On the MSE-Duality of the Broadcast Channel and the Multiple Access Channel

Hunger, Raphael; Joham, Michael; Utschick, Wolfgang

doi:10.1109/tsp.2008.2008253

Cited by 109 publications

(113 citation statements)

References 27 publications

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“…And as mentioned in [50], the user-wise MSE can be used to approximate the achievable rate of the users when they jointly decode their streams. In particular, when MMSE receivers are employed, the achievable rate of a user is written as the negative logarithm of the determinant of the MSE error covariance matrix, which is tightly related to the user MSE.…”

Section: A Rationale For Mse-based Optimizationsmentioning

confidence: 99%

MSE-Based Transceiver Designs for Full-Duplex MIMO Cognitive Radios

Cırık

Wang

Rong

et al. 2015

IEEE Trans. Commun.

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Abstract-We study two scenarios of full-duplex (FD) multipleinput-multiple-output cognitive radio networks: FD cognitive ad hoc networks and FD cognitive cellular networks. In FD cognitive ad hoc networks (also referred as interference channels), each pair of secondary users (SUs) operate in FD mode and communicate with each other within the service range of primary users (PUs). Each SU experiences not only self-interference but also interuser interference from all other SUs, and all SUs generate interference on PUs. We address two optimization problems: one is to minimize the sum of mean-squared errors (MSE) of all estimated symbols, and the other is to minimize the maximum per-SU MSE of estimated symbols, both of which are subject to power constraints at SUs and interference constraints projected to each PU. We show that these problems can be cast as a second-order cone programming, and joint design of transceiver matrices can be obtained through an iterative algorithm. Moreover, we show that the proposed algorithm is not only applicable to interference channels but also to FD cellular systems, in which a base station operating in FD mode simultaneously serves multiple uplink and downlink users, and it is shown to outperform HD scheme significantly.

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Section: A Rationale For Mse-based Optimizationsmentioning

confidence: 99%

MSE-Based Transceiver Designs for Full-Duplex MIMO Cognitive Radios

Cırık

Wang

Rong

et al. 2015

IEEE Trans. Commun.

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“…Because of the MSE duality between the vector BC [8] and the MAC in [9], [6], [10], it suffices to prove convexity in the MAC which is easier to handle. Fig.…”

Section: Conjecture On the Convexity Of The Multi-antenna Two Usementioning

confidence: 99%

On the Convexity of the MSE Region of Single-Antenna Users

Hunger

Joham

2008

IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference

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Abstract-We prove convexity of the sum-power constrained mean square error (MSE) region in case of two single-antenna users communicating with a multi-antenna base station. Due to the MSE duality this holds both for the vector broadcast channel and the dual multiple access channel. Increasing the number of users to more than two, we show by means of a simple counterexample that the resulting MSE region is not necessarily convex any longer, even under the assumption of single-antenna users. In conjunction with our former observation that the two user MSE region is not necessarily convex for two multi-antenna users, this extends and corrects the hitherto existing notion of the MSE region geometry.

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“…This paper has solved the latter problem directly in the downlink channel. In this channel, however, since the precoders of all users are jointly coupled, downlink MSE-based transceiver design problems have more complicated mathematical structure than their dual uplink problems [3], [8].…”

Section: Introductionmentioning

confidence: 99%

“…These two papers show that duality based approach of solving the downlink problem has easier to handle mathematical structure than that of [7]. Moreover, in some cases, duality solution approach can exploit the hidden convexity of the downlink channel MSE-based problems (for example minimization of sum MSE constrained with a total BS power problem [3], [8]). These duality are established by assuming that perfect channel state information (CSI) is available at the BS and mobile stations (MSs).…”

Section: Introductionmentioning

confidence: 99%

Robust Sum MSE Optimization for Downlink Multiuser MIMO Systems With Arbitrary Power Constraint: Generalized Duality Approach

Bogale

Vandendorpe

2012

IEEE Trans. Signal Process.

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Abstract-This paper considers linear minimum meansquare-error (MMSE) transceiver design problems for downlink multiuser multiple-input multiple-output (MIMO) systems where imperfect channel state information is available at the base station (BS) and mobile stations (MSs). We examine robust sum mean-square-error (MSE) minimization problems. The problems are examined for the generalized scenario where the power constraint is per BS, per BS antenna, per user or per symbol, and the noise vector of each MS is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. For each of these problems, we propose a novel duality based iterative solution. Each of these problems is solved as follows. First, we establish a novel sum average meansquare-error (AMSE) duality. Second, we formulate the power allocation part of the problem in the downlink channel as a Geometric Program (GP). Third, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. To solve robust sum MSE minimization constrained with per BS antenna and per BS power problems, we have established novel downlink-uplink duality. On the other hand, to solve robust sum MSE minimization constrained with per user and per symbol power problems, we have established novel downlink-interference duality. For the total BS power constrained robust sum MSE minimization problem, the current duality is established by modifying the constraint function of the dual uplink channel problem. And, for the robust sum MSE minimization with per BS antenna and per user (symbol) power constraint problems, our duality are established by formulating the noise covariance matrices of the uplink and interference channels as fixed point functions, respectively. We also show that our sum AMSE duality are able to solve other sum MSE-based robust design problems. Computer simulations verify the robustness of the proposed robust designs compared to the non-robust/naive designs.

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On the MSE-Duality of the Broadcast Channel and the Multiple Access Channel

Cited by 109 publications

References 27 publications

MSE-Based Transceiver Designs for Full-Duplex MIMO Cognitive Radios

MSE-Based Transceiver Designs for Full-Duplex MIMO Cognitive Radios

On the Convexity of the MSE Region of Single-Antenna Users

Robust Sum MSE Optimization for Downlink Multiuser MIMO Systems With Arbitrary Power Constraint: Generalized Duality Approach

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