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...lem (P3) is a convex optimization problem, since its objective function is concave over S and its constraints specify a convex set of S. Note that (P3) resembles a similar problem formulated in [15], =-=[16]-=- (see also [17] and references therein) under the cognitive radio (CR) setup, where the rate of a secondary MIMO link is maximized subject to a set of so-called interference power constraints to prote...

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...the power allocation scheme in Section III-B. D. Average Transmit Power Constraint and Average Interference Power Constraint In this scenario, the constraints are described as E[P (g0, g1)] ≤ P E[g0P (g0, g1)] ≤ Q } . (20) 1) Lagrangian method: Since the problem is strictly concave, by applying KKT, we get P (g0, g1) = ( 1 λ + µg0 − N0 g1 )+, (21) where (·)+ denotes max{·, 0}, and λ and µ are jointly determined by E[P (g0, g1)] = P E[g0P (g0, g1)] = Q } . (22) 2) Decoupling method: Though the above method is feasible, it is difficult to solve λ and µ from (22). Following the idea in [12], [13], we can develop a relatively simpler method to deal with the problem. We decouple the original problem into two sub-problems, which are easily solved individually. The validity of this decouping will be illustrated later. • Sub-Problem 1 (SP1): Maximize (1) subject to E[P (g0, g1)] ≤ P . • Sub-Problem 2 (SP2): Maximize (1) subject to E[g0P (g0, g1)] ≤ Q. Denote P (1)(g0, g1) and P (2)(g0, g1) as the optimal power allocation for SP1 and SP2 respectively. Lemma 1: E[g0P (1)(g0, g1)] ≤ Q and E[P (2)(g0, g1)] ≤ P cannot be satisfied simultaneously. Proof: Let R1 and R2 denote the feasible reg...

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...he following discussions. Specifically, the optimal transmit covariance to achieve the CR point-to-point MIMO channel capacity under both the PTPC and PIPCs can be obtained from the following problem =-=[13]-=-: Max. S log ∣∣I+HSHH ∣∣ (P1) s. t. Tr(S) ≤ P Tr ( GjSG H j ) ≤ Γj , j = 1, · · · , J S 0 where for conciseness we have removed the SU index k in the symbol notations since K = 1, while S 0 means ...

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...e-power constraint and the CR’s own transmit-power constraint, and in [9], [10] based upon the additional CSI on the PR fading channel. On the other hand, for the multi-antenna PR and CR channels, in =-=[11]-=- the authors proposed both optimal and suboptimal spatial adaptation schemes for the CR transmitter. Information-theoretic limits for multiuser multiantenna/fading CR channels have also been studied i...

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...s letter, by applying the GLRT principle we derive new eigenvalue-based spectrum sensing algorithms that are different from those in [17]. Finally, multiantenna transceivers have also been studied in =-=[18]-=- for transmit beamforming instead of spectrum sensing for CRs. II. SIGNAL MODEL Consider a CR terminal performing spectrum sensing based on a set of ...

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...receiver, in [12] based on the combined CSI from the secondary transmitter to both primary and secondary receivers, and in [13] based on the additional CSI on the primary user fading channel. In [6], =-=[14]-=-, both optimal and suboptimal spatial adaptation schemes are presented for the secondary transmitter equipped with multiple antennas to maximize the point-to-point secondary user channel capacity unde...

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... selection has been studied in [8], and capacity-achieving transmission schemes for a single secondary link and multiple primary receivers under different system configurations have been developed in =-=[9]-=-. Robust beamforming in a cognitive network context has been considered in [10], with the objective of maximizing the rate of the secondary user while keeping the interference to the primary user belo...

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...me theory and network duality, again under a network-wide power constraint. Studies concerning resource optimization of MIMO CRs were also reported recently. Point-to-point MIMO links were studied in =-=[35]-=- under CR interference constraints, and a similar setup was considered in [34]. Notably, a distributed algorithm in the MIMO ad hoc CR network setup was proposed in [24], where nulls were placed towar...

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...the transmit power level, bit-rate, bandwidth, and/or antenna beam of the CR are dynamically changed based upon the channel state information (CSI) in the coexisting PR and CR network (see, e.g., [7]-=-=[14]-=-). In this paper, we are particularly interested in the case where the CR transmitter is equipped with multi-antennas so that it can deploy joint transmit precoding and power control to effectively ba...