**3. System model**

The energy minimization problem in a WSN is considered. The data is to be delivered to the BS from *K* SNs distributed throughout the cell area of the BS. The SNs can communicate with the BS using a long range communication technology (e.g., UMTS/HSPA, WiMAX, or LTE), or with neighboring SNs using a short range technology (e.g., Bluetooth or WLAN). SNs form cooperating clusters for the purpose of energy minimization during cooperative

**Figure 1.** System model when multihop communications are allowed.

4 Will-be-set-by-IN-TECH

of IP addresses, which provides layer-2 multihop communication. A survey of the unicast admission control schemes designed for IEEE 802.11-based multi-hop mobile ad-hoc networks (MANETs) is presented in [10], where different admission control protocols are discussed and analyzed. In [27], cooperative rate adaptation in multihop IEEE 802.11 is considered. The problem is formulated as an optimization problem and shown to be NP-hard. Thus, a suboptimal method is presented. Energy efficiency is considered in terms of reducing the transmission power at the SNs' antennas. Enhancements of the performance of IEEE 802.11-based multihop ad hoc wireless networks from the perspective of spatial reuse were surveyed in [2]. Techniques adopting transmit power control, tuning the carrier sensing threshold, performing data rate adaptation, and using directional antennas were discussed. In this Chapter, the presented approach is general and not confined to a particular standard, it does not only consider transmit energy at the antenna, but also the energy drained from the battery during transmission and reception. Compared to mesh networks, not every SN needs to communicate with all other SNs. Instead, each SN needs to transmit the measured data using an optimum energy minimizing path to the BS. This path remains the same as long as

In addition to multihop, energy efficient clustering methods are also investigated in the literature. An algorithm is presented in [14] as an improvement on the methods in [12] and [15]. In [12, 14, 15], each node volunteers to be a cluster head in a probabilistic manner, and non-cluster nodes associate themselves with cluster heads based on the announcements received from these cluster heads. The actual energy drained from the battery of the device is considered. However, the problem is not formulated and solved as an optimization problem (as in this Chapter), but rather an efficient clustering algorithm that ensures fairness in energy consumption between nodes, due to the probabilistic selection, is presented. In [15], the use of a proxy node was added to the approach of [12], whereas in [14] the additional use of a main cluster head was implemented, with the main cluster head relaying the data from cluster heads to the BS. The work of [12] was extended in [4] to include multihop communications in addition to clustering. In addition, an approach to determine the optimal number of cluster heads is proposed. Clustering is performed on distance based criteria and a probabilistic random approach is adopted for the election of cluster heads. A cluster head selection based on proximity was adopted in [30], where the residual energy of the node is also considered in the selection process. A multihop time reservation using adaptive control for energy efficiency (MH-TRACE) is presented in [24]. Cluster formation is probabilistic and it is not based on connectivity information. In MH-TRACE, the interference level in the different time-frames is monitored continuously in order to minimize the interference between clusters. MH-TRACE clusters use the same spreading code or frequency and time division is adopted. In this Chapter, cluster head selection is not probabilistic or simply proximity based. Fading is considered in the selection approach since CSI affects the achievable rates and is thus

The energy minimization problem in a WSN is considered. The data is to be delivered to the BS from *K* SNs distributed throughout the cell area of the BS. The SNs can communicate with the BS using a long range communication technology (e.g., UMTS/HSPA, WiMAX, or LTE), or with neighboring SNs using a short range technology (e.g., Bluetooth or WLAN). SNs form cooperating clusters for the purpose of energy minimization during cooperative

the channel conditions remain constant.

incorporated in the optimization problem.

**3. System model**

data transmission. Within each cooperating cluster, the data is delivered from the SNs in that cluster to the BS using multihop communications. Fig. 1 shows the scenario considered. The maximum number of hops allowed *H* can be specified as a parameter. With two-hop communications (case *H* = 2), the problem becomes a clustering problem that consists of finding the best grouping of SNs into cooperating clusters, as shown in Fig. 2.

Each SN transmits its measured data to a single destination, which could be either the BS or another SN. We consider the energy minimization problem with multihop/clustering. The BS and SNs are denoted as "nodes", with node *k* = 0 corresponding to the BS and nodes *k* = 1, ...,*K* corresponding the SNs. As shown in Fig. 1, these nodes appear to form a direct

**Figure 2.** System model when 2-hops (clustering only) are allowed.

acyclic graph (DAG) starting from the node *k* = 0. If node *j* receives the data of node *k* on hop *h*, a parameter *α<sup>h</sup> kj* is set to one, marking the existence of an edge in the graph between *k* and *j*. Otherwise, *α<sup>h</sup> kj* is set to zero.

We define C*<sup>j</sup>* as the set of children of *j*, i.e., the set of nodes sending their data directly to *j*:

$$\mathcal{C}\_{\hat{\jmath}} = \left\{ k\_{\prime} \sum\_{h=1}^{H} a\_{kj}^{h} = 1 \right\} \tag{1}$$

The set D*<sup>j</sup>* is defined as the sub-DAG starting from *j*, i.e., having *j* as its root. It includes *j*, its children, the children of its children, etc. Thus, it can be expressed as:

$$\mathcal{D}\_{\hat{j}} = \{\hat{j}\} \cup \bigcup\_{k \in \mathcal{C}\_{\hat{\mathbb{L}}}} \mathcal{D}\_{k} \tag{2}$$

### **3.1. Data rates**

6 Will-be-set-by-IN-TECH

**Figure 2.** System model when 2-hops (clustering only) are allowed.

*kj* is set to zero.

*h*, a parameter *α<sup>h</sup>*

Otherwise, *α<sup>h</sup>*

acyclic graph (DAG) starting from the node *k* = 0. If node *j* receives the data of node *k* on hop

We define C*<sup>j</sup>* as the set of children of *j*, i.e., the set of nodes sending their data directly to *j*:

 *k*, *H* ∑ *h*=1 *αh kj* = 1

C*<sup>j</sup>* =

*kj* is set to one, marking the existence of an edge in the graph between *k* and *j*.

(1)

Server

Wired LAN

Given for each node: the transmit power *Pt*,*kj* that node *k* is using in order to transmit to node *j*, the channel gain *Hkj* of the channel between *k* and *j*, and the thermal noise power *σ*2, the received signal-to-noise ratio (SNR) *γkj* on the link between *k* and *j* can be calculated following *<sup>γ</sup>kj* <sup>=</sup> *Pt*,*kjHkj <sup>σ</sup>*<sup>2</sup> . Given the target bit error rate *Pe* and the SNR, the bit rates on the link between any two nodes *k* and *j* can be calculated as follows:

$$R\_{k\dot{j}} = W\_{k\dot{j}} \cdot \log\_2(1 + \beta \gamma\_{k\dot{j}}) \tag{3}$$

In (3), *Wkj* is the passband bandwidth of the channel between *k* and *j*, and *β* is called the SNR gap. It indicates the difference between the SNR needed to achieve a certain data transmission rate for a practical M-QAM system and the theoretical Shannon limit [9, 21]. It is given by: *<sup>β</sup>* <sup>=</sup> <sup>−</sup>1.5 ln(5*Pe*) . The channel gain is expressed as:

$$H\_{kj, \text{dB}} = (-\kappa - \upsilon \log\_{10} d\_{kj}) - \mathfrak{f}\_{kj} + 10 \log\_{10} F\_{kj} \tag{4}$$

In (4), the first factor captures propagation loss, with *dkj* the distance between nodes *k* and *j*, and *υ* the path loss exponent. The second factor, *ξkj*, captures log-normal shadowing with a standard deviation *σξ* , whereas the last factor, *Fkj*, corresponds to Rayleigh fading (generally considered with a Rayleigh parameter *a* such that *E*[*a*2] = 1).

### **4. Multihop problem formulations**

With each SN transmitting the data in blocks of size *ST* bits, the time needed to transmit this content on a link between nodes *k* and *j* having an achievable rate *Rkj* bps is given by *ST*/*Rkj*. Denoting the power drained from the battery of node *j* to receive the data from node *k* by *P*Rx,*kj*, then the energy consumed by *j* to receive the data from *k* is given by *ST* · *P*Rx,*kj*/*Rkj*. Similarly, denoting by *P*Tx,*kj* the power drained by the battery of node *k* to transmit the data to node *j*, then the energy consumed by *k* to transmit the content to *j* is given by *ST* · *P*Tx,*kj*/*Rkj*. It should be noted that *P*Tx,*kj* can be expressed as:

$$P\_{\text{Tx},kj} = P\_{\text{Tx}\_{\text{nt}},kj} + P\_{t,kj} \tag{5}$$

where *P*Txref,*kj* corresponds to the power consumed by the circuitry of node *k* during transmission on the communication interface with node *j*, and *Pt*,*kj* corresponds to the power transmitted over the air on the link from node *k* to node *j*.

In this section, a flexible formulation is presented that accommodates power adaptive or rate adaptive transmission. In the case of adaptive rate control, the node transmit power is

#### 8 Will-be-set-by-IN-TECH 172 Wireless Sensor Networks – Technology and Protocols

constant, i.e., *Pt*,*kj* = *Pt* and *P*Tx,*kj* = *P*Tx. Consequently, the rate *Rkj* on the link between nodes *k* and *j* is the rate achievable with the transmit power *Pt*. It is varied adaptively depending on the channel conditions between nodes *k* and *j*. High data rates result in low energy per bit consumption, thus leading to a gain in total energy consumption. For example, the WLAN technologies apply rate control [11].

In the case of adaptive power control, the nodes communicate at a constant rate *R*0*<sup>j</sup>* = *R*<sup>L</sup> on the LR or *Rkj* = *R*<sup>S</sup> (with *k >* 0) on the SR. The transmit power *Pt*,*kj* is varied adaptively depending on the channel conditions between nodes *k* and *j* in order to achieve the target data rate *R*<sup>L</sup> or *R*S. Thus, nodes that are in proximity of each other will communicate with lower power than nodes that are further apart. This will result in a reduction of consumed energy. Some technologies such as Bluetooth apply power control [5].

Hence, the energy consumed during cooperative multihop content distribution can be expressed as follows:

$$\begin{aligned} E\_{\text{coop}} &= S\_T \cdot \sum\_{k=1}^K \sum\_{j=0, j \neq k}^K \sum\_{h=1}^H \frac{a\_{kj}^h \cdot |\mathcal{D}\_k| \cdot P\_{\text{Tx}, kj}}{R\_{kj}} \\ &+ S\_T \cdot \sum\_{k=1}^K \sum\_{j=1, j \neq k}^K \sum\_{h=1}^{H-1} \frac{a\_{kj}^h \cdot |\mathcal{D}\_k| \cdot P\_{\text{Rx}, kj}}{R\_{kj}} \\ &= S\_T \cdot \sum\_{k=1}^K \sum\_{j=0, j \neq k}^K \sum\_{h=1}^H \frac{a\_{kj}^h \cdot |\mathcal{D}\_k| \cdot (P\_{\text{Tx}, kj} + P\_{\text{Rx}, kj})}{R\_{kj}} \end{aligned} \tag{6}$$

where the first term corresponds to the energy consumed by the nodes for transmission and the second term corresponds to the energy consumed by the nodes for reception. Hop *h* = *H* corresponds to transmission on the LR and node *k* = 0 corresponds to the BS. The multiplication by |D*k*|, with |·| denoting set cardinality, is used to indicate that an SN aggregates the data of its sub-DAG before transmitting it on the next hop. To be able to write the last equality in (6), it is assumed that *P*Rx,*k*<sup>0</sup> = 0 for all *k*. This corresponds to excluding the energy consumed at the BS to receive the data at hop *H*. In fact, power consumption of the BS is not considered in the energy minimization process since the interest is in the battery life of the SNs. This is justified by the fact that most BSs rely on power line cables and not on batteries and thus do not have as stringent power limitations as the SNs.

Consequently, the optimization problem can be formulated as follows:

$$\min\_{\mathcal{A}}\ E\_{\text{coop}} = \mathcal{S}\_T \cdot \sum\_{k=1}^{K} \sum\_{j=0, j \neq k}^{K} \sum\_{h=1}^{H} \frac{a\_{kj}^{h} \cdot |\mathcal{D}\_k| \cdot (P\_{\text{Tx},kj} + P\_{\text{Rx},kj})}{R\_{kj}} \tag{7}$$

subject to

$$\mathfrak{a}\_{k0}^{h} = 0 \text{ for } h < H \text{ and } k = 1, \ldots, K \tag{8}$$

$$\sum\_{j=0}^{K} \sum\_{h=1}^{H} \alpha\_{kj}^{h} = 1 \text{ for } k = 1, \dots, K \tag{9}$$

$$a\_{kj}^h \in \{0, 1\} \forall k \text{ } j, h \tag{10}$$


**Table 1.** Parameter Values in Different Scenarios

8 Will-be-set-by-IN-TECH

constant, i.e., *Pt*,*kj* = *Pt* and *P*Tx,*kj* = *P*Tx. Consequently, the rate *Rkj* on the link between nodes *k* and *j* is the rate achievable with the transmit power *Pt*. It is varied adaptively depending on the channel conditions between nodes *k* and *j*. High data rates result in low energy per bit consumption, thus leading to a gain in total energy consumption. For example,

In the case of adaptive power control, the nodes communicate at a constant rate *R*0*<sup>j</sup>* = *R*<sup>L</sup> on the LR or *Rkj* = *R*<sup>S</sup> (with *k >* 0) on the SR. The transmit power *Pt*,*kj* is varied adaptively depending on the channel conditions between nodes *k* and *j* in order to achieve the target data rate *R*<sup>L</sup> or *R*S. Thus, nodes that are in proximity of each other will communicate with lower power than nodes that are further apart. This will result in a reduction of consumed energy.

Hence, the energy consumed during cooperative multihop content distribution can be

*αh*

*H*−1 ∑ *h*=1

*αh*

where the first term corresponds to the energy consumed by the nodes for transmission and the second term corresponds to the energy consumed by the nodes for reception. Hop *h* = *H* corresponds to transmission on the LR and node *k* = 0 corresponds to the BS. The multiplication by |D*k*|, with |·| denoting set cardinality, is used to indicate that an SN aggregates the data of its sub-DAG before transmitting it on the next hop. To be able to write the last equality in (6), it is assumed that *P*Rx,*k*<sup>0</sup> = 0 for all *k*. This corresponds to excluding the energy consumed at the BS to receive the data at hop *H*. In fact, power consumption of the BS is not considered in the energy minimization process since the interest is in the battery life of the SNs. This is justified by the fact that most BSs rely on power line cables and not on

*αh*

*kj* · |D*k*| · *P*Tx,*kj Rkj*

> *kj* · |D*k*| · *P*Rx,*kj Rkj*

*kj* · |D*k*| · (*P*Tx,*kj* + *P*Rx,*kj*) *Rkj*

*kj* · |D*k*| · (*P*Tx,*kj* + *P*Rx,*kj*) *Rkj*

(6)

(7)

*H* ∑ *h*=1

*H* ∑ *h*=1

the WLAN technologies apply rate control [11].

expressed as follows:

Some technologies such as Bluetooth apply power control [5].

+ *ST* ·

= *ST* ·

min*<sup>α</sup> <sup>E</sup>*coop <sup>=</sup> *ST* ·

subject to

*H* ∑ *h*=1 *αh*

*αh*

*K* ∑ *j*=0

*αh*

*K* ∑ *k*=1

*K* ∑ *k*=1

batteries and thus do not have as stringent power limitations as the SNs. Consequently, the optimization problem can be formulated as follows:

> *K* ∑ *k*=1

*K* ∑ *j*=0,*j*�=*k*

*H* ∑ *h*=1 *αh*

*<sup>k</sup>*<sup>0</sup> = 0 for *h < H* and *k* = 1, ..., *K* (8)

*kj* ∈ {0, 1}∀*k*, *j*, *h* (10)

*kj* = 1 for *k* = 1, ..., *K* (9)

*K* ∑ *k*=1

*K* ∑ *j*=0,*j*�=*k*

*K* ∑ *j*=0,*j*�=*k*

*K* ∑ *j*=1,*j*�=*k*

*E*coop = *ST* ·

The first constraint (8) indicates that transmissions to the BS take place at the last hop *h* = *H* only. The second constraint (9) indicates that each SN should transmit its collected data exactly once to a single destination on one of the *H* hops (hop *H* on the LR and *H* − 1 hops on the SR). Finally, constraint (10) specifies that the optimization variable *α<sup>h</sup> kj* is a binary variable.

In the problem formulated in (7), the maximum number of hops can be specified as a parameter. Setting *H* = *K* allows full multihop communications, although the actual hops might be less than *K*, and in this case the parameters *α<sup>h</sup> kj* corresponding to the unnecessary hops will be set to zero in the optimal solution. Setting *H* = 2 corresponds to reducing the problem into a clustering problem where SNs are grouped into clusters. In each cluster, an SN selected as cluster head (CH) in the optimal solution sends the data on the LR to the BS after aggregating the data it receives on the SR from the SNs in its cluster. Furthermore, setting *H* = 1 corresponds to the non-cooperative approach where all SNs send the data on the LR to the BS. In this case, the energy is denoted by *E*No−coop. The normalized energy consumption *η* can be calculated as follows:

$$\eta = \frac{E\_{\text{coop}}}{E\_{\text{No-coop}}} \tag{11}$$

The value of *η* indicates whether the cooperation is beneficial in terms of energy consumption or not; if *η <* 1, then the cooperation results in a gain of energy consumption while *η >* 1 reflects a non-beneficial cooperation.

The formulation in (7) is applicable to any number of hops, allows communication using different wireless interfaces (different values of *P*Rx,*kj* and *P*Tx,*kj* can be set for each wireless link between any two nodes *k* and *j*), and permits any combination of power adaptive/rate adaptive transmissions. For example, a node may be transmitting to its parent in the DAG using rate adaptive transmission while another can be using power adaptive transmission. The values of the parameters in the different implementation scenarios are detailed in Table 1. Using, for each node in the network, the appropriate parameters from Table 1 according to its communication scheme adopted, then the formulation (7) can be customized to a huge variety of node combinations and hybrid wireless interfaces.

The problem formulated in (7) appears as a binary integer program that can be solved using known software solvers. However, this is not the case due to the dependence of |D*k*| on the parameters *α<sup>h</sup> kj*, which makes the problem intractable. In addition, even when the problem can be considered as a binary integer program, the complexity of finding the optimal solution of the problem (7) using software solvers increases tremendously when the number of nodes increases and is not suitable for real time implementation. In fact, binary integer programming is known to be NP-hard. In the next section, low complexity suboptimal schemes are presented that are able to achieve efficient multihop routing of sensor data with significant energy savings compared to the non-cooperative approach.
