Scalable Transmission over Heterogeneous Network: A Stochastic Geometry Analysis

Transcription

1 Scalable Transmission over Heterogeneous Network: A Stochastic Geometry Analysis Liang Wu, Yi Zhong, Wenyi Zhang, Senior Member, IEEE, and Martin Haenggi, Fellow, IEEE Abstract This paper ocuses on the transmission o layered source inormation, such as scalable video coding SVC, over heterogeneous cellular networks. Scalable transmission enables dynamic adaption o source inormation to the condition o user equipments UEs, and thus is suitable or cellular networks in which the transmission link quality varies substantially over space and time. Two novel transmission schemes are proposed, Layered Digital LD transmission and Layered Hybrid Digital-Analog LHDA transmission. Leveraging tools rom stochastic geometry, a comprehensive analysis is conducted ocusing on three key perormance metrics: outage probability, High-Deinition HD probability and average distortion. The results show that both proposed transmission schemes can provide a scalable video experience or UEs. For LHDA transmission, the optimal power allocation between digital and analog transmissions is also analyzed. When the proportion o requency resource allocated to the emto tier exceeds a certain threshold, LHDA transmission is preerable by enabling continuous quality scalability thus avoiding the cli eect. Index Terms Heterogeneous cellular networks, hybrid digitalanalog, rate distortion, stochastic geometry, scalable video coding. A. Motivation I. INTRODUCTION The advent o mobile communication and computing keeps driving the data traic to grow explosively, among which a substantial portion is attributed to multimedia such as mobile video. According to the Cisco Visual Networking Index, mobile video is expected to grow at an average growth rate o 66% until 9, and within the 4.3 exabytes o data per month crossing mobile networks by 9, 7.4 exabytes will be video related, such as video on demand, realtime streaming video, video conerencing, and so on. With the release o Copyright c 5 IEEE. Personal use o this material is permitted. However, permission to use this material or any other purposes must be obtained rom the IEEE by sending a request to pubs-permissions@ieee.org. L. Wu, Y. Zhong and W. Zhang are with the Key Laboratory o Wireless-Optical Communications, Chinese Academy o Sciences, and the Department o Electronic Engineering and Inormation Science, University o Science and Technology o China, Heei 37, China {tuohai,geners}@mail.ustc.edu.cn, wenyizha@ustc.edu.cn. M. Haenggi is with the Department o Electrical Engineering, University o Notre Dame, Notre Dame, IN 46556, USA mhaenggi@nd.edu. The paper was presented in part at the 5 International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks WiOpt []. The work o L. Wu, Y. Zhong and W. Zhang was supported in part by the National Basic Research Program o China 973 Program through grant CB364, by the National Natural Science Foundation o China through grant 63793, and by the Fundamental Research Funds or the Central Universities through grant WK353. The work o M. Haenggi was supported by the US NSF through grants CCF 647 and dierent types o UEs, the requirements on data rate o video transmission vary in a wide range. Advanced source coding techniques, such as Scalable Video Coding SVC, provide a new dimension o dynamically provisioning wireless resources or the varying requirements and the varying link conditions o UEs, thus creating the possibility o extracting video scaled in multiple dimensions, e.g., spatial, temporal, and quality. SVC is an extension o the H.64/MPEG-4 AVC video compression standard [], in which the bitstream is encoded into multiple layers, namely a Base Layer BL and at least one Enhancement Layer EL. The quality o reconstructed video depends on the number o layers decoded and stays the same until a higher enhancement layer is successully decoded. The number o layers and their code rates may be determined by the requirement and the link condition o the subscribing UE. On the other hand, cellular networks are evolving rom a homogenous architecture to a composition o heterogeneous networks, comprised o various types o base stations BSs [3], [4]. Each type o BSs has its characteristic transmit power and deployment intensity: or example, macro BSs MBSs have larger transmit power, aiming at providing global coverage; Femto Access Points FAPs are small BSs targeted or home or small business usages. As the distance between a UE and its serving FAP is small, the UE enjoys a high quality link and achieves power savings. Furthermore, the reduced transmission range also enhances spatial reuse and alleviates multiuser intererence. Thereore, when putting together the above two paradigm shits, namely, shiting rom a single-layer video to SVC with multiple layers and shiting rom a single-tier cellular network to heterogeneous cellular networks HCNs with multiple tiers, these two technologies appear to be inherently compatible and thus can be symbiotically exploited or an improved user experience. The macro cells aim at providing global coverage and thereore are suitable or supporting the BL video content or a majority o UEs, thus enabling the UEs to enjoy basic video e.g., standard deinition 4p experience; the small cells e.g., emto cells aim at providing small-area high-rate service enhancement or hot spots and thereore are suitable or supporting the EL video content or those UEs subscribing to services in their vicinity, thus enabling the UEs to enjoy enhanced video e.g., high deinition 7p experience. In this paper, we study the problem o scalable transmission over heterogeneous networks and demonstrate that the combination o multi-layer video transmission and multi-tier cellular networks can indeed be beneicially exploited.

2 B. Related Work The prior works that consider scalable transmission over wireless networks mainly use digital schemes, consisting o digital source coding e.g., quantization and entropy coding, digital modulation e.g., QPSK, 64QAM and digital channel coding e.g., turbo or LDPC. The analysis usually ocuses on homogeneous networks, and the common eature o the layered structure o SVC and HCNs is not exploited. In [5], an overview o SVC and its relationship to mobile content delivery are discussed ocusing on the challenges due to the time-varying characteristics o wireless channels. In [6], a per-subcarrier transmit antenna selection scheme is employed to support multiple scalable video sequences over a downlink cognitive network, and the outage probability is reduced because o video scalability. In [7], real-time use cases o mobile video streaming are presented, or which a variety o parameters like throughput, packet loss ratio and delay are compared with H.64 single-layer video under dierent degrees o scalability. In [8], the proposed scheme employs WiFi: the BL is always transmitted over a reliable network such as cellular, whereas the EL is opportunistically transmitted through WiFi. Technical issues associated with the simultaneous use o multiple networks are discussed. In [9], HCNs with storage-capable small-cell BSs are studied: versions and layers o video have dierent impacts on the delay-servicing cost tradeo, depending on the user demand diversity and the network load. Besides the above literature based on digital transmission, the recently revitalized analog transmission has shown promising potential in handling channel variations and user heterogeneities or wireless video communication. The analog scheme consists o analog source coding and analog modulation that directly maps a source signal into a linearly transormed channel signal without channel coding. SotCast [] is an analog video broadcast scheme that transmits a linear transorm o the video signal without quantization, entropy coding, or channel coding. It is claimed to realize continuous quality scalability. However, inormation-theoretic studies such as [], [] show that analog schemes with linear mapping rom source signals to channel signals are relatively ineicient or video transmission while hybrid digital-analog transmission is asymptotically optimal under matched channel conditions or optimally chosen power allocations between the analog and digital parts. The hybrid digital-analog scheme combines digital with analog schemes, transmitting digital and analog signals simultaneously using TDMA, FDMA, or superposition transmission. The authors in [3] propose a hybrid digital-analog scheme or broadcasting, showing a substantial perormance gain. However, these works did not consider the impacts o HCNs and the spatial distribution o wireless networks, let alone the design o scalable transmission algorithms utilizing the structure o HCNs. Considering scalable video transmission over HCNs, we propose two transmission schemes, which adopt digital transmission and hybrid digital-analog transmission, respectively. The system perormance is analyzed using stochastic geometry, which has been utilized as an eective tool or modeling and analyzing cellular networks; see, e.g., [4] [6] and reerences therein. Generally, the spatial distribution o BSs is modeled as a spatial point process, such as the homogeneous Poisson point process PPP or single-tier networks, or which the coverage probability is derived in [7]. For HCNs, the spatial distribution o heterogeneous BSs is oten modeled as multiple independent tiers o PPPs, and several key statistics are analyzed in [8], [9]. A comprehensive treatment o the application o stochastic geometry in wireless communication and content can be ound in [], []. C. Contributions In this work, we ocus on an analytical perormance assessment o SVC transmission over two-tier HCNs utilizing tools rom stochastic geometry. The contributions o this work are: An analytical ramework is proposed or scalable video transmission exploiting the common eature o a layered structure o SVC and HCNs, which can improve the reception o High-Deinition HD content and reduce the video distortion, while maintaining an acceptable basic transmission quality or the majority o UEs. A digital and a hybrid digital-analog transmission scheme are proposed and studied. The hybrid digitalanalog scheme can urther improve the system perormance by avoiding the cli eect and realizing continuous quality scalability when the proportion o requency resource allocated to the emto tier exceeds a certain threshold. 3 A distortion analysis is provided or dierent transmission schemes or both orthogonal and non-orthogonal spectrum allocation methods. The power allocation between the digital BL signal and the analog EL signal is also analyzed to minimize the average distortion. The impact o UE load, i.e., the number o UEs served in a cell, is also considered. The remaining part o this paper is organized as in Fig.. Section II describes the system model, including the transmission schemes and spectrum allocation methods. Section III derives the distributions o the number o UEs per cell, subband occupancy probabilities, and SINR distributions. Section IV employs the results obtained in Section III to evaluate the perormance metrics, namely outage probability, HD probability, and average distortion. Section V presents numerical results and related discussions. Section VI concludes this paper. A. Layered Video Model II. SYSTEM MODEL We consider the downlink perormance o SVC over a twotier HCN. The SVC video content is split into two layers, BL and EL. Two transmission schemes are proposed, Layered The cli eect reers to the drastic degradation in video quality when the signal strength ades below the decoding threshold as opposed to a graceul degradation. There exist certain SINR thresholds at which the video quality changes drastically; in between these thresholds, the quality stays approximately constant. This eect is commonly observed in digital transmission.

3 3 System model Network and video Model II-A,B Schemes: LD and LHDA II-C Spectrum Allocation: orthogonal and nonorthogonal II-D Basic parameters UE load III-A Sub-band occupancy III-B SINR distribution III-C Data rate III-D System metrics Outage probability IV HD probability IV Average distortion IV Results Fig.. Paper organization. Numerical results and related discussions V Digital LD and Layered Hybrid Digital-Analog LHDA. The BL is always modulated into a digital signal and the data rate is R B, while the EL is modulated into a digital signal or an analog signal in the two transmission schemes. I the EL is modulated into a digital signal, then the data rate is R E. Here we ocus on the streaming video service, the video can be decoded successully when the data rate requirements o the BL and the EL are met. Actually, the proposed analytical ramework can be extended to video signals that are encoded to J layers using a ine granularity, and the BS chooses the irst J layers or the BL and the ollowing J layers or the EL based on the channel quality or each UE, where J + J J. Here we clariy that SVC allows three types o scalable encoding spatial, temporal, SNR quality to be combined and create a single layer [] [5]. Our layered video model is generic, and we are not concerned with the speciications o the layered encoding and the optimal selection o scalability combinations. Each layer is generated by some combinations o video scalabilities, and the required data rates are the main parameters rom the view o networking. B. Network Model The two-tier HCN consists o two types o BSs, namely, MBSs and FAPs see Fig.. These two types o BSs are modeled by two independent tiers o homogeneous PPPs, Φ mb and Φ b, whose intensities are λ mb and λ b, respectively. FAPs aim at providing network access to UEs in their vicinity within a coverage radius R. Suppose that there exist N sub-bands each o bandwidth W. The transmit powers o an MBS and an FAP over each sub-band are set as P m and P, respectively. The path loss model is r α, and the small-scale ading distribution is exponential with mean unity in squared magnitude, i.e., Rayleigh ading. The ading is assumed to be requency-lat within each sub-band and independent among Here or simplicity we assume the path loss exponent to be the same or MBS and FAP and ignore the eect o shadowing; the extended case o heterogenous path loss exponents and shadowing can be similarly treated ollowing our analytical approach but with more tedious derivations. Fig.. Illustration o the system model. For the macro UE, UE obtains the BL and the EL rom the MBS based on the channel quality. There are two cases or a emto UE to receive its signal: UE obtains the BL rom the MBS and obtains the EL rom the FAP; UE3 obtains both the BL and the EL rom the FAP. dierent sub-bands. We denote the noise variance at each UE by σ. There are two types o UEs, macro UEs and emto UEs. The locations o macro UEs orm a homogeneous PPP Φ mu with intensity λ mu, and each macro UE connects to the nearest MBS. The locations o the emto UEs orm a Matern cluster process Φ u [] with parent process Φ b the FAPs, i.e., the UEs in each cluster orm a inite PPP o intensity λ u on the disk o radius R centered at each FAP, implying that the mean number o users per cluster is Ū = λ u πr. Each emto UE connects to the FAP located at the parent point o the corresponding cluster, called the parent FAP. The access mechanism is as ollows: a emto UE always connects to its parent FAP when accessing a emto BS and connects to the MBS closest to its parent FAP when accessing a macro BS; a macro UE can only connect to the nearest MBS, even i it is situated within the coverage o an FAP. 3 C. Transmission Schemes Macro UEs can only connect to their serving MBS and attempt to obtain the BL and the EL based on the channel quality. It is assumed that the channel quality can be estimated perectly. Femto UEs attempt to obtain their EL contents rom their serving FAPs and they attempt to obtain their BL contents rom their serving MBSs with probability p or rom their serving FAPs with probability p, independently. I a emto UE attempts to obtain the BL contents rom the MBS, the emto UE simultaneously connects to the MBS and the FAP by employing the multi-low technique [], which has been proposed in 3GPP enabling a UE to simultaneously connect to two BSs, with the two links using the same or dierent requency sub-bands. The probability p is an important tunning 3 This corresponds to a closed-access emto network, in which only subscribers are allowed to be served by an FAP.

4 4 parameter or load balancing between macro tier and emto tier. Here we clariy that or macro UEs, both the BL and the EL are modulated into digital signals in LD and LHDA. For a macro UE, the data stream is received rom the serving MBS based on the channel quality. The macro UE receives both the BL and the EL when the channel can support a data rate larger than R B + R E and receives only the BL when the channel can support a data rate between R B and R B + R E, while an outage occurs when the channel cannot even support the data rate R B 4. Based on the dierent modulations and transmissions o the BL and the EL or emto UEs, we propose the ollowing two transmission schemes: LD transmission: Both the BL and the EL are modulated into digital signals. For a emto UE, the data stream o encoded BL signals or small SINR or jointly encoded signals o both the BL and the EL or large SINR is transmitted rom the serving FAP when p = ; the digital BL data stream is transmitted rom its serving MBS, while the digital EL data stream is transmitted rom its serving FAP when p = ; a mixed transmission is adopted when < p <. LHDA transmission: The BL is modulated into a digital signal, while the EL is modulated into an analog signal. For a emto UE, the superposition o the digital BL signal and the analog EL signal is transmitted rom the serving FAP when p = ; the digital BL data stream is transmitted rom its serving MBS, while the analog EL data stream is transmitted rom its serving FAP when p = ; a mixed transmission is adopted when < p <. Since the video source is encoded into multiple layers, dierent layers are transmitted to the UE based on the channel quality, thus providing scalable video quality. Speciically, or those UEs in less avorable conditions, only the BL with relatively low data rate is received in order to ensure basic video experience. When the channel quality improves, the EL is also received or enhanced video experience. Thus, the LD transmission can provide two-level scalable video or the UEs, and LHDA can provide a continuous quality scalability. D. Spectrum Allocation Methods O the N sub-bands, let N m sub-bands be allocated to the macro tier and N sub-bands to the emto tier. Each UE requires one sub-band or each transmission. We consider the ollowing two spectrum allocation methods [3] see Fig. 3: Orthogonal Case: The N sub-bands are split as N = N m + N, where the N m sub-bands used by all the MBSs o the macro tier are orthogonal to those N sub-bands used by all the FAPs o the emto tier. So there is no inter-tier intererence. 4 Here we do not consider hybrid digital-analog transmission when macro UEs request both the BL and the EL in LHDA transmission due to its inerior perormance see Fig. 7. Since macro cells aim at providing coverage, the number o served UEs is usually large. From the latter analysis, hybrid digitalanalog transmission is beneicial when the UE load is low and the amount o requency resource exceeds a certain threshold. Thus, digital transmission or macro UEs is preerred. Fig. 3. Spectrum allocation methods. Sub-bands allocated to macro tier Sub-bands allocated to emto tier a Orthogonal allocation Sub-bands allocated to macro tier Sub-bands allocated to emto tier Sub-bands allocated to both the macro and emto tier b Non-orthogonal allocation Non-orthogonal Case: Compared with the orthogonal case, here the two sets o sub-bands may overlap: each MBS resp. FAP independently randomly selects N m resp. N sub-bands rom the N sub-bands. The values o both N m and N can be chosen rom to N lexibly and need not add to N. So there is inter-tier intererence, while the available spectrum will be abundant as N m and N grow large. III. UE LOAD, SUB-BAND OCCUPANCY, AND SINR DISTRIBUTION In this section, we establish several auxiliary results or our derivation o the key perormance metrics in Sec. IV. We irst provide an approximate characterization o the distribution o the number o UEs connected to a BS and then obtain the probability o a sub-band being occupied. The SINR distribution is subsequently derived, which is used to derive the achievable data rate. A. UE Load Since the distribution o emto UEs in an FAP coverage disk is a PPP with intensity λ u, the number o emto UEs connected to an FAP is a Poisson random variable r.v. with mean Ū, P{U = i} = Ū i e Ū, i =,,. i! An MBS not only serves the macro UEs situated in its Voronoi cell but also the emto UEs that belong to the FAPs in this Voronoi cell and connect to the MBS to receive the BL contents. We denote the number o macro UEs in the Voronoi cell as U MBS and the total number o emto UEs served by the MBS as U FAP, which is given by U FAP = N c i= N,i, where N c denotes the number o the FAPs in the Voronoi cell and

5 5 N,i denotes the number o emto UEs which belong to the ith FAP but connect to the MBS to receive the BL contents. The total number o UEs served by an MBS is thus U m = U MBS + U FAP. U MBS is conditionally independent o U FAP given the area o the Voronoi cell. Denote the area o a Voronoi cell by S, the probability generating unction pg o U m conditioned on S, denoted by G m z S, is G m z S = G MBS z SG FAP z S, 3 where G MBS z S and G FAP z S are the pgs o U MBS and U FAP conditioned on S, respectively. U MBS is a Poisson r.v. with mean λ mu S, and the conditional pg o U MBS is G MBS z S = e λ musz. 4 Since a emto UE attempts to connect to its serving MBS with probability p, a thinning occurs, i.e., N,i is a Poisson random variable with mean pū. Meanwhile, N c is also a Poisson r.v. with mean λ b S because o the PPP distribution o the FAP locations. U FAP is a compound Poisson r.v. with conditional pg G FAP z S = e λ bse pū z. 5 There is no known closed orm expression o the probability density unction pd o the area S o the typical Poisson Voronoi cell, but the ollowing approximation [4] S x λ mbc c x c e cλmbx, 6 Γc where c = 7 and Γc = t c e t dt, has been known to be handy and suiciently accurate see, e.g., [5]. Aided by this approximation, with some manipulations, the pg o U m is G m z = c c c λ mu λ mb z + λ b λ mb e pū z and the distribution o U m ollows as c, 7 P{U m = i} = Gi m, i =,,, 8 i! where G i m is the i-th derivative o G m z evaluated at z =. B. Sub-band Occupancy Since the number o served UEs or each BS is random, the sub-band requency resource will be under-utilized in some BSs and over-utilized in some other BSs. As the UE loads in the MBS and the FAP are dierent under the orthogonal and non-orthogonal spectrum allocations, the sub-band occupancy is calculated or the MBS and the FAP respectively. It is assumed that the available sub-bands are uniormly and independently allocated to the UEs by the BS. Orthogonal Spectrum Allocation: There are N m available sub-bands or the MBS, and each sub-band is equally likely to be chosen. I the number o UEs is smaller than that o sub-bands, the MBS randomly chooses U m out o the total N m sub-bands. Otherwise, all the sub-bands are chosen. The probability that a sub-band is used by an MBS is P m, busy = N m min{i, N m }P{U m = i}, 9 i= and similarly the probability that a sub-band is used by an FAP is P, busy = min{i, N }P{U = i}. N i= Non-orthogonal Spectrum Allocation: For the nonorthogonal case, both the MBS and the FAP choose a subband randomly rom N sub-bands, so the probability that a sub-band is used by an MBS is P m, busy = N min{i, N m }P{U m = i}, i= and similarly the probability that a sub-band is used by an FAP is P, busy = min{i, N }P{U = i}. N i= The spatial point process o BSs that use a given subband is an approximately independent thinning o the original point process Φ mb resp. Φ b by the probability P m,s busy resp. P,s busy, denoted by Φ mb resp. Φb with the intensity λ mb = λ mb P m,s busy resp. λb = λ mb P m,s busy [5], where the superscript s {, } indicates whether the orthogonal or the non-orthogonal spectrum allocation method is used. For each sub-band, the event that it is used by an MBS is assumed independent o the event that it is used by all other MBSs. Such an approximation essentially neglects the act that the areas o adjacent Poisson Voronoi cells are correlated; however, our numerical results reveal that the discrepancy between this approximation along with others and simulation experiments is rather slight see Fig. 9 in Sec. V. C. SINR Distribution The complementary cumulative distribution unction ccd o the SINR is deined as Pθ = P{SINR > θ}, where θ is the SINR threshold. The SINR distributions o a UE connected to the MBS and the FAP are derived under two transmission schemes. LD transmission: For analytical tractability, we assume that both the BL and the EL are modulated into digital signals according to a Gaussian codebook. For the typical UE which is assumed to be located at the origin and connected to its MBS, the received signal denoted by Y can be written as Y = P / m x α/ h x X x + + κ y Φ b P / x Φ mb \{x } Pm / x α/ h x X x y α/ h y X y + Z, 3

6 6 where the irst item o right side o the equation denotes the received signal symbol, the second and the third items denote the intererence symbols rom the macro and the emto tier, respectively, and Z denotes the Gaussian noise with zero mean and variance σ. We use x to denote the location o the serving MBS. Note that i the typical UE is a macro UE, the MBS transmits the encoded BL signals only or the jointly encoded signals o both the BL and the EL based on the link SINR. I the typical UE is a emto UE, the MBS transmits the encoded BL signals only. Actually, the MBS does not need to classiy the UE type, it just responds to the dierent requests by macro UEs and emto UEs. X x is the signal symbol, while X x is the intererence symbol transmitted by the interering MBS x. X x, X x CN,. X y is the intererence symbol transmitted by the interering FAP y, and X y CN,. The indicator κ {, } indicates the orthogonal and nonorthogonal spectrum allocation methods, respectively. Thus, the received SINR is γ m LD = P m x α h x I m + κi + σ, 4 where I m = x Φ mb \{x P } m x α h x is the intererence rom the macro tier, and I = y Φ b P y α h y is the intererence rom the emto tier. For the typical emto UE which is assumed to be located at the origin and connected to its FAP, the received signal can be written as Y = P / y α/ h y X y + P / y α/ h y X y + κ x Φ mb P / y Φ b \{y } m x α/ h x X x + Z, 5 where y denotes the location o the serving FAP. Note that the FAP transmits the encoded EL signals only or the jointly encoded signals o both the BL and the EL to the typical UE based on user request. X y is the signal symbol transmitted by the serving FAP, and X y is the intererence symbol transmitted by the interering FAP y. Thus, the received SINR is γ LD = P y α h y I + κi m + σ, 6 where I = y Φ b \{y } P y α h y denotes the intererence rom the emto tier and I m = x Φ mb P m x α h x denotes the intererence rom the macro tier. The ollowing theorem gives the ccd o the SINR or the typical UE, Theorem. For LD transmission, the ccd o the SINR or the typical UE connected to its serving MBS is PLDθ m = P{γLD m > θ} = πλ mb exp πvλ mb + λ mb ρθ, α θv/δ σ P m P θ κ P m δ v λ bδπ cscδπ dv, 7 and the ccd o the SINR or the typical emto UE connected to its serving FAP is PLDθ = P{γLD > θ} R = exp θv/δ σ R δπ cscδπθ δ v λb + κ P Pm δ λmb dv, P 8 where δ = /α, λmb = λ mb P m,s busy, λb = λ b P,s busy, and ρθ, α = θ δ dx. In orthogonal spectrum allocation, κ =, while in non-orthogonal spectrum allocation, θ δ +x /δ κ =. Proo: See Appendix A. LHDA transmission: The BL is modulated to a digital signal, while the EL is modulated to an analog signal. The digital modulation is based on a Gaussian codebook, and the EL signal ater analog modulation is also modeled as a Gaussian source with zero mean and unit variance [6], [7]. For analog modulation, it is assumed that the source bandwidth is equal to the channel bandwidth [], [3]. For the typical UE which is assumed to be located at the origin and connected to its serving MBS, the received signal can be written as Y = P / m x α/ h x X x + + κ y Φ b P / x Φ mb \{x } Pm / x α/ h x X x y α/ h y X y + Z, 9 which is nearly the same as 3 in LD transmission, the dierence lies in that X y is the analog EL intererence symbol or the superposition o digital BL and analog EL intererence symbol transmitted by the interering FAP y based on the transmission scheme o y, and X y CN,. Thus the received SINR is γ m LHDA = P m x α h x I m + κi + σ, where I m = x Φ mb \{x } P m x α h x is the intererence rom the macro tier and I = y Φ b P y α h y is the intererence rom the emto tier. For the typical emto UE which is assumed to be located at the origin and connected to its FAP, according to the transmission scheme, it receives only the EL, or it receives the superposition o the digital BL signal and the analog EL signal. Case : The typical emto UE connected to its FAP receives only the EL. The received signal or the typical emto UE is Y = P / y α hy Xy E + P / y α hy X y + κ x Φ mb P / y Φ b \{y } m x α hx X x + Z, where Xy E is the EL signal symbol transmitted by the serving FAP and X y is the intererence symbol transmitted by the interering FAP y.

7 7 Thus, the received SINR or the emto UE connected to its FAP to receive the EL is γ LHDA = P y α h y I + κi m + σ, where I = y Φ b \{y P } y α h y is the intererence rom the emto tier and I m = x Φ mb P m x α h x is the intererence rom the macro tier. Case : The typical emto UE connected to its FAP receives the superposition o the digital BL signal and the analog EL signal. The received signal or the typical emto UE is Y = y α/ h y P B Xy B + P EXE y + P / y α/ h y X y 3 y Φ b \{y } + κ m x α/ h x X x + Z, x Φ mb P / where Xy B is the BL signal symbol transmitted by the serving FAP, and Xy E is the EL signal symbol transmitted by the serving FAP. Thus, the received SINR or the typical emto UE connected to its FAP to receive the BL, denoted by γ,b LHDA, is γ,b LHDA = P B y α h y P E y α h y + I + κi m + σ. 4 Successive Intererence Cancellation SIC [8] is adopted to demodulate the EL signal. Conditioned on the successul reception o the BL, the received SINR or the typical emto UE connected to the FAP to receive the EL signal, denoted by γ,e LHDA, is LHDA = P E y α h y I + κi m + σ. 5 γ,e The ollowing theorem gives the ccd o the SINR or the typical UE, Theorem. For LHDA transmission, the ccd o the SINR or the typical UE connected to its serving MBS is P m LHDAθ B = P{γ m LHDA > θ B } = P m LDθ B, 6 the ccd o the SINR or the typical emto UE connected to its serving FAP to receive the EL is given by P LHDAθ E = P{γ LHDA > θ E } = P LDθ E, 7 and the joint ccd o the SINR or the typical emto UE connected to its serving FAP to receive the superposition o the digital BL and the analog EL is given by 8. Proo: See Appendix B. D. Data Rate The instantaneous data rate that a sub-band channel o bandwidth W can accommodate is R = W log + SINR. For LD transmission, since both the MBS and the FAP transmit digital signals, the channel rom the typical UE to its serving MBS can accommodate the data rate R m = W log +γld m, and the channel rom the typical UE to its serving FAP can accommodate the data rate R = W log +γld. For LHDA transmission, only the BL is modulated to a digital signal, so the data rate is deined only or the BL, the channel rom the typical UE to its serving MBS can accommodate the data rate R m = W log + γlhda m, and the channel rom the typical UE to its serving FAP can accommodate data rate R = W log + γ,b LHDA. The actually achieved UE data rates, ater taking into consideration the UE load and sub-band occupancy, are given below. Without loss o generality, we take an MBS as an example. When the number o UEs in a macro cell does not exceed the total number o sub-bands i.e., U m N m, each UE can exclusively occupy a sub-band, and its achieved data rate is R m ; when U m > N m, the U m UEs share the N m sub-bands, and the data rate is thus discounted into N m U m R m, assuming a round-robin sharing mechanism. So the average achieved data rate o a UE served by an MBS is given by R mu = ξ m R m, 9 where ξ m is the scheduling index denoting the probability that a UE is scheduled by the MBS, Nm i= ξ m = P{U m = i} + i=n m + P{U m = i} Nm i. 3 P{U m = } Similarly, the average achieved data rate o a UE served by an FAP is given by R u = ξ R, 3 where ξ is the scheduling index denoting the probability that a UE is scheduled by the FAP, N i= ξ = P{U = i} + i=n + P{U = i} N i. 3 P{U = } IV. SYSTEM PERFORMANCE In this section we evaluate several important perormance metrics, namely, the outage probability, the HD probability, and the average distortion. The outage probability is the probability that a UE cannot receive the BL, namely, the UE data rate is less than R B. The HD probability is the probability that a UE can receive high-deinition content, i.e., both the BL and the EL, namely, the UE data rate is greater than R B +R E. The average distortion evaluates the dierence between the received video and source video, which is measured using the distortion-rate unction. Note that, or LHDA transmission, the HD probability or the emto UE is not deined since the EL is transmitted as an analog signal and the data rate or an analog signal is undeined. Table I gives a map o system perormance metrics or dierent transmission schemes.

8 8 P LHDA θ B, θ E = P{γ,B LHDA > θ B, γ,e LHDA > θ E} R = θ B > e θbv /δ σ P B θ B P E + θ B θ E P B + θ E P E θ E P B + θ E P E R R R e θev /δ σ P E δπ cscδπθ δ B λb v P P B θ B P E δ +κ λ mb Pm P B θ B P E δ δπ cscδπθ δ E v λb P P E dv δ +κ λ mb P m P E δ dv. 8 TABLE I SYSTEM PERFORMANCE METRICS transmission perormance LD LHDA macro outage probability P LD,m out in 33 P LHDA,m out in 38 FAP outage probability P LD, out in 35 P LHDA, out in 4 macro HD probability P LD,m HD in 34 P LHDA,m HD in 39 emto HD probability PHD in 36 - average distortion D LD in 37 D LHDA in 47 A. LD Transmission For a macro UE, both the BL and the EL are transmitted via its serving MBS, so the outage probability, denoted by, is P LD,m out P LD,m out = P{R mu < R B } = P{γLD m < R B /ξ m W } = PLD m R B /ξm W. 33 The HD probability or a macro UE, denoted by P LD,m HD, is P LD,m HD = P{R mu > R B + R E } = P{γLD m > R B +R E /ξ m W } = PLD m R B +R E /ξ m W. 34 For a emto UE, it either connects to its serving MBS with probability p or its serving FAP with probability p to receive the BL, so the outage probability, denoted by P LD, out, is P LD, out = pp{r mu < R B } + pp{r u < R B } = pp{γld m < R B /ξ m W } + pp{γld < R B /ξ W } = p PLD m R B /ξm W + p PLD R B /ξ W. 35 To receive the high-deinition video content, a emto UE receives the BL rom the MBS and receives the EL rom the FAP with probability p, or it receives both the BL and the EL rom the FAP with probability p. Thus, the HD probability or a emto UE, denoted by P HD, is P HD = pp{r mu > R B, R u > R E } + pp{r u > R B + R E } a = pp{r mu > R B }P{R u > R E } + pp{r u > R B + R E } = pp{γld m > R B /ξm W }P{γ LD > R E /ξ W } + pp{r u > R B +R E /ξ W } = ppld m R B /ξm W PLD R E /ξ W + ppld R B +R E /ξ W, 36 where a ollows rom the tier independence approximation. For a emto UE, in the orthogonal case its connection to its serving MBS and its connection to its serving FAP are independent since these two connections use two dierent subbands and they are subject to independent intererences; in the non-orthogonal case, such an independence does not hold, since these two connections may use the same sub-band, thus the same intererence rom other interering BSs leads to a certain amount o dependence. Here we make use o a tier independence approximation; that is, or a emto UE, its rate rom the macro tier, R mu, and its rate rom the emto tier, R u, are independent r.v.s. Such an approximation is partially motivated by the randomized sub-band selection in the nonorthogonal spectrum allocation method and is ound to be accurate via simulation experiments, see Fig. 9. The distortion-rate unction DR [], [9] is used to measure the distortion per source sample when the source rate is R bits/sample. As the bandwidth o a sub-band is W and the data rate o the BL resp. the EL is R B resp. R E, the source rate is R B W resp. R E W. Since the source signal is modeled as a Gaussian signal with zero mean and unit variance, the distortion o the received video signal can be divided into three cases based on the reception. I the BL is not decoded correctly, the distortion is D = ; i the BL is decoded correctly while the EL is not, then the distortion is D B = R B W ; i both the BL and the EL are decoded correctly, the distortion is D HD = R B +R E W. The average distortion or emto UEs, denoted by D LD, is given by D LD = P LD, out D + P LD, out PHDD B + PHDD HD. 37 B. LHDA transmission For macro UEs, both the BL and the EL are digitally transmitted via its serving MBS, just the same as that in

9 9 LD transmission. From the SINR analysis in Section III-C, the outage probability P LHDA,m out, and the HD probability P LHDA,m HD or the macro UE are the same as that in LD transmission. P LHDA,m out P LHDA,m HD = P{R mu < R B } = P LD,m out 38 = P{R mu R B + R B } = P LD,m HD. 39 Here we do not adopt hybrid digital-analog transmission when macro UEs request both the BL and the EL in LHDA transmission due to its inerior perormance see Fig. 7 and ootnote 4. For a emto UE, since it receives the BL rom the MBS with probability p or receives the BL rom the FAP with probability p, the outage probability, denoted by P LHDA, out, is P LHDA, out = pp{r mu < R B } + pp{r u < R B } = pp{γ m LHDA < R B /ξ m W } + pp{γ,b LHDA < RB/ξ W } = p PLHDA m R B /ξ m W + p P LHDA R B /ξ W,. 4 The emto UE has two choices to receive the video content, and the average distortion is calculated accordingly. Case : The emto UE receives the BL rom MBS, and receives the EL rom FAP. Since the EL signal is analog, an MMSE estimator is employed or the estimation o the EL, and thus we have MMSE =, where +γlhda γlhda is the received SINR. Since there are multiple emto UEs in a FAP, a round-robin mechanism is used to schedule time slots or each emto UE to transmit the EL. I a UE is scheduled, its distortion or the EL is MMSE; otherwise, its distortion is unity. So the distortion is e LHDA = ξ +γ LHDA + ξ. Since the EL is estimated only i the BL is decoded successully, the cd o e LHDA conditioned on the successul reception o the BL is given by P{e LHDA < T R mu R B } a = P{e LHDA < T } { } = P ξ + γlhda + ξ < T { = P γlhda > T } T + ξ T = PLHDA, T + ξ 4 where a ollows rom the tier independence approximation. Since or a positive random variable X, E{X} = P{X > t}dt, the mean distortion or the EL, t> denoted by D E, is D E = E{e LHDA R mu R B } 4 T = ξ + PLHDA dt. T + ξ ξ Since the EL corresponds to the residual between the BL and the source signal, the distortion when both the BL and the EL are received, denoted by D HD, is given by D HD = D B D E. So the average distortion or the emto UE in Case, denoted by D LHDA, is D LHDA = P{R mu < R B }D + P{R mu R B }D HD = P m LHDA R B ξmw ξ + ξ + P m LHDA R B ξmw T P LHDA R B dt. T + ξ 43 Case : The emto UE receives both the BL and the EL rom the FAP. Since the EL signal is analog and superposed with the digital BL signal, an MMSE estimator is employed or the estimation o the EL conditioned on the correct reception o the BL, thus we have MMSE =, where γ,e LHDA is the received +γ,e LHDA SINR ater the cancellation o the BL. The distortion or the EL is e LHDA = ξ + ξ +γlhda E. The cd o e LHDA conditioned on the successul reception o the BL is given by P{e LHDA < T R u R B } = P{ξ + γhc E + ξ < T R u R B } = P{γ,E LHDA > = P LHDA RB/ξ T W, P LHDA R B /ξ W, T T + ξ γ,b LHDA > R B/ξ W } T +ξ. 44 Then, we can obtain the distortion o the EL as D E = E{e LHDA < T R u R B } 45 = ξ + ξ P LHDA RB W ξ T, T +ξ P LHDA R B W ξ, dt. So the average distortion or the emto UE in Case, denoted by D LHDA, is D LHDA = P{R u < R B }D + P{R u R B }D HD = P LHDA R B /ξ W, + P LHDA R B /ξ W, R B ξ + P LHDA R B /ξ T W, ξ P LHDA R B /ξ W, T +ξ dt. 46 Since a emto UE ollows Case with probability p and ollows Case with probability p, the average distortion or a emto UE, denoted by D LHDA, is D LHDA = pd LHDA + pd LHDA. 47

10 TABLE II SYSTEM PARAMETERS Symbol Description Typical Value N number o sub-bands W bandwidth o a sub-band MHz 5 P m MBS transmit power per sub-band dbm 39 P FAP transmit power per sub-band dbm 3 σ noise power dbm 4 λ mb MBS intensity m E-5 λ b FAP intensity m 5E-5 λ mu macro UE intensity m E-4 λ u emto UE intensity in coverage m 8E-3 R coverage radius o FAP m α path loss exponent 4 R B rate or the BL transmission Mbps.5 R E rate or the EL transmission Mbps C. Power Allocation in LHDA Transmission For LHDA transmission, the FAP transmits the superposition o the digital BL signal and the analog EL signal when the emto UE claims both the BL and the EL rom the FAP. Since the total transmit power is limited in each FAP, i more power is allocated to transmit the BL, not only less UEs encounter video outage, but also less UEs enjoy HD video. Otherwise, i more power is allocated to transmit the EL, the transmission o the BL suers while the transmission o the EL is enhanced. Hence, the overall perormance depends on the power allocation. In order to optimally allocate the transmit power between the digital BL signal and the analog EL signal, we ormulate the ollowing optimization problem: min P B,P E s.t. P B D LHDA + P E P. 48 The aim is to ind the optimal power allocation or the FAP to minimize the video distortion under the condition that the total transmit power is limited. Since this is a univariate optimization problem, it is practically eicient to ind the optimal transmit power allocation among the BL and the EL using a line search. V. NUMERICAL ILLUSTRATION In this section, the outage probabilities, the HD probabilities and the average distortions are evaluated or LD and LHDA transmission schemes considered under orthogonal and nonorthogonal spectrum allocation methods. Meanwhile, the optimal power allocation or the digital BL and the analog EL or LHDA transmission is assessed. We also give the comparison o our analytical results and Monte Carlo simulations to veriy the tier independence approximation and the approximate statistics o the Poisson Voronoi cell area in Fig. 9. Unless otherwise speciied, the system parameters are listed in Table II. Fig. 4a displays the perormance o LD transmission in the orthogonal case. In that case, N m sub-bands or the macro tier and N sub-bands or the emto tier are orthogonal with N m +N = N. As N m increases, more resources are allocated 5 From Youtube Live encoder settings, we set the basic video 4p data rate R B as.5 Mbps, and the HD video data 7p rate as 5 Mbps, thus R E = 4.5 Mbps. outagehd probability outagehd probability Perormance o LD in orthogonal case emto HD p= macro outagep= FAP outagep= emto HD p= macro outage p= FAP outage p= emto HD p=.5 macro outage p=.5 FAP outagep= Sub bands or Macro tier N m a Perormance o LD in non orthogonal case emto HD p= macro outagep= FAP outagep= emto HDp= macro outagep= FAP outagep= emto HDp=.5 macro outagep=.5 FAP outagep= Sub bands or Macro tier N m b Fig. 4. Perormances o LD in both orthogonal and non-orthogonal cases. to the macro tier, and the outage probabilities decrease or both macro UEs and emto UEs, except that the emto UE outage probabilities slightly increase or very large values o N m. The HD probability o the emto UE with p = decreases with N m because the EL transmission via FAPs deteriorates as the resources or the emto tier are reduced. The HD probabilities o the emto UE or p =.5 and p = increase or small N m and then decrease as N m grows large, relecting the tension between the resources or the BL transmission and the EL transmission. Fig. 4b displays the perormance o LD transmission in the non-orthogonal case. For comparison with Fig. 4a, we still let N m + N = N, but let the sub-bands be selected by each BS independently. The general trend is similar to that in the orthogonal case, but the dierence lies in that the curves show less variability with N m except or those values near to N. The reason or such a practically desirable insensitivity is due to the lessened tension between the resources or macro tiers and emto tiers rom randomized sub-band selection. Note that i p is large, the emto UE tends to connect to an MBS to receive the BL, the outage probability increases and the HD probability decreases, i.e., the perormance deteriorates. However, since an MBS can provide continuous coverage while an FAP cannot, i a emto UE is moving, then it may preer to connect to an MBS to receive the BL, which

11 outage distortion outagedistortion Perormance o LHDA in orthogonal case distortion p= FAP outage p= distortion p= FAP outage p= distortion p=.5 FAP outage p= Sub bands or Macro tier N m a Perormance o LHDA in non orthogonal case distortionp= FAP outagep= distortion p= FAP outagep= distortionp=.5 FAP outagep= Sub bands or Macro tier N m b Fig. 5. Perormances o LHDA in both orthogonal and non-orthogonal cases. outage distortion outagedistortion Comparison o LD and LHDA in orthogonal case distortion LD FAP outage LD distortion LHDA FAP outagelhda 5 5 Sub bands or Macro tier N m a Comparison o LD and LHDA in non orthogonal case distortion LD FAP outage LD distortionlhda FAP outagelhda 5 5 Sub bands or Macro tier N m b Fig. 6. Comparisons between LD and LHDA in both orthogonal and nonorthogonal cases. prevents requent handover between emto cells and enables uninterrupted reception o the BL video. Fig. 5a displays the perormance o LHDA transmission in the orthogonal case. The outage probability or macro UE is the same as that in LD transmission, so we just neglect it in LHDA transmission. Since the requency resource allocated to the macro tier increases, the resource or the emto tier decreases. The outage probability or the emto UE connected to the FAP corresponding to p = to receive the BL increases while the outage probability or the emto UE connected to the MBS corresponding to p = to receive the BL decreases. The case where p =.5 shows a tradeo o these two extreme cases: the outage probability or emto UE irst decreases and then slightly increases when the allocated resource or the FAP is small. When N m is small, the perormance o the macro tier is poor, and thus the distortion or the UE connected to the MBS to receive the BL is large. When increasing N m, the perormance o the macro tier becomes good while that o the emto tier is poor. Fig. 5b displays the perormance o LHDA transmission in the non-orthogonal case. The general trends o the curves o the outage and the average distortion are almost the same as that o Fig. 5a. The dierence lies in that the outage probability is lower in the non-orthogonal case than that in the orthogonal case when N m is small. Fig. 6 displays a comparison between LD transmission and LHDA transmission. Since the comparisons or dierent p are more or less the same, we set p =.5 as an example. In both orthogonal and non-orthogonal cases, LHDA outperorms LD when the proportion o requency resource allocated to the emto tier exceeds a certain threshold, or example, 35% i.e., N 7 in the current deployment, as the outage probability is slightly increasing while the average distortion is obviously decreasing when N m is small. The reason is that analog transmission avoids the cli eect and oers the continuous quality scalability. Fig. 7 displays the HD probability and distortion or the macro UE. Compared to that o the emto UE, the HD probability is generally low and the distortion is larger, which is owing the large number o UEs served by the MBS. I we adopt the hybrid digital-analog transmission o the digital BL and the analog EL or macro UEs in LHDA transmission, the distortion o video is even deteriorated or a large range o N m compared to that in LD, which veriy the conclusion that hybrid digital-analog transmission perorms well when the amount o requency resource exceeds a certain threshold in Fig. 6. Thus we do not adopt the hybrid digital-analog transmission or macro UEs. Fig. 8 displays the power allocation between the digital BL

12 HD probability and distortion or the macro UE.8 Comparison o numerical and analytical evaluations or LD HD probability distortion LHDA, ortho LHDA, nonortho LD, ortho LD, nonortho LD, nonortho HD LD, ortho HD distortion HD probability 5 5 Sub bands or Macro tier N m Fig. 7. HD probability and distortion or the macro UE. outage HD probability emto HD analytical FAP outageanalytical emto HD numerical FAP outage numerical. 5 5 Sub bands or Macro tier N m a.7 Perormance o power allocation between BL and EL Comparison o numerical and analytical evaluations or LHDA.9 outage distortion distortion ortho FAP outage ortho distortion non ortho FAP outage non ortho Normalized transmit power or BL: P B /P Fig. 8. Power allocation between the BL and the EL in FAPs or LHDA transmission. and the analog EL or LHDA transmission. I the power allocated to the BL is increasing, the outage probability decreases monotonously and then approaches stable as the network is intererence-limited. With P B increasing, the distortion or the BL is sharply decreasing while the distortion or the EL is increasing. Thus, the total distortion irstly decreases owing to superior transmission o the BL, then increases owing to inerior transmission o the EL. Because o the tradeo between the transmissions o the BL and the EL, the average distortion varies little when the power allocation ratio P B /P lies in a wide range, thus the power allocation is robust. Fig. 9 displays a comparison between Monte Carlo simulation and analytical results o the perormance. Since the comparisons with dierent p are more or less the same, we set p = as a representative example. The simulation region in Monte Carlo simulation is km* km. In order to mitigate the boundary eect, we only use the central [3/4 length * 3/4 width] part o the entire region to analyze. The deployment parameters or the BSs and UEs are listed in the Table II. The statistics o the system parameters are derived rom that o the total o UEs in the central area. A small gap exists between the curves o Monte Carlo simulation and the analytical results, suggesting that the approximations we adopt in the analysis are sensible. Here we consider some practical issues on implementation. outage distortion distortion analytical FAP outage analytical distortion numerical FAP outage numerical. 5 5 Sub bands or Macro tier N m b Fig. 9. Comparisons between numerical evaluation and analytical evaluation or LD transmission and LHDA transmission. Firstly, the cooperation between the MBS and its associated FAPs which reside in its Voronoi cell is relatively easy to manage, since the cooperation relationship is location-determined. Secondly, in order to realize analog transmission, we encode the video source by only linear real codes or both compression and error protection, such as 3D DCT or compression and a scaling matrix to adjust the magnitude o the DCT components or error protection, thus ensuring the inal coded samples are linearly related to the original pixels. The details can be ound in [], [3]. VI. CONCLUSION In this paper, we proposed an analytical ramework or scalable video transmission, which exploits the common eature o a layered structure o SVC and HCNs. Speciically, we presented two scalable transmission schemes, LD and LHDA, which are shown to be an eective means or providing dierentiated services or users. Through the analysis and comparison o system perormance metrics, i.e., outage probability, HD probability and average distortion, under orthogonal and non-orthogonal spectrum allocation methods, we observe that: Compared to the traditional non-scalable video transmission, our schemes can adaptively provide basic or high-

13 3 deinition video; The requency resource should be elaborately allocated between tiers to achieve good perormance, and the choice o orthogonal and non-orthogonal spectrum allocation methods depend on the system coniguration; 3 The hybrid digital-analog transmission can urther improve the system perormance by reducing video distortion and providing continuous quality scalability o high-deinition video; 4 The perormance is quite insensitive to the power allocation between the digital BL and the analog EL. APPENDIX A Let x be the distance rom the typical UE to its serving MBS, which is the nearest MBS, so the pd o x is x r = e λ mbπr πλ mb r. The SINR experienced by the typical UE connected to its serving MBS is given by γld m = P m x α h x I m+κi +σ, where I m = x Φ mb \{x P } m x α h x is the intererence rom the macro tier, and I = y Φ b P y α h y is the intererence rom the emto tier. κ {, } is the indicator that whether the orthogonal or the non-orthogonal spectrum allocation is used. Due to the independent thinning approximation, the set o interering MBSs is a PPP Φ mb with intensity λ mb and the set o interering FAPs is a PPP Φ b with intensity λ b. The ccd o the SINR experienced by the typical UE connected to its serving MBS PLDθ m = P{γLD m > θ} { = πλ mb re πλ mbr Pm h x r α } P I m + κi + σ > θ dr a = πλ mb re πλ mbr θrα σ θr α Pm L Im +κi P m dr. 49 where a ollows rom h x Exp. Ater excluding the serving BS x, Φ mb \{x } is still a PPP, so we apply the pgl o PPP to obtain the Laplace transorm o I m L Im s = exp π λ mb xdx + sp m x α r = e π λ mb r ρ spm r α,α. 5 Since Φ b is a PPP, we apply the pgl o PPP to obtain the Laplace transorm o I L I s = exp π λ b + sp x α xdx = e δπ cscδπ λ b sp δ. 5 Substituting 5 and 5 into PLD m θ, we can obtain 7. Let y be the distance between the typical emto UE and its serving FAP. Since emto UEs are uniormly distributed in the circular coverage area o radius R o each FAP, the pd o y is given by y r = r. R The received SINR or the typical emto UE connected to its serving FAP ollows as γld = P y α h y I +κi m+σ, where I = y Φ b P y α h y is the intererence rom the emto tier, and I m = x Φ mb P m x α h x is the intererence rom the macro tier. The ccd o the SINR experienced by the typical emto UE connected to its serving FAP is PLDθ = P{γLD > θ} R { r P h y r α } = P I + κi m + σ > θ dr = R R r R e θr α δ P θr α L I +κi m dr, 5 P which, ater expanding the Laplace transorm o I m, I and urther manipulations, leads to 8. APPENDIX B The received SINR or the typical UE connected to its serving MBS is γlhda m = Pm x α h x I m +κi +σ, where I m = x Φ mb \{x } P m x α h x is the intererence rom the macro tier, and I = y Φ b P y α h y is the intererence rom the emto tier. Similar to the derivation o PLD m θ, the ccd o γm LHDA ollows as P m LHDAθ = P{γ m LHDA > θ} = P m LDθ. 53 According to the transmission scheme, the FAP transmits the analog EL signal with probability p or the superposition o the digital BL signal and the analog EL signal with probability p. Case : The received SINR or the typical emto UE connected to the FAP receives the EL ollows as γ LHDA = P y α h y I +κi m +σ. I = y Φ b P y α h y is the intererence rom the emto tier, I m = x Φ mb P m x α h x is the intererence rom the macro tier. Similar to the derivation o PLD θ, the ccd o γ LHDA ollows as P LHDAθ = P{γ LHDA > θ} = P LDθ. 54 Case : The received SINR or the typical emto UE connected to the FAP receives the superposition o the digital BL signal and the analog EL signal ollows as γ,b LHDA = P B y α h y P E y α h y + I + κi m + σ, 55 where P E y α h y is the intererence o the superposed EL, the intererence rom the emto tier is I = y Φ b P y α h y and the intererence rom the macro tier is I m = x Φ mb P m x α h x. The ccd o γ,b LHDA ollows as P{γ,B LHDA > θ} = r R e θr α σ θr α P B θp E L I +κi m P B θp E dr = R R λb exp θv/δ σ P B θp E P B P θp E δ + κ λ mb δπ cscδπθ δ v P B P m θp E δ dv. 56 SIC is adopted to decode the EL signal. Ater successul reception o the BL, the received SINR or the EL signal is γ,e LHDA = P E y α h y I +κi m +σ.

14 4,E The ccd o γlhda ollows as α α r θrp Eσ θr,e P{γLHDA > θ} = e L dr I +κi m R PE R /δ θv P E σ δπ cscδπθδ v λ b PPE δ +κλ mb PPmE δ e = dv. R 57,B,E is The joint ccd o γlhda and γlhda,e,b > θb, γlhda > θe } PLHDA θb, θe = P{γLHDA { } θ I θe Itotal B total = P hx >, h > x PB θb PE x α PE x α { } θb Itotal θe Itotal = P hx > max, PB θb PE x α PE x α θe PB,B = P{γLHDA > θb } θb > + θe PE θe PB,E + P{γLHDA, 58 > θe } θb + θe PE where Itotal = I + κim + σ. ACKNOWLEDGEMENT The authors wish to thank the anonymous reviewers or their constructive comments. R EFERENCES [] L. Wu, Y. Zhong, W. Zhang, and M. Haenggi, Scalable transmission over heterogenous networks, in Proc. International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks WiOpt, 5, pp [] H. Schwarz, D. Marpe, and T. Wiegand, Overview o the scalable video coding extension o the H. 64/AVC standard, IEEE Trans. Circuits Syst. Video Technol., vol. 7, no. 9, pp. 3, 7. [3] V. Chandrasekhar, J. G. 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Haenggi, Coordinated multipoint joint transmission in heterogeneous networks, IEEE Trans. Commun., vol. 6, no., pp , 4. [] F. Baccelli and B. Blaszczyszyn, Stochastic Geometry and Wireless Networks: Volume : THEORY. Now Publishers Inc, 9, vol.. [] M. Haenggi, Stochastic Geometry or Wireless Networks. Cambridge University Press,. [] 3GPP, 3GPP TR 5.87 V.. -9 High Speed Packet Access HSDPA multipoint transmission. Technical Speciication,. [3] W. C. Cheung, T. Q. Quek, and M. Kountouris, Throughput optimization, spectrum allocation, and access control in two-tier emtocell networks, IEEE J. Sel. Areas Commun., vol. 3, no. 3, pp ,. [4] J.-S. Ferenc and Z. Ne da, On the size distribution o Poisson Voronoi cells, Physica A: Statistical Mechanics and its Applications, vol. 385, no., pp , 7. [5] Y. Zhong and W. Zhang, Multi-channel hybrid access emtocells: a stochastic geometric analysis, IEEE Trans. Commun., vol. 6, no. 7, pp , 3. [6] V. M. Prabhakaran, R. Puri, and K. Ramchandran, Hybrid digital-analog codes or source-channel broadcast o Gaussian sources over Gaussian channels, IEEE Trans. In. Theory, vol. 57, no. 7, pp ,. [7] Y. Kochman and R. Zamir, Analog matching o colored sources to colored channels, IEEE Trans. In. Theory, vol. 57, no. 6, pp ,. [8] M. Wildemeersch, T. Q. Quek, M. Kountouris, A. Rabbachin, and C. H. Slump, Successive intererence cancellation in heterogeneous networks, IEEE Trans. Commun., vol. 6, no., pp , 4. [9] X. Xu, D. Gunduz, E. Erkip, and Y. Wang, Layered cooperative source and channel coding, in Proc. IEEE Intl. Con. on Communications, 5, pp. 4. [3] H. Cui, R. Xiong, C. Luo, Z. Song, and F. Wu, Denoising and resource allocation in uncoded video transmission, IEEE J. Sel. Topics Signal Process., vol. 9, no., pp., 5. Liang Wu received his B.S. degree in Electronic Engineering rom Jilin University in, Jilin, China. He is now a Ph.D. student in Electronic Engineering at University o Science and Technology o China, Heei, China. His research interests include heterogeneous cellular networks, scalable video transmission, wireless caching and stochastic geometry.

15 5 Yi Zhong S, M 5 received his B.S. and Ph.D. degree in Electronic Engineering rom University o Science and Technology o China USTC in and 5 respectively. From August to December, he was a visiting student in Pro. Martin Haenggi s group at University o Notre Dame. From July to October 3, he worked as an intern in Qualcomm, Corporate Research and Development, Beijing. Now, he is a PostDoctoral research ellow with Singapore University o Technology and Design in the WNDS group led by Pro. Tony Q.S. Quek. His research interests include heterogeneous and emtocelloverlaid cellular networks, wireless ad hoc networks, stochastic geometry and point process theory. Wenyi Zhang S, M 7, SM is with the aculty o the Department o Electronic Engineering and Inormation Science, University o Science and Technology o China. Prior to that, he was ailiated with the Communication Science Institute, University o Southern Caliornia, as a postdoctoral research associate, and with Qualcomm Incorporated, Corporate Research and Development. He studied at Tsinghua University Bachelor s degree in Automation, in, and the University o Notre Dame, Indiana, USA Master s and Ph.D. degrees, both in Electrical Engineering, in 3 and 6, respectively. Martin Haenggi S-95, M-99, SM-4, F-4 is the Frank M. Freimann Proessor o Electrical Engineering and a Concurrent Proessor o Applied and Computational Mathematics and Statistics at the University o Notre Dame, Indiana, USA. He received the Dipl.-Ing. M.Sc. and Dr.sc.techn. Ph.D. degrees in electrical engineering rom the Swiss Federal Institute o Technology in Zurich ETH in 995 and 999, respectively. Ater a postdoctoral year at the University o Caliornia in Berkeley, he joined the University o Notre Dame in. In 7-8, he spent a Sabbatical Year at the University o Caliornia at San Diego UCSD. For both his M.Sc. and Ph.D. theses, he was awarded the ETH medal, and he received a CAREER award rom the U.S. National Science Foundation in 5 and the IEEE Communications Society Best Tutorial Paper award. He served an Associate Editor o the Elsevier Journal o Ad Hoc Networks rom 5-8, o the IEEE Transactions on Mobile Computing TMC rom 8-, and o the ACM Transactions on Sensor Networks rom 9-, as a Guest Editor or the IEEE Journal on Selected Areas in Communications in 8-9 and the IEEE Transactions on Vehicular Technology in -3, and as a Steering Committee Member or the TMC. Presently he is the chair o the Executive Editorial Committee o the IEEE Transactions on Wireless Communications. He also served as a Distinguished Lecturer or the IEEE Circuits and Systems Society in 5-6, as a TPC Co-chair o the Communication Theory Symposium o the IEEE International Conerence on Communications ICC, and as a General Co-chair o the 9 International Workshop on Spatial Stochastic Models or Wireless Networks SpaSWiN 9 and the DIMACS Workshop on Connectivity and Resilience o Large-Scale Networks, and as the Keynote Speaker o SpaSWiN 3. He is a co-author o the monograph Intererence in Large Wireless Networks NOW Publishers, 9 and the author o the textbook Stochastic Geometry or Wireless Networks Cambridge University Press,. His scientiic interests include networking and wireless communications, with an emphasis on ad hoc, cognitive, cellular, sensor, and mesh networks.