Device to device communication as an underlay to cellular networks [22] is ongoing stan- dardization in LTE-A [25]. In addition, studying D2D using stochastic geometry tool is fairly a new topic. A recent work by the authors in [194] investigate the inter-tier and intra-tier interferences in D2D underlaying cellular networks, taking into consideration the specific radio channel properties of D2D. On the other hand, several works related to het- erogeneous cellular networks are presented in the literature. For example the authors in [3] derive a mathematical framework for predicting the SINR in a cellular network for the
downlink direction assuming that base stations are distributed according to a PPP. While the authors in [88,89] are utilizing α-Ginibre point process, rather than PPP due to the for- mer capability of modeling the spatial mutual repulsion of base stations, aiming to resemble the actual deployment of base stations more accurately. Accordingly, the study derives a computable coverage probability in multi-tier networks.
Studying multi-tier cellular network using stochastic geometry is gaining an increasing popularity, with the recent emphasis on heterogeneous base stations deployment in modern cellular networks. For example, the authors in [85] are also deriving a tractable expression for the SINR resulting from a multi-tier cellular network. Most of the literature papers assume a certain coordination between the transmitting nodes (or base stations) in order to mitigates mutual interference. The authors in [192] are focussing on this issue by studying the capability of cognitive femtocell in achieving high spectrum reuse gain in a two-tier cellular network.
On the other hand, the authors in [107] address the two-hop cellular system and obtain its outage probability. The first hop starts from the cellular base station, while the second one forwards the traffic via a relay node to farther terminals located in dead spots, they assume that cellular base stations are deployed in a deterministic square lattice layout, while users have a PPP distribution. The effect of relays mobility is addressed in [105], where the authors study the theoretical coverage and capacity extensions using mobile relays. The focus of the section is the impact of mobility on the probability of route establishment and the expected availability duration. The section addresses a single cell with idealized circular coverage area, while here we address the network-level performance of D2D relays in extending network coverage during disasters.
The work in [103] derives mathematical expressions for the downlink coverage and ca- pacity of two-hop cellular networks utilizing tools from stochastic geometry, while in our analysis we deal with both the downlink and the uplink connections in order to estimate the network-level performance, in addition we analyse the coverage expansion resulting from n-hop relays. The work in [104] addresses the expansion of cellular network coverage us- ing relay nodes aiming to find the optimum relay location within a cell, where the utilized simulation scenario constitute of a single circular cell. Similarly the work in [106] tries to optimize the deployment locations of relays within a hexagonal cell using brute-force simulation. While a step further is taken in [195] for providing a methodology to calcu- late the coverage and spectral efficiency resulting from a multi-hop cellular network using simulation, where base stations are deployed in a deterministic lattice layout.
the network performance covering both single hop and multi-hop scenarios using stochastic geometry tools. The network performance takes into consideration both uplink and down- link connections. In addition, we introduce a novel expression that describes the chain-relay success probability in a series form. To the best of our knowledge, the available litera- ture does not explicitly quantify the alleviation of the network damage when utilizing D2D technique.
4.1.2
System Model
Our study focusses on Frequency Division Duplex (FDD) implementation under LTE-A, where the downlink and the uplink utilize two separate frequency bands denoted here as fUL
and fDL. It is well known that LTE is based on the Orthogonal Frequency Division Multiple
Access (OFDMA) technology that allows the utilization of a unity cellular frequency reuse factor. In order to allow this high reuse scheme, several interference mitigation techniques are implemented within LTE-A, exploiting the ability of OFDMA technology in assigning adjacent and granular portions of the radio resource to different users. Accordingly, for a transitional area between two cells (that is the most affected area by interference), base sta- tions use coordinated frequency-time radio resources assignments for UEs inside these areas in order to mitigate intercell interference [196]. Several other techniques are introduced in LTE-Advanced under the name (eICIC) Enhanced Intercell Interference Coordination [97], that further mitigate the possible interference in heterogeneous networks. In this section we use the term interference mitigation factor ηbto denote the virtual reduction of the interfer-
ing base stations power due to the interference mitigation techniques.
Another important point in our model is that D2D communication is taking place only in the fULfor both directions of communication, as it was decided by 3GPP [25]. In this work
we assume that the relaying UE denoted as (UEr) is located within the network coverage and is operating as a decode-and-forward relay node for helping a farther UE that is located outside the cellular coverage area, having a Signal to Interference plus Noise Ratio (SINR) below a certain threshold Θ i.e. (SINR < Θ). Moreover we assume that the latter UE can also play the role of a relay node, thus even helping more farther UEs and so on, forming a multi-hop relay chain as depicted in Fig. 4.3.
In a similar manner to the intercell interference coordination, D2D communication can favor a certain interference mitigation factor ηr, by exploiting multiple-access spectrum
sharing between the neighbouring D2D transmitters that can take place either in a coordi- nated manner or in uncoordinated manner (when no signaling is required) using spectrum
Fig. 4.3 The relay chain principle, for extending healthy cells coverage.
Table 4.1 Interference Matrix
Spectral Band Main Signal Interferers
fDL eNB to UE Other eNBs
fUL1 UE to eNB Other UEs
fUL2 Device to Device Other D2D Transmitters
sensing [126] and cognitive radio (CR) techniques [165]. A centralized resource coordina- tion might be highly vulnerable to failures during the aftermath of a natural disaster, while the uncoordinated CR techniques, would be more resistant to such disasters. We model the effect of this self-organized spectrum sharing using the interference mitigation factor ηr,
assuming that D2D devices can transmit in slotted time periods.
In this study we assume that the uplink communication from the UEs to their serving eNB can only occur in the a sub-band designate as fUL1 while device to device communi-
cation takes place in another sub-band designated as fUL2. The reason for this separation
is that the coordinated spectrum sharing between the cellular network and the underlay- ing D2D might not be possible in all situations, especially during the partial failure of the cellular network. However the assigned spectrum ratio between fUL1 and fUL2 could be
adjusted in a semi-static manner whenever the network conditions allow. Fig. 4.4 depicts the proposed spectrum sharing concept. In fact, implementing this scheme is a straightfor- ward task in OFDM-based wireless systems, by assigning different number of subcarriers to D2D connections and to the cellular uplink connections. Although this scheme might result lower spectrum efficiency than centralized resource management, however, the urgency of re-establishing network coverage during the aftermath of a natural disaster supersedes the importance of spectrum efficiency. The possible interference matrix between the different network nodes is listed in Table4.1and depicted in Fig. 4.5.
Fig. 4.4 The proposed semi-static spectrum allocation.
In order to model the effect of a natural disaster on the wireless network we propose a damage ratio denoted as D ∈ [0,1] that represents the percentage of the phased out base stations over the total number of base stations. Mathematically speaking, if the density of base stations prior a disaster was λb, then in case that a disaster has occurred, a thinning
factor [197] of (1 −D) will affect the original base station density and the resulting new density will become (1 −D)λb. The implicit assumption of the random BS phase-out pro-
cess is due to the inherited random nature of the effect of natural disasters. While utilizing stochastic geometry will allow capturing the average behaviour of the network before and during the natural disaster. This random phase-out scheme allows tractable analysis and for- mulation of the network performance. While, for comparison purposes, we explore another phase-out process in Section4.1.11assuming that the effect of a disaster is propagating in a radial manner out of the central point of the disaster, where base stations are phased-out in non-random manner.
For studying the performance of the network during a natural disaster, we obtain the network performance behaviour in terms of the service success probability for a range of damage ratio D. As the thinning of a PPP will yield another PPP [80], the cellular base stations after the disaster will still follow a PPP when randomly phased-out.