol and Initial Simulation
"... Abstract—In this report, the problem of interference in dense wireless network deployments is addressed. Two example scenarios are: 1) overlapping basic service sets (OBSSes) in wireless LAN deployments, and 2) interference among closeby femtocells. The proposed approach is to exploit the interfere ..."
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Abstract—In this report, the problem of interference in dense wireless network deployments is addressed. Two example scenarios are: 1) overlapping basic service sets (OBSSes) in wireless LAN deployments, and 2) interference among closeby femtocells. The proposed approach is to exploit the interference cancellation and spatial multiplexing capabilities of multipleinput multipleoutput (MIMO) links to mitigate interference and improve the performance of such networks. Both semidistributed and fully distributed protocols for 802.11based wireless networks standard are presented and evaluated. The philosophy of the approach is to minimize modifications to existing protocols, particularly within clientside devices. Thus, modifications are primarily made at the access points (APs). The semidistributed protocol was fully implemented within the 802.11 package of ns3 to evaluate the approach. Simulation results with two APs, and with either one client per AP or two clients per AP, show that within 5 seconds of network operation, our protocol increases the goodput on the downlink by about 50%, as compared against a standard 802.11n implementation. Index Terms—MIMO, multiple antennas, beamforming, combining, overlapping basic service set, dense wireless networks I.
Signal Alignment: Enabling Physical Layer Network Coding for MIMO Networking
"... Abstract—We apply signal alignment (SA), a wireless communication technique that enables physical layer network coding (PNC) in multiinput multioutput (MIMO) wireless networks. Through calculated precoding, SA contracts the perceived signal space at a node to match its receive capability, and hen ..."
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Abstract—We apply signal alignment (SA), a wireless communication technique that enables physical layer network coding (PNC) in multiinput multioutput (MIMO) wireless networks. Through calculated precoding, SA contracts the perceived signal space at a node to match its receive capability, and hence facilitates the demodulation of linearly combined data packets. PNC coupled with SA (PNCSA) has the potential of fully exploiting the precoding space at the senders, and can better utilize the spatial diversity of a MIMO network for higher system degreesoffreedom (DoF). PNCSA adopts the idea of ‘demodulating a linear combination ’ from PNC. The design of PNCSA is also inspired by recent advances in IA, though SA aligns signals not interferences. We study the optimal precoding and power allocation problem of PNCSA, for SNR (singaltonoiseratio) maximization at the receiver. The mapping from SNR to BER is then analyzed, revealing that the DoF gain of PNCSA does not come with a sacrifice in BER. We then design a general PNCSA algorithm in larger systems, and demonstrate general applications of PNCSA, and show via network level simulations that it can substantially increase the throughput of unicast and multicast sessions, by opening previously unexplored solution spaces in multihop MIMO routing. Index Terms—Network coding; physical layer letwork coding; interference alignment; signal alignment; MIMO networks. I.
On Precoding for Constant KUser MIMO Gaussian Interference Channel with Finite Constellation Inputs”, Available at: arXiv:1210.3819v1
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Interference Alignment with Distributed Antenna Systems by
, 2011
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Iterative Reweighted Least Squares Approach to Interference Alignment
"... Abstract—This paper investigates the interference alignment (IA) solution for a Kuser static flatfading multiple input multiple output (MIMO) interference channel. Optimal users’ precoders and postcoders are designed through a rank constraint rank minimization (RCRM) framework with IA conditions i ..."
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Abstract—This paper investigates the interference alignment (IA) solution for a Kuser static flatfading multiple input multiple output (MIMO) interference channel. Optimal users’ precoders and postcoders are designed through a rank constraint rank minimization (RCRM) framework with IA conditions inserted within the constraints and the cost function of a complex matrix optimization problem. With RCRM formulation, the interference is forced to span the lowest dimensional subspace possible, under the condition that the useful signal subspaces span all available spatial dimensions. Using the recent advances in matrix completion theory and low rank matrix recovery theory, we propose an Iterative Reweighted Least Squares (IRLS) approach to IA. Through this approach, we provide an adequate relaxation for the rank function which in some cases attain the same results obtained using the standard nuclear norm with lower elapsed time per iteration and lower number of iterations and in some cases perform better than any of the previous approaches.