and energy efficiency in cognitive-femtocell networks under macrocell infrastructure

The network coverage and energy ef ﬁ ciency issues in heterogeneous cognitive-femtocell networks over the macrocell network is studied. Cognitive functions in wireless network nodes are serviceable with the macrocell infrastructure to achieve a balance between two desirable but incompatible features: coverage and energy ef ﬁ ciency. There are two basic but related aspects of cognitive radios (CRs) in the context of wireless communications: optimum CRs for energy ef ﬁ ciency and the act of the functioning of CRs with energy ef ﬁ ciency. To fully utilise the cognitive capability, a dual-tier network architecture is assumed where both the macrocell and the femtocell have a bearing on the cognitive capability. Owing to the salient features of femtocells, they can improve the coverage and enhance the spectrum ef ﬁ ciency by reutilising the frequency spectrum allocated to the macrocell, although, the resulting intercell interference accompanied by the same frequency coverage cannot be underestimated. The effectiveness of the scheme is veri ﬁ ed by extensive Matlab simulation.

† We develop a dual-tier network model to provide high-quality coverage to subscribers when the network is suffering from the coverage problem in deep indoor situations, underground structures where the macrocell cannot reach and, particularly, at cell edges where the maximum number of outage users are located due to the large location gap between the service network entity [macro base station (MBS)] and users. † We propose the analytical view of instantaneous received power and interference power to obtain the final expression of the instantaneous signal-to-interference ratio (SIR). The battery draining issue of mobile operators can be eliminated by means of energy efficiency of the networks resulting in prolongation of the battery life of handsets. † We present comprehensive numerical outcomes to vindicate the developed simplified network model and to exhibit the effectiveness of our proposed scheme.
System model: A proper functioning of the system relies on a conversance with the interferences from another transmitter inside its accessibility radius, R ac . Owing to the propagation path loss, a transmitter at the external side of the accessibility area experiences only an insignificant amount of interference. Hence, the purpose is to model a sensible interference-limited environment, and the receiver accessibility radius is accounted to be much higher than the cell radius, that is, R ac . Unity gain omnidirectional antennas are assumed throughout the whole Letter. Here, we assume an interference-limited environment; the quality of a signal received at a receiver is typically measured by means of the obtained SIR, which is basically the ratio of the power of the required signal to the total residue power of the unwanted signals. Let the transmit and the received powers be symbolised by P t and P r , respectively. The path gain between y (the transmitter) and z (the receiver) is symbolised by G yz . For the sake of simplicity, the node is specified by a single subscript x, y, or z, and a double subscript such as xz specifies the connection of a link between the node x and the node z. A node is an entity, either a MBS or a femto base station (BS), which is capable of communicating. For one interfering user y illustrated in Fig. 1 SIR z = P tx G xz P ty G yz (1) Considering fixed transmit powers, P tx = P ty = Const, (1) simplifies to where the path losses between transmitter T Xx and R Xz , T Xy and R Xz are symbolised by L yz and L xz , accordingly. The loss parameter L is expressed in terms of propagation loss, shadowing, and multipath fading.

Fig. 1 Model to derive SIR from single neighbouring cell
The loss parameters for the dual-layer environment [5] can be re-expressed as where C =Ĉ/C in whichĈ is the constant representing the wanted link whereas C is related to the unwanted link which means an interference link. d o is the distance which is constant and d is the distance which is a random variable, γ is the path loss exponent, ξ is the random variable due to shadowing, β = ln(10)/10 and |H( f )| is a random variable modelling the channel envelope. The path loss model considered in this Letter takes into account the incorporation of the large-scale path loss as well as the small-scale fading. Considering, the interference possibility explained in this Section, the path loss for the required path and the path loss between the unwanted (interfering transmitter) y and the receiver z are where d yz is considered to represent the distance between the interference caused by the transmitter x and the fatality receiver y, y xz and y yz are the path loss exponents, ξ xz and ξ yz are the Gaussian distributed random variables representing the shadow fading with zero mean and variances ν xz and ν yz , respectively, and H xz and H yz are the channel envelopes representing the channel fading. Using (3) and (5) From (7), the SIR has six random variable components, , |H xz | and |H yz | Theorem 1 [6]: The coverage probability for a typical portable user connecting to the strongest BS, underestimating noise, and including Rayleigh fading is where C(α ) = 2π 2 csc(2π/α)/α and k represents the number of tiers. Key consideration β i > 1 for each tier guarantees that each mobile has at most one BS at which it associates.
Proof: Initially, considering the coverage probability of the single-tier cellular network (K = 1) is given by P cov (SINR > β) = π /C(α)β 2/α . Note that SINR and SIR can be placed interchangeably since we have considered an interference-limited environment.
From Theorem 1, it also proceeds ahead with an interference-limited condition then P cov max It signifies that the coverage probability is not influenced by the number of tiers. Hence, it is possible to increase the network sum rate by adding the number of BSs in any tier keeping unaffected coverage.
where the energy consumed by the sensing component is symbolised by E s c with the sensing period of T s and the non-sensing components symbolised as E t c and E i c for transmission (if traffic for CFUs) and idling (if no traffic for CFUs), respectively. In reception mode, λ c represents a receiving component if some traffic interrupts where F c is the frequency available for CFBS users.
Proof: Three states responsible for energy consumption are sensing, transmission, and idling. The non-sensing time period can be considered as (T s − 1) for periodic sensing with T s and the non-receiving component in reception mode can be considered as (1 − λ c ) without any traffic interruption. Hence, (10) is justified.
Let n c be considered to be the number of interferers of type y to type z while communicating with type x. In general, the total throughput of the cross-layer network can be considered as C c = T s − 1/T s F c /n clog2 (1 + SIR z ). As per the system model ( Fig. 1), n c = 1, hence, (11) is justified.  Fig. 2 Coverage probabilities for provided area of network (Fig. 2a) and provided coverage radius of network (Fig. 2b) Results and discussion: In this Section, we demonstrate interpretative numerical results to validate the effectiveness of the proposed network model. The network parameters and location of the MBS and the FBS for our simulations are shown in Fig. 1, whereas MBS users and FBS users are randomly located in a 100 × 100 m 2 network grid. In Fig. 2a, the coverage probability of dual-tier networks is shown against the number of mobile users in which different coverage areas are set for simulation. The coverage probability increases gradually at a certain point of time for a particular number of users and then it decreases with a further increase in the number of users by maintaining the same slope where the coverage probability is relatively higher for the 100 × 100 m 2 grid as compared with the 120 × 120 m 2 grid at any instant.
In Fig. 2b, the coverage probability of dual-tier networks is shown against the number of mobile users in which different coverage radii are set for simulation. The coverage probability is higher for a large coverage radius at any instant for a specific number of users.
In Fig. 3a, the energy efficiency of the proposed network is shown against the number of mobile users in which different coverage areas are set for simulation. The energy efficiency increases with increase in the number of users and it is highest for the largest coverage area.  Fig. 3 Energy efficiency for provided area of network (Fig. 3a) and provided coverage radius of network (Fig. 3b) In Fig. 3b, the energy efficiency of the proposed network is shown against the number of mobile users in which different coverage radii are set for simulation. The energy efficiency increases with increase in the number of users and it has the highest value for the largest coverage radius.