On low complexity robust beamforming with positive semidefinite constraints

This paper addresses the problem of robust beamforming for general-rank signal models with norm bounded uncertainties in the desired and received signal covariance matrices as well as positive semidefinite constraints on the covariance matrices. Two novel minimum variance robust beamformers are derived in closed-form. The first one basically is the closed-form version of an existing iterative algorithm, while the second one offers even better performance with respect to the first one. Both of them have the advantage of low complexity. The effectiveness and performance improvement of the proposed beamformers are verified by simulation results. © 2009 IEEE.published_or_final_versio

Rationality, Culture and Deterrence / September 2013

The views expressed herein are those of the author and do not necessarily reflect the official policy or position of the Naval Postgraduate School, the Defense Threat Reduction Agency, the Department of Defense, or the United States Government.Deterrence strategies involve trying to influence the decision-making of another actor. Because of this, efforts to determine whether to employ a strategy of deterrence or how to implement such a strategy require attempting to forecast what things will influence the other actor and how that influence will be exerted. There are several models or frameworks available that could assist with efforts to anticipate how another actor will be influenced. In practice, the most prominent public debates related to deterrence in the United States have tended to reflect two main approaches. People tend to assume either that the other side will behave like a rational actor or that it will be driven by a unique strategic culture. While both approaches have merit, extensive critiques have revealed that both also have significant limitations.U.S. Naval Postgraduate School (NPS) Center on Contemporary Conflict (CCC) Project on Advanced Systems and Concepts for Countering WMD (PASCC)Approved for public release; distribution is unlimited

Robust joint design of linear relay precoder and destination equalizer for dual-hop amplify-and-forward MIMO relay systems

This paper addresses the problem of robust linear relay precoder and destination equalizer design for a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system, with Gaussian random channel uncertainties in both hops. By taking the channel uncertainties into account, two robust design algorithms are proposed to minimize the mean-square error (MSE) of the output signal at the destination. One is an iterative algorithm with its convergence proved analytically. The other is an approximated closed-form solution with much lower complexity than the iterative algorithm. Although the closed-form solution involves a minor relaxation for the general case, when the column covariance matrix of the channel estimation error at the second hop is proportional to identity matrix, no relaxation is needed and the proposed closed-form solution is the optimal solution. Simulation results show that the proposed algorithms reduce the sensitivity of the AF MIMO relay systems to channel estimation errors, and perform better than the algorithm using estimated channels only. Furthermore, the closed-form solution provides a comparable performance to that of the iterative algorithm. © 2006 IEEE.published_or_final_versio

Bayesian robust linear transceiver design for dual-hop amplify-and-forward MIMO relay systems

In this paper, we address the robust linear transceiver design for dual-hop amplify-and-forward (AF) MIMO relay systems, where both transmitters and receivers have imperfect channel state information (CSI). With the statistics of channel estimation errors in the two hops being Gaussian, we formulate the robust linear-minimum-mean-square-error (LMMSE) transceiver design problem using the Bayesian framework, and derive a closed-form solution. Simulation results show that the proposed algorithm reduces the sensitivity of the relay system to channel estimation errors, and performs better than the algorithm using estimated channel only.published_or_final_versionThe IEEE Global Telecommunications Conference (GLOBECOM 2009), Honolulu, HI., 30 November-4 December 2009. In Proceedings of GLOBECOM, 2009, p. 1-

Author's reply to "comments on 'timing estimation and resynchronization for amplify-and-forward communication systems'"

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Timing estimation and resynchronization for amplify-and-forward communication systems

This paper proposes a general framework to effectively estimate the unknown timing and channel parameters, as well as design efficient timing resynchronization algorithms for asynchronous amplify-and-forward (AF) cooperative communication systems. In order to obtain reliable timing and channel parameters, a least squares (LS) estimator is proposed for initial estimation and an iterative maximum-likelihood (ML) estimator is derived to refine the LS estimates. Furthermore, a timing and channel uncertainty analysis based on the CramrRao bounds (CRB) is presented to provide insights into the system uncertainties resulted from estimation. Using the parameter estimates and uncertainty information in our analysis, timing resynchronization algorithms that are robust to estimation errors are designed jointly at the relays and the destination. The proposed framework is developed for different AF systems with varying degrees of timing misalignment and channel uncertainties and is numerically shown to provide excellent performances that approach the synchronized case with perfect channel information. © 2006 IEEE.published_or_final_versio

Exact performance analysis of dual-hop semi-blind AF relaying over arbitrary nakagami-m fading channels

Relay transmission is promising for future wireless systems due to its significant cooperative diversity gain. The performance of dual-hop semi-blind amplify-and-forward (AF) relaying systems was extensively investigated, for transmissions over Rayleigh fading channels or Nakagami-m fading channels with integer fading parameter. For the general Nakagami-m fading with arbitrary m values, the exact closed-form system performance analysis is more challenging. In this paper, we explicitly derive the moment generation function (MGF), probability density function (PDF) and moments of the end-to-end signal-to-noise ratio (SNR) over arbitrary Nakagami-m fading channels with semi-blind AF relay. With these results, the system performance evaluation in terms of outage probability, average symbol error probability, ergodic capacity and diversity order, is conducted. The analysis developed in this paper applies to any semi-blind AF relaying systems with fixed relay gain, and two major strategies for computing the relay gain are compared in terms of system performance. All analytical results are corroborated by simulation results and they are shown to be efficient tools to evaluate system performance. © 2011 IEEE.published_or_final_versio

Robust Tomlinson-Harashima precoding for non-regenerative multi-antenna relaying systems

Conference Theme: PHY and FundamentalsIn this paper, we consider the robust transceiver design with Tomlinson-Harashima precoding (THP) for multi-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying systems. THP is adopted at the source to mitigate the spatial inter-symbol interference and then a joint Bayesian robust design of THP at source, linear forwarding matrices at relays and linear equalizer at destination is proposed. Based on the elegant characteristics of multiplicative convexity and matrix-monotone functions, the optimal structure of the nonlinear transceiver is first derived. Based on the derived structure, the optimization problem is greatly simplified and can be efficiently solved. Finally, the performance advantage of the proposed robust design is assessed by simulation results. © 2012 IEEE.published_or_final_versionThe 2012 IEEE Wireless Communications and Networking Conference (WCNC), Paris, France, 1-4 April 2012. In IEEE Wireless Communications and Networking Conference Proceedings, 2012, p. 753-75

Uplink LMMSE beamforming design for cellular networks with AF MIMO relaying

In this paper, linear beamforming design for uplink amplify-and-forward relaying cellular networks, in which multiple mobile terminals rely on one relay station to communicate with the base station, is investigated. In particular, the base station, relay station and mobile terminals are all equipped with multiple antennas. Based on linear minimum mean-square-error (LMMSE) criterion and exploiting a hidden convexity in the problem, the precoder matrices at multiple mobile terminals, forwarding matrix at relay station and equalizer matrix at base station are jointly designed. Furthermore, several existing linear beamforming designs for multi-user (MU) MIMO systems and AF MIMO relaying systems can be considered as special cases of the proposed solution. Simulation results are presented to demonstrate the performance advantage of the proposed algorithm. © 2011 IEEE.published_or_final_versionThe 2011 IEEE Global Telecommunications Conference (GLOBECOM 2011), Beijing, China, 5-9 December 2011. In Globecom. IEEE Conference and Exhibition, 2011, p. 1-

Maximum mutual information design for amplify-and-forward multi-hop MIMO relaying systems under channel uncertainties

Conference Theme: PHY and FundamentalsIn this paper, we investigate maximum mutual information design for multi-hop amplify-and-forward (AF) multiple-input multiple-out (MIMO) relaying systems with imperfect channel state information, i.e., Gaussian distributed channel estimation errors. The robust design is formulated as a matrix-variate optimization problem. Exploiting the elegant properties of Majorization theory and matrix-variate functions, the optimal structures of the forwarding matrices at the relays and precoding matrix at the source are derived. Based on the derived structures, a water-filling solution is proposed to solve the remaining unknown variables. © 2012 IEEE.published_or_final_versionThe 2012 IEEE Wireless Communications and Networking Conference (WCNC), Paris, France, 1-4 April 2012. In IEEE Wireless Communications and Networking Conference Proceedings, 2012, p. 781-78