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Table 3 Covariance matrices and ATP and IAP constraints of conventional and equivalent single-user MIMO systems

From: Practical decentralized high-performance coordinated beamforming for both downlink and uplink in time-division duplex systems

  Conventional Downlink equivalent (5) Uplink equivalent (8)
Source covariance Φ s = E s s * = σ s 2 I m Φ s k = E s k s k * = σ s k 2 I m k Φ ¯ s k = E s ¯ k s ¯ k * = σ ¯ s k 2 I m ¯ k
Noise covariance Φ n  = E(nn*) = β I r Φ n k = E n k n k * = β k I u k E G ¯ k , R n ¯ k n ¯ k * G ¯ k , R * = β ¯ k I d ¯ k where Φ ¯ n k = E n ¯ k n ¯ k * = β ¯ k I b ¯ k 14
Transmit covariance E Fs s * F * = σ s 2 F F * E F k , R s k s k * F k , R * = σ s k 2 F k , R F k , R * generally σ s k 2 F k F k * E F ¯ k s ¯ k s ¯ k * F ¯ k * = σ ¯ s k 2 F ¯ k F ¯ k *
ATP P = tr F F * σ s 2 P k = tr F k , R F k , R * σ s k 2 = tr F k F k * σ s k 2 ( 9 , 10 ) P ¯ k = tr F ¯ k F ¯ k * σ ¯ s k 2
IAP L = λ max F F * σ s 2 L k = λ max F k , R F k , R * σ s k 2 = λ max F k F k * σ s k 2 ( 12 , 13 ) L ¯ k = λ max F ¯ k F ¯ k * σ ¯ s k 2