Heterogeneous Statistical QoS Provisioning Over Cognitive-Radio Based 5G Mobile Wireless Networks

Abstract

As one of the critical techniques to support the multimedia services over mobile wireless networks, the statistical quality of service (QoS) technique has been proved to be effective in statistically guaranteeing delay-bounded video transmissions over the time-varying wireless channels. In the meantime, the full-duplex spectrum sensing (FD-SS) has been widely recognized as the promising candidate technique for maximizing the spectrum efficiency while provisioning the heterogeneous statistical QoS guarantees over cognitive radio-based 5G mobile wireless networks. However, due to the heterogeneity caused by different scenarios and applications of the multimedia traffics over CRNs, supporting diverse delay-bounded QoS guarantees for cognitive radio networks imposes many new challenges not encountered before. To effectively overcome the aforementioned problems, in this book chapter, we propose the heterogeneous statistical QoS provisioning schemes by applying the multiple-input-multiple-output generalized frequency division multiplexing (MIMO-GFDM) techniques to implement the FD-SS-based multimedia services in CRNs. In particular, under the Nakagami-m wireless channels, we derive the MIMO-GFDM-based physical (PHY)-layer model and the self-interference cancelation model. We develop the MIMO-GFDM-based FD-SS schemes and derive the miss-detection and false-alarm probabilities. Under the heterogeneous statistical QoS constraints, we develop the Markov chain model to characterize the aggregate effective capacity under the optimal power allocation policies using our proposed MIMO-GFDM architecture over FD-SS CRNs. Also conducted is a set of simulations which validate our proposed schemes, evaluate their performances, and show that our proposed schemes can outperform the other existing solutions under the heterogeneous statistical delay-bounded QoS constraints over cognitive radio-based 5G mobile wireless networks.

Appendices

Appendix A: Proof of Theorem 1

Proof.

The aggregate effective capacity, denoted by $\widetilde{C}_{AF,0}(\theta _{1},\theta _{2},\ldots,\theta _{K})$, for different links in the relay-based cognitive radio networks can be derived as follows:

$$ \displaystyle\begin{array}{rcl} \widetilde{C}_{AF,0}(\theta _{1},\theta _{2},\ldots,\theta _{K})& \triangleq & -\frac{1} {\theta _{o}}\log \left \{\mathbb{E}_{\gamma }\left [\exp \left \{-\sum _{k=1}^{K}\theta _{ k}T_{f}B\right.\right.\right. \\ & & \cdot \left.\left.\left.\log _{2}\left (1 + \frac{4P_{S}^{(k)}(\boldsymbol{\mu })P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2P_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\right )\right \}\right ]\right \}.{}\end{array}$$

(78)

Then, the value of θ _o needs to be derived before solving the optimization problem. The optimal θ _o needs to satisfy the following equation:

$$\displaystyle\begin{array}{rcl} & & \sum _{k=1}^{K} -\frac{1} {\theta _{k}}\log \left \{\!\mathbb{E}_{\gamma }\left [\exp \!\left \{-\theta _{k}T_{f}B\log _{2}\!\left (\!1 + \frac{4P_{S}^{(k)}(\boldsymbol{\mu })P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2P_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\!\right )\!\right \}\!\right ]\!\right \} \\ & & \quad = -\frac{1} {\theta _{o}}\sum _{k=1}^{K}\log \Bigg\{\mathbb{E}_{\gamma }\Bigg[\exp \Bigg\{-\theta _{ k}T_{f}B \\ & & \qquad \qquad \qquad \quad \qquad \,\,\,\, \cdot \log _{2}\Bigg(1 + \frac{4P_{S}^{(k)}(\boldsymbol{\mu })P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2P_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\Bigg)\Bigg\}\Bigg]\Bigg\} {}\end{array}$$

(79)

The aggregate effective capacity, denoted by $\widetilde{C}_{AF,0}(\theta _{1},\theta _{2},\ldots,\theta _{K})$, for different links in the relay-based cognitive radio networks can be derived as follows:

$$ \displaystyle\begin{array}{rcl} \widetilde{C}_{AF,0}(\theta _{1},\theta _{2},\ldots,\theta _{K})& \triangleq & -\frac{1} {\theta _{o}}\log \left \{\mathbb{E}_{\gamma }\left [\exp \left \{-\sum _{k=1}^{K}\theta _{ k}T_{f}B\right.\right.\right. \\ & & \cdot \left.\left.\left.\log _{2}\left (1 + \frac{4P_{S}^{(k)}(\boldsymbol{\mu })P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2P_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\right )\right \}\right ]\right \}.{}\end{array}$$

(78)

Then, the value of θ _o needs to be derived before solving the optimization problem. The optimal θ _o needs to satisfy the following equation:

$$\displaystyle\begin{array}{rcl} & & \sum _{k=1}^{K} -\frac{1} {\theta _{k}}\log \left \{\!\mathbb{E}_{\gamma }\left [\exp \!\left \{-\theta _{k}T_{f}B\log _{2}\!\left (\!1 + \frac{4P_{S}^{(k)}(\boldsymbol{\mu })P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2P_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\!\right )\!\right \}\!\right ]\!\right \} \\ & & \quad = -\frac{1} {\theta _{o}}\sum _{k=1}^{K}\log \Bigg\{\mathbb{E}_{\gamma }\Bigg[\exp \Bigg\{-\theta _{ k}T_{f}B \\ & & \qquad \qquad \qquad \quad \qquad \,\,\,\, \cdot \log _{2}\Bigg(1 + \frac{4P_{S}^{(k)}(\boldsymbol{\mu })P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2P_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\Bigg)\Bigg\}\Bigg]\Bigg\} {}\end{array}$$

(79)

Considering that the effective capacity for one link can be increased when using the QoS-driven power allocation as compared with the effective capacity using the average transmit power control, we have

$$\displaystyle\begin{array}{rcl} & & -\frac{1} {\theta _{k}}\log \left \{\mathbb{E}_{\gamma }\left [\exp \left \{-\theta _{k}T_{f}B\log _{2}\left (1 + \frac{4P_{S}^{(k)}(\boldsymbol{\mu })P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2P_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\right )\right \}\right ]\right \} \\ & & = -\frac{1} {\theta _{k}}\log \Bigg\{\mathbb{E}_{\gamma }\Bigg[\exp \Bigg\{-\theta _{k}T_{f}B \\ & & \qquad \qquad \qquad \quad \cdot \log _{2}\Bigg(1 + \frac{4P_{S}^{(k)}(\boldsymbol{\mu })P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2P_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2P_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\Bigg)\Bigg\}\Bigg]\Bigg\} + I_{k}, {}\end{array}$$

(80)

for 1 ≤ k ≤ K where I _k represents the increased aggregate effective capacity when using the heterogeneous-statistical-QoS-driven power allocation scheme for the kth downlink. Then, substituting Eq. (80) back into Eq. (79), we can obtain the expression for θ _o in Eq. (81) as follows:

$$\displaystyle\begin{array}{rcl} \theta _{o}& =& \\ & & \,\,\, \frac{\prod \limits _{n=1}^{K}\theta _{n}\!\left [\!\sum \limits _{k=1}^{K}\!\log \!\left \{\!\mathbb{E}_{\gamma }\!\left [\exp \!\left \{\!-\theta _{k}T_{f}B\log _{2}\!\!\left (\!1\! +\! \frac{4\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\overline{P}_{ R}^{(k)}(\boldsymbol{\mu })\gamma _{ S,0}^{(k)}\gamma _{ R,0}^{(k)}} {\!1+2\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}+2\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}} \!\right )\!\right \}\!\right ]\right \}\!\right ]\! -\!\varLambda _{1}} {\!\sum \limits _{k=1}^{K}\!\left [\!\left (\!\prod \limits _{n\neq k}^{K}\theta _{n}\!\!\right )\!\log \!\left \{\!\mathbb{E}_{\gamma }\!\left [\exp \!\left \{\!-\theta _{k}T_{f}B\log _{2}\!\!\left (\!1\! +\! \frac{4\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {\!1+2\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}+2\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}} \!\right )\!\right \}\!\right ]\right \}\!\!\right ]\!\! -\!\varLambda _{2}},{}\end{array}$$

(81)

where

$$\displaystyle{ \left \{\begin{array}{@{}l@{\quad }l@{}} \varLambda _{1} \triangleq \sum \limits _{k=1}^{K}\theta _{k}I_{k}\left (\prod \limits _{n=1}^{K}\theta _{n}\right );\quad \\ \varLambda _{2} \triangleq \prod \limits _{k=1}^{K}\theta _{k}\left (\sum \limits _{n=1}^{K}I_{n}\right ). \quad \end{array} \right. }$$

(82)

According to [7], the approximation of θ _o can be classified into the following four cases based on the values of Nakagami-m channel parameter m:

Case 1: m ≤ 1. For this case, because the average transmit power is the determining factor for the effective capacity, we have

$$\displaystyle\begin{array}{rcl} & & -\frac{1} {\theta _{k}}\log \Bigg\{\mathbb{E}_{\gamma }\Bigg[\exp \Bigg\{-\theta _{k}T_{f}B \\ & & \phantom{-\frac{1} {\theta _{k}}\log }\qquad \qquad \quad \cdot \log _{2}\Bigg(1 + \frac{4\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\Bigg)\Bigg\}\Bigg]\Bigg\} \gg I_{k}{}\end{array}$$

(83)

for 1 ≤ k ≤ K. Thus, we can omit the terms containing I _k in Eq. (81).

Case 2: m > 1 and θ _max is small (θ _max ≤ 10⁻²). We consider θ is large if θ > 10⁻² and if θ ≤ 10⁻², we claim that θ is small [7]. For small θ, the optimal power-adaptation law allocates more power to worse channel. In contrast, for large θ, the power control assigns less power to the better channel, but more power to the worse channel. Because the average transmit power is the determining factor for the effective capacity, it is the same as Case 1.

Case 3: m > 1 and θ _min is large (θ _min > 10⁻²). For this case, because the QoS-driven power control is the determining factor for the effective capacity, we only need to consider each term containing I _k in Eq. (81), we have

$$\displaystyle\begin{array}{rcl} & & -\frac{1} {\theta _{k}}\log \Bigg\{\mathbb{E}_{\gamma }\Bigg[\exp \Bigg\{-\theta _{k}T_{f}B \\ & & \phantom{-\frac{1} {\theta _{k}}\log }\qquad \qquad \quad \cdot \log _{2}\Bigg(1 + \frac{4\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\Bigg)\Bigg\}\Bigg]\Bigg\} \ll I_{k}{}\end{array}$$

(84)

for 1 ≤ k ≤ K. Thus, we can obtain

$$\displaystyle{ \theta _{o} \approx \frac{\sum \limits _{k=1}^{K}\theta _{k}I_{k}} {\sum \limits _{k=1}^{K}I_{k}} \approx \frac{\sum \limits _{k=1}^{K}\theta _{k}} {K}. }$$

(85)

Case 4: m > 1, θ _min is small and θ _max is large. For this case, because we have

$$\displaystyle\begin{array}{rcl} & & -\frac{1} {\theta _{k}}\log \Bigg\{\mathbb{E}_{\gamma }\Bigg[\exp \Bigg\{-\theta _{k}T_{f}B \\ & & \phantom{-\frac{1} {\theta _{k}}\log }\,\,\,\,\,\, \cdot \log _{2}\Bigg(1 + \frac{4\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\Bigg)\Bigg\}\Bigg]\Bigg\} \gg I_{k}\quad \text{and}\quad I_{n}{}\end{array}$$

(86)

and

$$\displaystyle\begin{array}{rcl} & & -\frac{1} {\theta _{k}}\log \left \{\mathbb{E}_{\gamma }\left [\exp \left \{-\theta _{k}T_{f}B\log _{2}\left (1 + \frac{4\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)}\gamma _{R,0}^{(k)}} {1 + 2\overline{P}_{S}^{(k)}(\boldsymbol{\mu })\gamma _{S,0}^{(k)} + 2\overline{P}_{R}^{(k)}(\boldsymbol{\mu })\gamma _{R,0}^{(k)}}\right )\right \}\right ]\right \} \\ & & \gg -\frac{1} {\theta _{n}}\log \Bigg\{\mathbb{E}_{\gamma }\Bigg[\exp \Bigg\{-\theta _{n}T_{f}B \cdot \log _{2}\Bigg(1 + \frac{4\overline{P}_{S}^{(n)}(\boldsymbol{\mu })\overline{P}_{R}^{(n)}(\boldsymbol{\mu })\gamma _{S,0}^{(n)}\gamma _{R,0}^{(n)}} {1 + 2\overline{P}_{S}^{(n)}(\boldsymbol{\mu })\gamma _{S,0}^{(n)} + 2\overline{P}_{R}^{(n)}(\boldsymbol{\mu })\gamma _{R,0}^{(n)}}\Bigg)\Bigg\}\Bigg]\Bigg\}{}\end{array}$$

(87)

where θ _k (1 ≤ k ≤ N ≤ K) is small (θ _k ≤ 10⁻²) and θ _n ((N + 1) ≤ n ≤ K) is large (θ _n > 10⁻²). Then, we can derive Eq. (60).

In order to derive the value of θ _o , we also need to obtain the optimal values of $\overline{P}_{S}^{(k)}$ and $\overline{P}_{R}^{(k)}$ (1 ≤ k ≤ K), which can be obtained by solving the optimization problem P ₂ . Therefore, the proof for Theorem 1 follows. □

Appendix B: Proof of Theorem 2

Proof.

Since P ₄ is a strictly convex optimization problem, and thus it has the unique optimal solution. We construct the Lagrangian function for P ₄ , denoted by J, as follows:

$$\displaystyle\begin{array}{rcl} J = \left ( \frac{MP_{R}\left (\lambda _{R}^{(k)}\right )^{2}} {KP_{R}(\boldsymbol{\nu })\left (1 -\left (\lambda _{R}^{(k)}\right )^{2}\right ) + 1}\right )^{-\beta _{2} } +\mu \left (\mathbb{E}\left [P_{R}\right ] -\overline{P}_{R}\right )& &{}\end{array}$$

(88)

where μ is the Lagrangian multiplier associated with the constraint specified by Eq. (58). Thus, the optimal solutions for the recourse adaptation law, and the optimal Lagrangian multiplier μ ^opt of the problem P ₄ need to satisfy the following Karush-Kuhn-Tucker (KKT) conditions:

$$\displaystyle{ \left \{\begin{array}{@{}l@{\quad }l@{}} \frac{\partial J} {\partial P_{R}}\Big\vert _{P_{R}=P_{R}^{\mathrm{opt}}} = 0; \quad \\ \mu ^{\mathrm{opt}}\left (\mathbb{E}\left [P_{R}\right ] -\overline{P}_{R}\right ) = 0;\quad \\ \mu ^{\mathrm{opt}} \geq 0; \quad \\ P_{R}> 0. \quad \end{array} \right. }$$

(89)

Taking derivative of J with respect to P _R , we can obtain

$$\displaystyle{ \frac{\partial J} {\partial P_{R}} = \frac{-\beta _{2}\left (P_{R}\right )^{-\beta _{2}-1}\left (M\left (\lambda _{R}^{(k)}\right )^{2}\right )^{-\beta _{2}}} {\left (KP_{R}\left (1 -\left (\lambda _{R}^{(k)}\right )^{2}\right ) + 1\right )^{-\beta _{2}+1}} +\mu. }$$

(90)

Then, for our proposed massive MIMO system (M → ∞), associated with Eq. (89), we can derive the optimal solutions expressed by Eq. (76). Therefore, the proof for Theorem 2 follows. □