建站服务,建模培训机构排名,长沙百度贴吧,wps免费模板网站标题很帅 STAR-RIS Enhanced Joint Physical Layer Security and Covert Communications for Multi-antenna mmWave Systems文章末尾的一个推导。 lim M → ∞ ∥ Φ ( w k ⊗ Θ r ) Ω r w H g ∗ ∥ 2 2 M lim M → ∞ Tr ( g T Ω r w ( w k ⊗ Θ r ) H Φ H Φ… 标题很帅 STAR-RIS Enhanced Joint Physical Layer Security and Covert Communications for Multi-antenna mmWave Systems文章末尾的一个推导。 lim M → ∞ ∥ Φ ( w k ⊗ Θ r ) Ω r w H g ∗ ∥ 2 2 M lim M → ∞ Tr ( g T Ω r w ( w k ⊗ Θ r ) H Φ H Φ ( w k ⊗ Θ r ) Ω r w H g ∗ ) M → ( a ) Tr ( Ω r w H Ω r w ( w k ⊗ Θ r ) H Φ H Φ ( w k ⊗ Θ r ) ) M ( b ) Tr ( ∑ l 1 L ( w k H Ψ B R l w k ) ⊗ ( Ω r w H Ω r w Θ r H Ψ ^ B R l Θ r ) ) M ( c ) ∑ l 1 L ( w k H Ψ B R l w k ) Tr ( Ω r w H Ω r w Θ r H Ψ ^ B R l Θ r ) M ∑ l 1 L ( w k H Ψ B R l w k ) ( ϑ r T Ξ T ( ( Ψ ^ B R l ) T ⊗ ( Ω r w H Ω r w ) ) Ξ ϑ r ∗ ) M , \begin{array}{l} \lim _{M \rightarrow \infty} \frac{\left\|\boldsymbol{\Phi}\left(\mathbf{w}_{k} \otimes \boldsymbol{\Theta}_{\mathrm{r}}\right) \boldsymbol{\Omega}_{\mathrm{rw}}^{H} \mathbf{g}^{*}\right\|_{2}^{2}}{M} \\ \lim _{M \rightarrow \infty} \frac{\operatorname{Tr}\left(\mathbf{g}^{T} \boldsymbol{\Omega}_{\mathrm{rw}}\left(\mathbf{w}_{k} \otimes \boldsymbol{\Theta}_{\mathrm{r}}\right)^{H} \mathbf{\Phi}^{H} \boldsymbol{\Phi}\left(\mathbf{w}_{k} \otimes \boldsymbol{\Theta}_{\mathrm{r}}\right) \boldsymbol{\Omega}_{\mathrm{rw}}^{H} \mathbf{g}^{*}\right)}{M} \\ \stackrel{(a)}{\rightarrow} \frac{\operatorname{Tr}\left(\boldsymbol{\Omega}_{\mathrm{rw}}^{H} \boldsymbol{\Omega}_{\mathrm{rw}}\left(\mathbf{w}_{k} \otimes \boldsymbol{\Theta}_{\mathrm{r}}\right)^{H} \boldsymbol{\Phi}^{H} \boldsymbol{\Phi}\left(\mathbf{w}_{k} \otimes \boldsymbol{\Theta}_{\mathrm{r}}\right)\right)}{M} \\ \stackrel{(b)}{} \frac{\operatorname{Tr}\left(\sum_{l1}^{L}\left(\mathbf{w}_{k}^{H} \mathbf{\Psi}_{\mathrm{BR}}^{l} \mathbf{w}_{k}\right) \otimes\left(\boldsymbol{\Omega}_{\mathrm{rw}}^{H} \boldsymbol{\Omega}_{\mathrm{rw}} \boldsymbol{\Theta}_{\mathrm{r}}^{H} \widehat{\mathbf{\Psi}}_{\mathrm{BR}}^{l} \boldsymbol{\Theta}_{\mathrm{r}}\right)\right)}{M} \\ \stackrel{(c)}{} \frac{\sum_{l1}^{L}\left(\mathbf{w}_{k}^{H} \mathbf{\Psi}_{\mathrm{BR}}^{l} \mathbf{w}_{k}\right) \operatorname{Tr}\left(\boldsymbol{\Omega}_{\mathrm{rw}}^{H} \boldsymbol{\Omega}_{\mathrm{rw}} \boldsymbol{\Theta}_{\mathrm{r}}^{H} \widehat{\boldsymbol{\Psi}}_{\mathrm{BR}}^{l} \boldsymbol{\Theta}_{\mathrm{r}}\right)}{M} \\ \frac{\sum_{l1}^{L}\left(\mathbf{w}_{k}^{H} \boldsymbol{\Psi}_{\mathrm{BR}}^{l} \mathbf{w}_{k}\right)\left(\boldsymbol{\vartheta}_{\mathrm{r}}^{T} \mathbf{\Xi}^{T}\left(\left(\widehat{\Psi}_{\mathrm{BR}}^{l}\right)^{T} \otimes\left(\boldsymbol{\Omega}_{\mathrm{rw}}^{H} \boldsymbol{\Omega}_{\mathrm{rw}}\right)\right) \boldsymbol{\Xi} \boldsymbol{\vartheta}_{\mathrm{r}}^{*}\right)}{M}, \end{array} limM→∞M∥Φ(wk⊗Θr)ΩrwHg∗∥22limM→∞MTr(gTΩrw(wk⊗Θr)HΦHΦ(wk⊗Θr)ΩrwHg∗)→(a)MTr(ΩrwHΩrw(wk⊗Θr)HΦHΦ(wk⊗Θr))(b)MTr(∑l1L(wkHΨBRlwk)⊗(ΩrwHΩrwΘrHΨ BRlΘr))(c)M∑l1L(wkHΨBRlwk)Tr(ΩrwHΩrwΘrHΨ BRlΘr)M∑l1L(wkHΨBRlwk)(ϑrTΞT((Ψ BRl)T⊗(ΩrwHΩrw))Ξϑr∗),
具体推导过程在论文Large System Performance of Linear Multiuser Receivers in Multipath Fading Channels中
其中步骤(a)的推导来自于
