Performance analysis of downlink and uplink decoupled access in clustered heterogeneous cellular networks

Abstract

The performance of heterogeneous cellular networks (HCNs) is typically analyzed with the assumption that the users connect with the same base station in uplink and downlink. However, recent investigations have shown that downlink–uplink decoupling (DUDe) can provide network performance gains relative to the conventional coupled access. Many authors have evaluated HCN performance while assuming that the network users are distributed according to a homogeneous Poisson point process (HPPP). However, the HPPP cannot accurately model the uplink interference when the users are clustered in urban hotspots such as shopping malls and sports stadiums. This work investigates DUDe access for an HCN with user-clustering modeled by the Matern cluster process. We derive analytical expressions of the coverage probability and average throughput for DUDe access as well as the conventional coupled access. The results show that DUDe outperforms the coupled access scheme in terms of coverage and throughput. The user-clustering is also shown to benefit the coverage and throughput performance relative to the case of HPPP distributed users. The derived results are validated by Monte Carlo simulations.

Appendix

1.1 Proof of Eq. (17)

In DUDe scheme, the typical user is in coverage if the instantaneous SINR at the tagged SBS is greater than the predefined threshold. Then the coverage probability is expressed as

$$\begin{aligned} P_{c}^{D}&\triangleq E_{X_{S}}\left[ Pr\left[ SINR_{X_{S}}^{UL}>\tau \vert X_{S}\right] \right] \nonumber \\&=\int _{0}^{\infty } Pr\left[ SINR_{X_{S}}^{UL}>\tau \vert X_{S}\right] \cdot f^{(2)}_{X_{S}}(x_{s})d_{x_{s}}\nonumber \\&{\mathop {=}\limits ^{1}}\int _{0}^{\infty } Pr\left[ \dfrac{P_{u}h_{X_{S}}\Vert X_{S}\Vert ^{-\alpha }}{\sum _{j\epsilon \Phi _{u}}P_{u}h_{X_{j}}\Vert X_{j}-X_{S}\Vert ^{-\alpha } + \sigma _{N}^{2}}>\tau \vert X_{S}\right] \nonumber \\&\qquad \cdot \, f^{(2)}_{X_{S}}(x_{s})d_{x_{s}}\nonumber \\&{\mathop {=}\limits ^{2}}\int _{0}^{\infty } Pr\left[ h_{X_{S}}>\dfrac{\tau X_{S}^{\alpha }}{P_{u}}\left( \sigma _{N}^{2} + I\right) \right] \cdot f^{(2)}_{X_{S}}(x_{s})d_{x_{s}}\nonumber \\&{\mathop {=}\limits ^{3}}\int _{0}^{\infty } \exp \left( \dfrac{-\tau \sigma _{N}^{2} X_{S}^{\alpha }}{P_{u}}\right) \cdot L_{I}\left( s\right) \cdot f^{(2)}_{X_{S}}(x_{s})d_{x_{s}} \end{aligned}$$

(25)

where ${\mathop {=}\limits ^{1}}$ is obtained by substituting (2) in $P_{c}^{D}$, ${\mathop {=}\limits ^{2}}$ is obtained using $I=\sum _{j\epsilon \Phi _{u}}P_{u}$$h_{X_{j}}\Vert X_{j} - X_{S}\Vert ^{-\alpha }$ and ${\mathop {=}\limits ^{3}}$ follows from the assumption of Rayleigh fading channel gains. Finally, (17) is obtained by substituting (13) and (15) into (25).