Resistencia y especificaciones

Device-to-Device (D2D) discovery is the inextricable prelude for the direct exchange of localized traffic between cellular users in proximity (D2D communications). The D2D discovery process can be based on either autonomous actions taken by D2D-enabled devices (direct D2D discovery), or core network functionalities to estimate proximity between D2D-enabled peers (network-assisted D2D discovery). A key advantage of the latter is its potential to exploit fundamental knowledge on the cellular network layout towards better handling with the energy, signaling, and interference burden for D2D discovery. In this paper, we analyze the performance of network-assisted D2D discovery in random spatial networks and derive useful design guidelines for fine-tuning its performance. Specifically, we derive the distance distribution between two D2D peers conditioned on the core network's knowledge on the cellular network layout, assuming that the base stations are distributed according to a Poisson point process. The derived expressions are used for analyzing the behavior of the D2D discovery probability with respect to key system parameters, as well as for identifying conditions under which D2D discovery probability is maximized with respect to the BS density. Exact and approximate expressions for the optimal BS density are also derived. Numerical results validate the accuracy of our findings and provide valuable insights on the performance tradeoffs inherent to network- assisted D2D discovery.

The remainder of this paper is organized as follows. In section 3.1, we present our system model and assumptions, while in section 3.2 we derive analytical expressions for the conditional pdf and ccdf of the distance between two D2D peers given certain combinations of location information parameters. In section 3.3, we investigate how the BS density affects the D2D discovery probability and derive analytical expressions for computing the optimal BS density (when relevant). The impact of the key system parameters on the D2D discovery performance is assessed in Section 3.4, where we additionally provide useful design guidelines for network-assisted D2D discovery. Section 3.5 concludes our work.

3.1 System Model

3.1.1 Performance Metrics

Since, the performance of D2D discovery is tightly coupled with the definition of proximity between D2D peers [127], in this work we consider that two D2D- enabled devices are in proximity whenever the long-term averaged received signal power from the D2D source is greater than or equal to the receiver sensitivity at the D2D target. We choose to follow this definition for two main reasons. Firstly, the D2D discovery process is most likely to be based on the long-term average and not the instantaneous received power at the D2D target, i.e. small-scale fading is averaged out. Secondly, this notion of proximity is closer to the one used between the user equipments and the cellular BSs during cell search [93]. Assuming that the path loss is inversely proportional to the distance between the D2D peers and governed by a path loss exponent , the D2D discovery probability is defined as

≜ [ ≥ | ], (3.1) where denotes the available knowledge on the cellular network layout (at the EPC), the transmit power at the D2D source, the receiver sensitivity at the D2D target, and the distance between the D2D peers. The receiver sensitivity is typically fixed and depends on the system parameters that specify the reference measurement channel [128], e.g. duplexing mode and bandwidth. By rearranging (3.1), it can be easily shown that the D2D discovery probability corresponds to the cdf of the distance at the point , conditioned on the available knowledge at the EPC.

3.1.2 System Description

We consider a D2D-enabled cellular network, where the locations of all cellular BSs, including both macrocells and small cells, are distributed according to a homogeneous PPP Φ with intensity in the Euclidean plane. Without assuming a specific distribution for the users, we consider that a) the Point Process Φ describing the user locations is stationary and isotropic, and b) the and coordinates of a tagged user are independent of those of other users in Φ . We consider that all users associate with the nearest BS in Φ [94] and focus on the network-assisted D2D discovery process between a tagged user, referred to as

D2D source, and a (specific) target D2D-enabled user, referred to as D2D target.

We further focus on the scenario where the network is capable of identifying the associated BS of the D2D peers, and utilize UE and BS positioning measurements to enhance the performance of D2D discovery.

Table 6: Cellular-based Location Information Parameters

Parameter Notation Estimation methodology

Distance between the D2D source and

its associated BS

By using Timing Advance measurements at the respective BS (standard capability in LTE/LTE-A [16]).

Angle between the D2D source and its

associated BS

By performing AoA measurements at the associated BS of the D2D source with respect to the reference direction from the associated BS of the D2D source to the associated BS of the D2D target. AoA is a standard measurement capability in LTE/LTE-A [16].

Distance between the D2D target and

its associated BS

In a similar manner with the estimation of .

Angle between the D2D target and its

associated BS

By exploiting AoA measurements at the associated BS of the D2D target, similarly to the estimation of .

Neighboring degree between the associated BS of the

D2D source and the associated BS of the

By utilizing knowledge from the network planning phase or by performing Timing Advance measurements for the associated BS of the D2D target. This estimation can also be based on the RSRP from the associated BS of the D2D target [16].

D2D target Inter-site distance

between the associated BS of the

D2D source and the associated BS of the

D2D target

By using a similar methodology with the estimation of . However, comparably higher accuracy is required.

Table 6 lists the measurements considered in this paper and highlights how they can be performed in LTE/LTE-Advanced. Note that we do not assume that all of these measurements are available to the EPC. Instead, we investigate how certain combinations of these measurements (location information parameters) can enhance the network-assisted D2D discovery process at the EPC. Figure 17 depicts all parameters and random variables involved in our analysis. The following lemma states that, if not fixed and known at the EPC, the distance between a random point in the system and its -th nearest (neighboring) BS in Φ follows a generalized Gamma distribution.

Figure 17: System model parameters and related Random Variables

Lemma 3.1. The pdf ( ) of the distance between a random point in the system and the -th neighboring BS in the PPP is given by

( ) = ( )

[ ] , (3.2)

where Γ[ ] is the Gamma function.

Proof. The proof is derived by using Slivnyak's theorem and the result in [96].

□ Lemma 3.1 provides the pdf of the inter-site distance between a tagged BS and its -th neighbor. However, for = 1, it also provides the pdf of the distances

and : Rayleigh-distributed RVs with parameter = . If not fixed and known at the EPC, in a similar manner with [129], we assume that the angles and satisfy the following property:

Assumption 3.1. The angle between the D2D source and its associated BS as