#  SCIENCE CHINA Information Sciences, Volume 61 , Issue 2 : 022302(2018) https://doi.org/10.1007/s11432-016-9042-8

## Fractional full duplex cellular network: a stochastic geometry approach Wenping BI 1,2,3, Limin XIAO 1,2,3, Xin SU 1,2,3, Shidong ZHOU 1,2,3,*
• AcceptedFeb 28, 2017
• PublishedJul 28, 2017
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### Abstract ### Acknowledgment

This work was supported by National Basic Research Program of China (Grant No. 2012CB316002), National Natural Science Foundation of China (Grant No. 61631013), National High Technology Research and Development Program of China (863 Program) (Grant No. 2015AA01A706), National Natural Science Foundation of China (Grant No. 61321061), Tsinghua University Initiative Scientific Research Program (Grant No. 2015Z02-3), National S&T Major Project (Grant No. 2014ZX03001011), Key Project of International Science and Technology Innovation Cooperation Between the Government (Grant No. 2016YFE0122900), and Huawei Technologies.

### Supplement

Appendix

Proof of Lemma sect. 3.1

Starting with the definition of laplace transform, we can get \begin{equation} \begin{aligned} {L_{{I_{{\rm h}q}}}}\left( s \right) \mathop = \limits^{\left( {\rm a} \right)} {{{\rm E}}_{{\Phi _{{\rm h}q}}}}\left\{ {\prod\limits_{z \in {\Phi _{{\rm h}q}}\backslash c_o} {{{{\rm E}}_{{h_{z,d_o}}}}\exp \left( { - s{h_{z,d_o}}D_{z,d_o}^{ - {\alpha _{\rm bu}}}} \right)} } \right\}\mathop = \limits^{\left( {\rm b} \right)} \exp \left\{ { - 2\pi {\lambda _{\rm s}}\int\nolimits_R^\infty {\left\{ {1 - {{{\rm E}}_{{\rm h}}}\left[ {{{\mathop{\rm e}\nolimits} ^{\left( { - s{h}v^{ - {\alpha _{\rm bu}}}} \right)}}} \right]} \right\}v{\rm d}v} } \right\}, \end{aligned} \tag{23}\end{equation} where $c_o$ and $d_o$ are $b_o$ ($u_o$) and $u_o$ ($b_o$) if $q=d(u)$, respectively. (a) follows the fact that $\Phi~_{{\rm~h}q}$ and $h_{z,d_o}$ are independent from each other. Therefore, the expectation order can be exchanged. (b) follows from the probability generating function of PPP. Carrying on the proof in (23), the followings can be obtained \begin{align} &\exp \left\{ { - 2\pi {\lambda _{\rm s}}\int\nolimits_R^\infty {\left\{ {1 - {{{\rm E}}_{\rm h}}\left[ {\exp \left( { - sh{v^{ - {\alpha _{\rm bu}}}}} \right)} \right]} \right\}v{\rm d}v} } \right\} \\ &\mathop = \limits^{\left( {\rm c} \right)} \exp \left\{ - \frac{2}{{{\alpha _{\rm bu}}}}\pi {\lambda _{\rm s}}{{{\rm E}}_{\rm h}}\left\{ - {{\left( {sh} \right)}^{\frac{2}{{{\alpha _{\rm bu}}}}}}\Gamma \left( { - \frac{2}{{{\alpha _{\rm bu}}}}} \right)- \frac{{{\alpha _{\rm bu}}}}{2}{R^2} + {{\left( {hs} \right)}^{\frac{2}{{{\alpha _{\rm bu}}}}}}\Gamma \left( { - \frac{2}{{{\alpha _{\rm bu}}}},hs{R^{ - {\alpha _{\rm bu}}}}} \right) \right\} \right\}, \tag{24} \end{align} where (c) is proofed in . Based on the Rayleigh fading assumption, $h\sim~\exp(1)$, we can obtain the expectations as \begin{eqnarray}&\displaystyle{{{\rm E}}_{\rm h}}\left\{ {{{ h }^{\frac{2}{{{\alpha _{\rm bu}}}}}}} \right\} = \int\nolimits_0^\infty {{{ x }^{\frac{2}{{{\alpha _{\rm bu}}}}}}{{\rm e}^{ - x}} {\rm d}x} \mathop = \limits^{\left( {\rm d} \right)} \Gamma \left( {\frac{2}{{{\alpha _{\rm bu}}}} + 1} \right) , \tag{25} \\ &\displaystyle{ {\rm E}_{\rm h}}\left\{ {{{ h}^{\frac{2}{{{\alpha _{\rm bu}}}}}}\Gamma \left( { - \frac{2}{{{\alpha _{\rm bu}}}},hs{R^{ - {\alpha _{\rm bu}}}}} \right)} \right\}= \int\nolimits_0^\infty {{x^{\frac{2}{{{\alpha _{\rm bu}}}}}}\Gamma \left( { - \frac{2}{{{\alpha _{\rm bu}}}},xs{R^{ - {\alpha _{\rm bu}}}}} \right){{\rm e}^{ - x}}{\rm d}x}\mathop = \limits^{\left( {\rm e} \right)} J\left( {\frac{2}{{{\alpha _{\rm bu}}}} + 1,1, - \frac{2}{{{\alpha _{\rm bu}}}},s{R^{ - {\alpha _{\rm bu}}}}} \right), \tag{26} \end{eqnarray} where $J(\mu~,\beta~,\nu~,\gamma~)$ is defined in (11) and proofed in . (d) and (e) can be obtained by Eqs. (3.478) and (3.381) 3), respectively. Substitute (25) and (26) into (24) and we can get the result of Lemma sect. 3.1.

Gradshteyn I, Ryzhik I. Table of Integrals, Series, and Products. Manhattan: Academic Press, 2014. 346–370.

Proof of Lemma 3.2

Starting with the definition of laplace transform, we can get \begin{align} &{L_{{I_{{\rm f}q}}}}\left( s \right) \mathop = \limits^{\left({\rm f}\right)}{{{\rm E}}_{D,h,{\Phi _{\rm fd}}}}\left\{ {\prod\limits_{z \in {\Phi _{{\rm fd}\backslash b_o}}} {\exp \left( { - s{P_{\rm fd}}{h_{z,d_o}}{{k}_{z,d_o}}D_{z,d_o}^{ - {\alpha _{\rm d}}}} \right)} } \right\}{{{\rm E}}_{D,h,{\Phi _{\rm fu}}}}\left\{ {\prod\limits_{x \in {\Phi _{\rm fu}}\backslash c_o} {\exp \left( { - s{P_{\rm fu}}{h_{x,d_o}}{{k}_{x,d_o}}D_{x,d_o}^{ - {\alpha _{\rm u}}}} \right)} } \right\} \\ & \mathop = \limits^{\left({\rm g}\right)} \exp \left\{ { - 2\pi {\lambda _{\rm s}}{{\rm E}_{\rm h}}\int\nolimits_{R_{\rm d}}^\infty {\left\{ {1 - \left[ {\exp \left( { - {s_{\rm d}}h{v^{ - {\alpha _{\rm d}}}}} \right)} \right]} \right\}v{\rm d}v} } \right\} \exp \left\{ { - 2\pi {\lambda _{\rm s}}{{\rm E}_{\rm h}}\int\nolimits_{R_{\rm u}} ^\infty {\left\{ {1 - \left[ {\exp \left( { - {s_{\rm u}}h{v^{ - {\alpha _{\rm u}}}}} \right)} \right]} \right\}v{\rm d}v} } \right\}, \tag{27} \end{align} where $c_o$ and $d_o$ are $\emptyset$ ($u_o$) and $u_o$ ($b_o$) if $q=d({\rm~u})$, respectively. (f) follows the fact that $\Phi~_{\rm~fu}$ and $\Phi~_{\rm~fd}$ are assumed to be independent. In Step (g), when we focus on the downlink, the inter-user interference distance can be arbitrarily close, therefore the integration lower bound $R_{\rm~u}$ is $\eta~_{\rm~uu}R$ when taking the interference cancelation strategy into consideration. Based on the association principle, the interfering distance between focused downlink user and neighbor BSs is at least $R$, so $R_{\rm~d}~=~R$. While when considering uplink transmission, the inter-BS interference distance between focused BS and the neighbor BSs can also be arbitrarily close, as a consequence $R_{\rm~d}$ is $\eta~_{\rm~bb}R$ when SIC is applied. In the same way, the distance from the neighbor uplink users to the focused BS is at least $R$, which gives $R_{\rm~u}=~R$. Then following the proof in sect. 1, we can get the result in (13).

Proof of Lemma 3.3

Before solving joint LT of $I_{\rm~d}$ and $\hat~I_{\rm~d}$, some properties of the sum of two exponential distribution random variables are analysed.

We define $G$ as the sum of two exponential distribution random variables as follows: \begin{equation} G = {s_2}{h_1} + {s_2}{h_2}, \tag{28}\end{equation} where both $h_1$ and $h_2$ follow exponential distribution, i.e, $h_1~~\text{and}~~h_2\sim~{\rm~exp}(1)$. Then, when $s_1=s_2=s$, $G$ is the sum of two exponential random variables with same rate. As presented in , $G$ follows Erlang distribution. While, if $s_1~\ne~s_2$, $G$ follows the hypo-exponential distribution.

Based on the PDF of $G$, we can have \begin{equation} {{{\rm E}}_G}\left( {{G^\delta }} \right) = \left \{ \begin{aligned} &{s^\delta }\Gamma \left( {\delta + 2} \right), \text{if $s_1=s_2=s$}, \\ &\frac{1}{{{s_2} - {s_1}}}\Gamma \left( {\delta + 1} \right)\left( {{s_2}^{\delta + 1} - {s_1}^{\delta + 1}} \right), \text{otherwise}, \end{aligned} \right. \tag{29}\end{equation} where (29) can be obtained by Eq. (3.478)$^{3)}$. Furthermore, according to Eq. (3.381)$^{3)}$, we can also obtain \begin{equation} \begin{array}{l} {{\rm E}_G}\left( {{G^{\mu - 1}}\Gamma \left( {\nu ,\gamma G} \right)} \right) = \left\{ \begin{array}{l} {s}^2J\left( {\mu {\rm{ + }}1,{s}^{ - 1},\nu ,\gamma } \right), {\rm{ if }} {{\rm{s}}_{\rm{1}}}{\rm{ = }}{{\rm{s}}_{\rm{2}}}{\rm{ = s }}, \\ \frac{1}{{{s_2} - {s_1}}}\left( {J\left( {\mu ,\frac{1}{{{s_2}}},\nu ,\gamma } \right) - J\left( {\mu ,\frac{1}{{{s_1}}},\nu ,\gamma } \right)} \right), {\rm{ otherwise}}, \end{array} \right. \end{array} \tag{30}\end{equation} where $J(~{\cdot,~\cdot,~\cdot,~\cdot~})$ is defined in Eq. (11). We also start with the definition of joint LT. \begin{align}&{\mathcal{L}_{{{\hat I}_{\rm d}},{I_{\rm d}}}}\left( {{s_{\rm h}},{s_{\rm f}}} \right) = {{{\rm E}}_{{{\hat I}_{\rm d}},{I_{\rm d}}}}\left( {{{\rm e}^{ - {s_{\rm h}}{{\hat I}_{\rm d}} - {s_{\rm f}}{I_{\rm d}}}}} \right) \\ &\mathop = \limits^{\left(k \right)}{\rm E}\left( \exp \left( - {s_{\rm hd}}\left( {\sum\limits_{z \in {\Phi _{\rm hd}}\backslash b_o} {{h_{z,u_o}}{D_{z,u_o}}^{ - {\alpha _{\rm bu}}}} } \right)- \left( {\sum\limits_{z \in {\Phi _{{\rm fd}\backslash b_o}}} {{s_{\rm fd}}{h_{z,u_o}}{{ {{D_{z,u_o}}} }^{ - {\alpha _{\rm bu}}}}} + \sum\limits_{x \in {\Phi _{\rm fu}}} {{s_{\rm fu}}{h_{x,u_o}}{{ {{D_{x,u_o}}} }^{ - {\alpha _{\rm uu}}}}} } \right) \right) \right) \\ &\mathop = \limits^{\left( l \right)} {\rm E}\left( \exp \left( - \left( {\sum\limits _{z \in {\Phi _{\rm fd}}\backslash b_o} {\left( {{s_{\rm hd}}{h_{z,u_o}} + {s_{\rm fd}}{h_{z,u_o}}} \right){D_{z,u_o}}^{ - {\alpha _{\rm bu}}}} } \right) - {s_{\rm fu}}\left( {\sum\limits_{x \in {\Phi _{\rm fu}}} {{h_{x,u_o}}{{\left( {{D_{x,u_o}}} \right)}^{ - {\alpha _{\rm uu}}}}} } \right) \right) \right) \\ &\mathop = \limits^{\left( m \right)} \exp \left\{ { - 2\pi {\lambda _{\rm s}}{\rm E}\int\nolimits_R^\infty {1 - {{\mathop{\rm e}\nolimits} ^{\left( { - \left( {{{s}_{\rm fd}}{h_{\rm fd}} + {{s}_{\rm hd}}{h_{\rm hd}}} \right){v^{ - {\alpha _{\rm bu}}}}} \right)}}v{\rm d}v} } \right\}\exp \left\{ { - 2\pi {\lambda _{\rm s}}{\rm E}\int\nolimits_{\eta _{\rm uu}R} ^\infty {1 - {{\mathop{\rm e}\nolimits} ^{\left( { - {{s}_{\rm fu}}{h_{\rm fu}}{v^{ - {\alpha _{\rm uu}}}}} \right)}}v{\rm d}v} } \right\} \\ &\mathop = \limits^{\left( n \right)}\exp \left\{ - 2\pi {\lambda _{\rm s}}{{\rm E}_{{G_{\rm u}}}}\left\{ - \frac{1}{{{\alpha _{\rm bu}}}}{G_{\rm u}}^{\frac{2}{{{\alpha _{\rm bu}}}}}\Gamma \left( - \frac{2}{{{\alpha _{\rm bu}}}}\right) - \frac{1}{2}{R^2}+ \frac{1}{{{\alpha _{\rm bu}}}}{G_{\rm u}}^{\frac{2}{{{\alpha _{\rm bu}}}}}\Gamma \left( - \frac{2}{{{\alpha _{\rm bu}}}},\frac{{{G_{\rm u}}}}{{{R^\alpha }}}\right) \right\} \right\}\omega \left( {{\alpha _{\rm uu}},s_{\rm fu}\eta _{\rm uu}R } \right), \tag{31} \end{align} where ${s}_{\rm~fd}={{s_{\rm~f}}}{{P_{\rm~fd}}}{{k}_{\rm~fd}},~~{s}_{\rm~hd}={{s_{\rm~h}}}{{P_{\rm~hd}}}{{k}_{\rm~hd}}$ and${s_{\rm~fu}}={{s_{\rm~f}}}{{P_{\rm~fu}}}{{k}_{\rm~fu}}$ in Step (k). In Step (l), the interference BS sets in HD RBs and FD RBs are the same, therefore, the interfering distances between the focused downlink user and the BSs after classifying the user as CEU is the same as the distances when the focused user is regarded as cell CCU. Hence, we can write them together as the first sum item of Step (l). $G_{\rm~u}={{{s}_{\rm~fd}}{h_{\rm~fd}}~+~{{s}_{\rm~hd}}{h_{\rm~hd}}}$ which is the same as (28) and its properties have already been given by (29) and (30). Then the conclusion of Lemma 3.3 is obtained.

Proof of Theorem sect. 4.1

The proof begins with the definition of the CEU and coverage probability, then we can obtain \begin{align} &F_{{\rm edge},q}\left( {T} \right) = \mathbb{P}\left( {{{{\rm SINR}}} > T|{\rm SINR} < {{\gamma}_q}} \right) \\ &\mathop = \limits^{\left({\rm h}\right)} \frac{{{\rm E}\left( {\mathbb{P}\left( {{{\rm SINR}} > T,{\rm SINR} < {{\gamma}_q}|R,{I_{{\rm f}q}},{I_{{\rm h}q}}} \right)} \right)}}{{{\rm E}\left( {\mathbb{P}\left( {{\rm SINR} < {{\gamma}_q}|R,{I_{{\rm f}q}}} \right)} \right)}}\mathop = \limits^{\left(I\right)} \frac{{{\rm E}\left( {{{\mathop{\rm e}\nolimits} ^{\left( { - {s_{\rm h}}\left( {{\sigma ^2} + {{\hat I}_{\rm e}}} \right)} \right)}}\left( {1 - {{\mathop{\rm e}\nolimits} ^{\left( { - {s_{\rm f}}\left( {{\sigma ^2} + {I_{\rm e}} + {\delta }{I_{\rm SI}}} \right)} \right)}}} \right)} \right)}}{{{\rm E}\left( {\left( {1 - {{\mathop{\rm e}\nolimits} ^{\left( { - {s_{\rm f}}\left( {{\sigma ^2} + {I_{\rm e}} + {\delta }{I_{\rm SI}}} \right)} \right)}}} \right)} \right)}}, \tag{32} \end{align} where SINR and $I_{\rm~e}$ denote the received SINR and interference when the user is regarded as CCU. While SINR$~and~$hat I_rm e$~represent~the~received~SINR~and~interference~after~the~user~is~classified~as~CEU.~SINR~is~defined~as~(\ref{equation2}).~Step~(h)~follows~Bayes~theorem.~Step~(I)~is~obtained~based~on~two~facts.~one~is~the~independency~of~the~small~scale~fading~over~FD~and~HD~RBs,~the~other~fact~is~that~the~small~scale~fading~is~assumed~to~be~Rayleigh,~i.e,~$h∼ rm exp1)$,~so~$mathbbPh<t)=1-exp (-t).~Then~carry~on~the~proof~in~Step~(I)~and~we~have \begin{align} \label{equation_coverage_edge} &F_{{\rm edge},q}\left( {T} \right) = \mathbb{P}\left( {{{\rm SINR}} > T|{\rm SINR} < {{\gamma}_q}} \right)= \frac{{\int\nolimits_{R = 0}^\infty {{\rm E}\left( {{{\mathop{\rm e}\nolimits} ^{\left( { - {s_{\rm h}}{\sigma ^2}} \right)}}\left( {{{\mathop{\rm e}\nolimits} ^{ - {s_{\rm h}}{{\hat I}_{\rm e}}}} - {{\mathop{\rm e}\nolimits} ^{\left( { - {s_{\rm f}} {{{\sigma }^2} + {s_{\rm h}}{\hat I_{\rm e}} + {s_{\rm f}}{I_{\rm e}}} } \right)}}} \right)} \right){f_R}\left( R \right){\rm d}R} }}{{\int\nolimits_{R = 0}^\infty {{\rm E}\left( {1 - {{\mathop{\rm e}\nolimits} ^{\left( { - {s_{\rm f}}\left( {{{\sigma }^2} + {I_{\rm e}}} \right)} \right)}}} \right){f_R}\left( R \right){\rm d}r} }}\nonumber\\ &\mathop = \limits^{\left({\rm j}\right)} \frac{{\int\nolimits_{R = 0}^\infty {\left( {{{\mathop{\rm e}\nolimits} ^{ - {s_{\rm h}}{\sigma ^2}}}\left( {{L_{{I_{{\rm h}q}}}}\left( {{s_{\rm h}}} \right) - {{\mathop{\rm e}\nolimits} ^{ - {s_{\rm f}}\sigma {^2}}}{L_U}\left( {{s_{\rm h}},{s_{\rm f}}} \right)} \right)} \right){f_R}\left( R \right){\rm d}R} }}{{\int\nolimits_{R = 0}^\infty {\left( {1 - {{\mathop{\rm e}\nolimits} ^{ - {s_{\rm f}}\sigma {^2}}}{L_{{I_{{\rm f}q}}}}\left( {{s_{\rm f}}} \right)} \right){f_R}\left( R \right){\rm d}R} }}, \end{align} where~f_R(R)$~is~defined~in~(\ref{distribution_r}).~We~can~obtain~Step~(j)~according~to~the~definition~of~LT.~$L_I_m$~is~the~LT~of~interference~$I_m$~($m ∈ łeft rm hq,rm fq right$~)~and~they~are~defined~in~(\ref{laplace_hd})~and~(\ref{laplace_fq}).~The~joint~LT~$L_U$~is~different~in~the~downlink~and~uplink~transmission.~In~downlink~transmission,~the~interfering~BSs~are~the~same~before~and~after~allocating~HD~RBs~to~the~CEUs,~which~results~in~$hat I_rm e$~and~$I_rm e$~are~correlated~with~each~other.~As~discussed~in~Lemma~\ref{Theorm_laplace_jiont},~$L_U$~is~defined~in~\ref{L_U}.~While~in~the~uplink,~the~uplink~interfering~user~sets~have~already~changed~when~the~serving~RBs~of~CEU~switch~from~FD~RBs~to~HD~RBs.~Therefore,~in~uplink~$L_U$~can~be~written~as~$L_rm hułeft(s_rm hright)L_rm fułeft(s_rm fright). Then the conclusion of Theorem sect. 4.1 is obtained.

### References

 Sabharwal A, Schniter P, Guo D, et al. In-band full-duplex wireless: challenges and opportunities. IEEE J Sel Area Commun 2014, 32: 1637--1652. Google Scholar

 Kim D, Lee H, Hong D. A survey of in-band full-duplex transmission: from the perspective of phy and mac layers. IEEE Commun Surv Tut, 2015, 17: 2017--2046. Google Scholar

 Bharadia D, McMilin E, Katti S. Full duplex radios. SIGCOMM Comput Commun Rev, 2013, 43: 375--386. Google Scholar

 Duarte M, Dick C, Sabharwal A. Experiment-driven characterization of full-duplex wireless systems. IEEE Trans Wirel Commun 2012, 11: 4296--4307. Google Scholar

 Goyal S, Liu P, Panwar S, et al. Full duplex cellular systems: will doubling interference prevent doubling capacity? IEEE Commun Mag 2015, 53: 121--127. Google Scholar

 Liao Y, Song L, Han Z, et al. Full duplex cognitive radio: a new design paradigm for enhancing spectrum usage. IEEE Commun Mag 2015, 53: 138--145. Google Scholar

 Liu G, Yu F, Ji H, et al. In-band full-duplex relaying: a survey, research issues and challenges. IEEE Commun Surv Tut 2015, 17: 500--524. Google Scholar

 Riihonen T, Werner S, Wichman R. Hybrid full-duplex/half-duplex relaying with transmit power adaptation. IEEE Trans Wirel Commun 2011, 10: 3074--3085. Google Scholar

 Ahmed E, Eltawil A, Sabharwal A. Rate gain region and design tradeoffs for full-duplex wireless communications. IEEE Trans Wirel Commun 2013, 12: 3556--3565. Google Scholar

 Chai X, Liu T, Xing C, et al. Throughput improvement in cellular networks via full-duplex based device-to-device communications. IEEE Access 2015, 4: 7645--7657. Google Scholar

 Shao S, Liu D, Deng K, et al. Analysis of carrier utilization in full-duplex cellular networks by dividing the co-channel interference region. IEEE Commun Lett 2014, 18: 1043--1046. Google Scholar

 Bai J, Sabharwal A. Distributed full-duplex via wireless side-channels: bounds and protocols. IEEE Trans Wirel Commun 2013, 12: 4162--4173. Google Scholar

 Nguyen D, Tran L, Pirinen P, et al. Precoding for full duplex multiuser mimo systems: spectral and energy efficiency maximization. IEEE Trans Signal Process 2013, 61: 4038--4050. Google Scholar

 Nguyen D, Tran L, Pirinen P, et al. On the spectral efficiency of full-duplex small cell wireless systems. IEEE Trans Wirel Commun 2014, 13: 4896--4910. Google Scholar

 Boudreau G, Panicker J, Guo N, et al. Interference coordination and cancellation for 4G networks. IEEE Commun Mag 2009, 47: 74--81. Google Scholar

 Shen Z, Khoryaev A, Eriksson E, et al. Dynamic uplink-downlink configuration and interference management in TD-LTE. IEEE Commun Mag 2012, 50: 51--59. Google Scholar

 Lee J, Quek T. Hybrid full-/half-duplex system analysis in heterogeneous wireless networks. IEEE Trans Wirel Commun 2015, 14: 2883--2895. Google Scholar

 AlAmmouri A, ElSawy H, Amin O, et al. In-band $\alpha$-duplex scheme for cellular networks: a stochastic geometry approach. IEEE Trans Wirel Commun 2016, 15: 6797--6812. Google Scholar

 Thomsen H, Popovski P, Carvalho E, et al. Compflex: comp for in-band wireless full duplex. IEEE Wirel Commun Lett 2016, 5: 144--147. Google Scholar

 Li Y, Fan P Z, Leukhin A, et al. On the spectral and energy efficiency of full-duplex small cell wireless systems with massive MIMO. IEEE Trans Veh Tech 2017, 66: 2339--2353. Google Scholar

 Andrews J, Baccelli F, Ganti R. A tractable approach to coverage and rate in cellular networks. IEEE Trans Commun 2011, 59: 3122--3134. Google Scholar

 Simeone O, Erkip E, Shamai S. Full-duplex cloud radio access networks: an information-theoretic viewpoint. IEEE Wirel Commun Lett, 2014, 3: 413--416. Google Scholar

 Sato H. The capacity of the gaussian interference channel under strong interference. IEEE Trans Inf Theory 1982, 27: 786--788. Google Scholar

 Novlan T, Dhillon H, Andrews J. Analytical modeling of uplink cellular networks. IEEE Trans Wirel Commun 2013, 12: 2669--2679. Google Scholar

 Access E U T R. Further advancements for E-UTRA physical layer aspects. 3GPP Technical Specification TR, 2010, 36: V2. Google Scholar

• Figure 1

An exemplary interference scenario of HD/FD cellular network. (a) Synchronous TDD cellular network; protectłinebreak (b) FD cellular network.

• Figure 2

Resource blocks allocation.

• Figure 9

SE vs. successive interference cancellation capability.

• Table 1   Simulation parameters
 RB band width Number of RB Thermal noise $P_b$ $P_{\rm~u}$ $\eta~$ $\lambda_{\rm~s}$ $\lambda_{\rm~u}$ $\gamma_{\rm~d}$ ${\left|~{{\varepsilon~}}~\right|^2}$ Path loss  1 MHz 128 $-$174 dBm$\cdot$Hz$^{-1}$ 0.1 W 0.1 W 0 ${10^{{\rm{~-~}}3}}$ m$^{-2}$ ${1}$ m$^{-2}$ 0 dB $-110$ dB 140.7 + 36.7lg$R$ ($R$ in km)