In multiple sink-centric cluster WSNs, each sensor node will choose at least one sink as its management sink (also denoted as centric sink). It means that the total coverage area by all sinks should be big enough to cover all sub nodes. In this paper, the reachability is defined as the ratio of the number of nodes reached by any one sink to the total nodes deployed in network. Reachability is similar to connectivity.

The sensor networks should function for as long as possible since it may be inconvenient or impossible to recharge node batteries. Therefore, all aspects of the node, from the hardware to the protocols, must be designed to be extremely energy efficient. In this paper, power efficiency is defined as the mean number of “one-hop” sink (sink to sensor node is one-hop) as each sensor node.

After the implementation of power allocation, each sink obtains an appropriate transmission power for broadcast operations. Sensor nodes may receive the broadcast packets from more than one “one-hop” sink. These nodes need to decide which sink should to be chosen as centric sink. At this time, clustering interference is taking place.

In this paper, we analyze an efficient multiple sink transmission power control scheme for a sink-centric cluster routing protocol in multiple sink wireless sensor networks. All sinks in the network know their location, and at the same time other sink nodes share their location information. Then every sink decides its communication radius by an absolutely distributed algorithm that uses the location information of the other sink nodes.

The rest of the paper is organized as follows. A summary of related work is presented in Section 2. Section 3 describes the system model of the MSCWSNs-PC protocol. Section 4 describes the design of the MSCWSNs-PC protocol in detail. The performance of MSCWSNs-PC is evaluated in Section 5 and compared with its improved versions using simulation. The paper concludes in Section 6 and some possible improvements to MSCWSNs-PC are pointed out.

We assume the WSNs consist of many common sensor nodes and some sink nodes. Each sink node is aware of its own location by using GPS or some other localization mechanism. A sink node broadcasts power control assistant messages (PCAM) to the other sink nodes by one-hop communication. PCAM contains the sender’s location information. We also make some assumptions about the sensor nodes and the underlying network model. For the sink nodes, we assume that all sink nodes can transmit with enough power to reach each other, and that the sink nodes can use a power control scheme to vary the amount of transmission power. Otherwise, each node has the computational power to support different MAC protocols and perform signal processing functions.

In order to obtain satisfactory network connectivity, sink nodes need to negotiate the broadcast radius. A sink node working outside its radio range employs an energy dissipation algorithm to adjust the actual broadcast range.

In [9], the total energy dissipation of node i described as: (1) e i T ( d ) = α d n + βwhere α,β ∈ ℛ are real numbers. β is the overhead energy, representing the sum of the receiver, sensing and computation energy which is a constant value with varying distance d.

A more acknowledged model is proposed in [25]. If node X send a packet with power P_t, which is heard by node Y with power P_r, the following equation holds: (2) P X = P Y   ( λ 4 π d ) n g t   g rwhere λ is the carrier wavelength, d is the distance between the transmitter and the receiver, n is the path loss coefficient, and gt and gr are the antenna gains at the transmitter and receiver. The typical value of n is 2. Usually, λ = LightVelocity/Frequency = 0.1 m or so in 2.4 GHz WSNs applications.

Theorem 1. Consider a set of two sinks in an a×b rectangle work area Z, and a diagonal line l. If the two sinks lie in on different sides of l, the intersections of the two radio range circles must be outside the rectangle work area, at the same time the corresponding diagonal vertex (in same position direction) must be inside the radio range of the sink, or else only the sink nearer to the centre of rectangle needs to work, the radio radius chooses the distance between the farthest vertex and itself.

Proof. Firstly, assume two sinks were deployed at different sides of the diagonal line [see Figure 2(a)], a straight line through the two intersection points E and F, and | S₂ D |> | S₂ C |, | S₁ B |> | S₁ A |, so the intersection of AEFB and EDCF always contains the rectangle work area ABCD. If the corresponding diagonal vertex (in same position direction, such as S₂ and D) is inside the radio range of the sink, the radio range of all sinks contains the whole work area. When two sinks are on the same side, the sink nearer to the centre of rectangle uses the distance between the farthest vertex and itself as radio radius, the other three vertices must be in the radio range. It means that the sink has enough transmission power to cover the whole work area. The other sink does not need to work at this time.

Consider a WSN with two sink nodes, as shown in Figure 2. According to the Theorem 1, the radio radius R_Si in Figure 2(a), i ∈ {1,2}, is given by: (3) { ( x S 1 − x ) 2 + ( y S 1 − y ) 2 = R S 1 2 ( x S 2 − x ) 2 + ( y S 2 − y ) 2 = R S 2 2where (x,y) is a point in the radio range circle. In order to not only minimize the total transmission power, but also ensure the coverage rate of network, we also define f : (4) f = min ∑ i = 1 2 R S i n s.t. ( x S 1 − x A ) 2 + ( y S 1 − y A ) 2 ≤ R S 1 2 ( x S 2 − x C ) 2 + ( y S 2 − y C ) 2 ≤ R S 2 2 0 < x E ,   x F < a y E ≥ b           y F ≤ 0where n is the path loss coefficient in equation (2). R_Si in Figure 2(b), i ∈ {1,2}, is given by: (5) ( x S 2 − x C ) 2 + ( y S 2 − y C ) 2 ≤ R S 2 2

In this paper, we only analyse the conditions of two sinks, more sinks, and so forth.

In MSCWSNs-PC, only one packet frame format need to be defined, which is denoted as the HELLO frame. As shown in Figure 3 the HELLO packet carries the ID and location information of the sender. After the network initialization, each sink first pre-detects its coarse position in the work area, such as topside, underside, leftside or rightside. Let all sink nodes belong to the corresponding set of Topside, Underside, Leftside or Rightside. Each sink knows its neighborhood sink by the process of sink discovery communication between them.

Assume deployment of M sink nodes in an X × Y region of space, denoted as S_i, and the location be set as (x_i,y_i), i ∈ M. Let Z(x,y) be the rectangle area, where x is the length and y is the width. CS(x_i,y_i,r_i) is the circle area, where the point (x_i, y_i) acts as the centre and r_i is the radio radius. To ensure the network’s coverage rate up to 100%, the value r_i, i∈ M, must satisfy the following condition: (6) Z ( X , Y ) ⊂ CS ( x 1 ,   y 1 ,   r 1 ) ∪ CS ( x 2 ,   y 2 ,   r 2 ) ∪ ... ∪   CS ( x M ,   y M ,   r M )

In [26] the network is represented as the graph G = (N,E), where N is a set of m+n nodes (containing m sinks and n sensor nodes), and S⊂N is the set of sink nodes (with |S| = m). The set of weighted edges is denoted as E, and we note di;j as the distance along the shortest path between i and j. With each sink k we associate the Voronoi cluster V_k containing the nodes whose closest sink is k. More formally, a Voronoi cluster V_k is defined as: (7) V k = { i : min j ∈ S   d i , j = d i , k }

In the Voronoi algorithm, each node must be aware of the location of all sink and itself.

In MSCWSNs, firstly each sink pre-detects its coarse position in the work area and the corresponding set of coordinates is (X_Topside, Y_Topside), (X_Underside, Y_Underside), (X_Leftside, Y_Leftside), (X_Rightside, Y_Rightside). The sink number of each group is nunsink_Topside, nunsink_Underside, nunsink_Leftside, and nunsink_Rightside. Secondly, we make four sequences in a given order, respectively, according to the value of X_Topside, X_Underside, Y_Leftside, and Y_Rightside. Then the sink with the lowest order in each group uses the distance between the corresponding vertices of the rectangle and itself as its radius, then each these sink has three cross points with the boundary of the rectangle, (e.g., node A in Figure 4). The other sink at least have two cross points with the corresponding nearest border by employing an enough transmission power, (e.g., node B in Figure 4). Set a current sink node w(x_w,y_w) wants to pre-detect its coarse position in work area.

In our opinion, if the intersection of all circle cut off from the edges contained total rectangle borders, the coverage rate of the rectangle work area would be guaranteed. In this time, the r_i, i ∈ M, must satisfy as the following conditions: (8) X ⊂ ( 2 x 1 ) ∪ r 2 2 − ( x 2 − 2 x 1 ) 2 ∪ ... ∪ r t 2 − ( x t − 2 x t − 1 ) 2 x t ∈ X Topside X ⊂ ( 2 x 1 ) ∪ r 2 2 − ( x 2 − 2 x 1 ) 2 ∪ ... ∪ r u 2 − ( x u − 2 x u − 1 ) 2 x u ∈ X Underside Y ⊂ ( 2 y 1 ) ∪ r 2 2 − ( y 2 − 2 y 1 ) 2 ∪ ... ∪ r l 2 − ( y l − 2 y l − 1 ) 2 y l ∈ Y Leftside Y ⊂ ( 2 y 1 ) ∪ r 2 2 − ( y 2 − 2 y 1 ) 2 ∪ ... ∪ r r 2 − ( y r − 2 y r − 1 ) 2 y r ∈ Y Rightside  

Figure 5 shows three conditions of radio radius choice, which are too large, appropriate, and too small. It is sure that the appropriate radius is the most desirable. In this article, we attempt to provide a distributed power allocation algorithm by which appropriate radius will be choosen for all sink nodes.

After all sink nodes knowing their groups as Topside, Underside, Leftside, and Rightside, four sequences in given order are obtained respectively according to the value of X_Topside, X_Underside, Y_Leftside, and Y_Rightside. In this paper, two modes of sink ordering orientation are proposed. The axis orientation (See Figure 6 (a)) and the Anticlockwise mode (or clockwise mode, See Figure 6 (b)), they are different in the axis orientation of topside and rightside.

Assume the four vertexs of the objective area are q₁(0,0), q₂ (X,0), q₃(X,Y), q₄(0,Y). Before implementation of the MSCWSNs-PC, coordinate axis modification must to be done due to each sink to reckon its radio radius according to the local coordinate information.

Coordinates axis modification in axis orientation mode, is (9) { x i , j = x j y i , j = Y − y j       i ∈ M , j ∈ numsink Topside { x i , j = x j y i , j = y j                     i ∈ M , j ∈ numsink underside { x i , j = x j y i , j = y j                 i ∈ M , j ∈ numsink Leftside { x i , j = X − x j y i , j = y j       i ∈ M , j ∈ numsink Rightside

While the coordinates axis modification in anticlockwise (or clockwise) orientation mode is (10) { x i , j = X − x j y i , j = Y − y j       i ∈ M , j ∈ numsink Topside { x i , j = x j y i , j = y j                     i ∈ M , j ∈ numsink underside { x i , j = x j y i , j = Y − y j                 i ∈ M , j ∈ numsink Leftside { x i , j = X − x j y i , j = y j       i ∈ M , j ∈ numsink Rightside

In original MSCWSNs-PC, sink calculates its radio radius always according to the radio range of previous sink. It often induces a border communication void problem. As shown in Figure 7, the border |mn| is defined as border communication void. For this reason, we provide most significant bit sink radius correction (MSBSRC) scheme. After each sink working out its radio radius using original MSCWSNs-PC, then each sink has highest order in each group decides its radius by comparing R_ij and Distance(S_i,j, vert_i), i ∈ M, where Distance(m,n) denotes the distance between m and n, and vert_i is the vertices set of rectangle work area, i ∈ {Topside, Underside, Leftside, Rightside} and j ∈ { numsink_Topside, numsink_Underside, numsink_Leftside, numsink_Rightside}. Set w(x_w,y_w) is a sink node has highest order wants to decide its radius.

Distance(m,n) computes the euclidean distance between nodes m and n in two dimensions, ( x m − x n ) 2 + ( y m − y n ) 2.

Although the most significant bit sink radius correction (MSBSRC) scheme is provided, when only a few sink nodes were deployed, the sink border group is absent [see Figure 8(a)] which would result in a communication void. In our opinion, if one or more of the sink groups in Topside, Underside, Leftside, or Rightside was empty, this situation will easily produce a sink communication void problem. In addition, the power allocation algorithm is only focused on the borders of the objective area, and the center communication void problem also needs to be considered [see Figure 8(b)]. We denote all of these conditions collectively as the border constraint problem.

For the sink group absence problem, if a sink found that any sink border group was empty, it would chose the distance between the farthest vertex of the border and itself as current radius. In order to solve the center communication void problem, the sink, nearest to the center point of the rectangle in each border group checks if the point has been covered by themselves. If not, they adjust their radio radius equal to the distance between the center point and itself. After these measures, the border constraint problem will be improved greatly.

Let the vertices of the rectangle work area vert_i, i ∈ {I,II,III,IV}, I,II,III,IV denote the quadrants.

In this section, we describe the implementation details of MSCWSNs-PC protocol using flowchart. The two main processes are route request and route reply. A flowchart of this distributed power control algorithm is shown in Figure 9.

Figure 10 gives a simple illustration of a radio radius calculation. For the underside border of the work area, the first sink A has the euclidean distance |Aa₂| as its transmission range R_A,1, then sink B can calculate R_B,2 according to R_A,1 by: (11) R B , 2 = ( ( x B − x A ) − R A , 1 2 − y A 2 ) 2 + y B 2

From what has been discussied above, we may safely draw a conclusion that the R_i,j, i ∈ M, j ∈ {numsink_Topside, numsink_Underside, numsink_Leftside, numsink_Rightside}, can be calculated by: (12) { R i , j = ( ( x j − x j − 1 ) − R i , j − 1 2 − y j − 1 2 ) 2 + y j 2 i ∈ M , j ∈ numsink Topside   or   j ∈ numsink Underside R i , j = ( ( y j − y j − 1 ) − R i , j − 1 2 − x j − 1 2 ) 2 + x j 2 i ∈ M , j ∈ numsink Leftside   or   j ∈ numsink Rightside

Finally, r_i, i ∈ M, be calculated by: (13) r i = max { R i , j }             i ∈ M , j ∈ { numsink Topside ,   numsink underside ,   numsink Leftside ,   numsink Rightside }

For the sensor nodes, we assume that all nodes can transmit with enough power to reach the sink if needed, that the nodes can use power control to vary the amount of transmit power, and that each node has the computational power to support different MAC protocols and perform signal processing functions. It means that the created clusters allow energy-efficient communication from the sensors to the sinks, all sensor nodes communicate directly to the sink or they use multi-hop communication in non-sinks as cluster head condition.

Sink mobility brings new challenges to routing and data dissemination in large sensor networks. Once any sink has changed its location, all sinks in the border-based sink groups would need to re-build their transmission power. It is important to note that only the sinks in the same group (previously and currently) as the mobile sink would need to take part in transmission power adjustment. It can be seen that our scheme is also suited for mobile networks.

Transmission power maintenance is the process of real-time adjustment of the transmission power for some special conditions, such a a routing failure; at this time alternate routing or a router discovery mechanism need to start for setting up new transmission power allocation for all or some sink nodes. The MSCWSNs-PC protocol since the process of establishment of the radio radius is based on the local connectivity state of adjacent sink nodes, transmission power maintenance can be attributed to the issue of how frequently power control assistant messages (PCAMs) are periodically exchanged.

Many research works have focused on how to deploy sink nodes at optimal locations, so that the resulting network could cover a relatively larger distance. In our opinion, it is more practical to improve the network’s topology after the sink nodes are deployed using a routing protocol. Transmission power control for MSCWSNs has a significant effect on the percentage of network coverage. In this section, we will illustrate the coverage rate performance of MSCWSNs-PC by using geometric figures. Without loss of generality, we generally not only consider the fixed deployment of sink nodes, but also randomly deployed sinks.

Figure 11 shows that whether sinks are fixed or randomly deployed, both conditions can obtain a satisfactory percentage of network coverage. The network is more regular in fixed mode [seen in Figure 11(a)], but more easy to deploy in random mode [as seen in Figure 11(b)].

In order to measure the reachability between any sink node and a sensor after execution of our algorithm, we introduce a parameter, mean connectivity, which is denoted as γ. Mean connectivity is defined as the percentage of the total sensor nodes covered by any sink node in the network. In this section, four schemes described above will be proposed: original MSCWSNs-PC, considering MSBSRC, considering BCP, and considering both of MSBSRC and BCP. For these simulations, two modes of axis ordering orientation are employed simultaneously. In these experiments, generally all results are the statistical average of 1,000 rounds. Figure 12 shows the mean connectivity using the original MSCWSNs-PC at variety sink number. With an increasing number of sinks, the mean connectivity of the network becomes nearly 100%. For the modes of axis ordering orientation, anticlockwise mode brings higher mean connectivity compared to axis mode, with a low sink density of (less than six), but with an increase of the number of sinks the gap between the two lines gradually narrows.

Figure 13 shows the relationship between the number of sinks and the mean connectivity of sensor nodes, when only considering MSBSRC. It can be seen that by employing MSBSRC a great improvement in network coverage is achieved. Unlike in original MSCWSNs-PC, axis mode provides higher mean connectivity compared to anticlockwise mode.

Figure 14 shows the relationship between the number of sinks and the mean connectivity of sensor nodes, when only considering BCP. Although BCP results in an obvious increase of mean connectivity compared to the original algorithm, the degree of improvement is smaller compared to the condition only considering MSBSRC. It is noteworthy that with the increase of sinks neither mode of axis ordering orientation is always dominant. The demarcation point is when the number of sinks reaches six, before which anticlockwise mode shows its advantages, while the axis mode is better under other conditions.

Figure 15 shows the mean connectivity result when considering both BCP and MSBSRC schemes. In this condition, the MSCWSNs-PC combines the advantages of the BCP and MSBSRC schemes, and as a result the simulation result is very attractive. Like in Figure 12, axis mode results in higher mean connectivity compared to anticlockwise mode.

The sensor networks should function for as long as possible since it may be inconvenient or impossible to recharge node batteries. Therefore, all aspects of the node, from the hardware to the protocols, must be designed to be extremely energy efficient. In this paper, power efficiency is defined as sensor nodes have different number of “one-hop” sink (sink to node is one-hop) when total them with controlled transmission power over maximum transmission power.

Equation (2) gives the relationship of transmission and reception power for wireless devices. Thus, the transmission power of sink node to the sub nodes in a cluster is given by: (14) P t = P r / [ ( λ 4 π d ) n g t   g r ]

Assume has S sink in the network, the total transmission power is given by: (15) P t = ∑ i = 1 s P t , i = ∑ i = 1 s P r , i / [ ( λ 4 π d ) n g t   g r ] = P r , i   ( 4 π ) n g t   g r   λ n ∑ i = 1 s d n

Figure 16 shows the comparisons of the total transmission power between MSCWSNs-PC and maximum transmission power per round. As shown in Figure 16, MSCWSNs-PC achieves an improvement of several orders of magnitude compared to maximum power transmissions and with the increase of the number of sink the gap between the two lines gradually widens. For the two modes of axis ordering orientation, more total transmission power is needed in axis mode, but the gap between the two modes is very small.

In the well-known energy model of nodes (First Order Radio Model) in [5], the model took into account nodes’ transmitting and receiving energy consumptions, compared to the actual work that node energy model more suitable for constant rate and peer-to-peer links in the mobile node. The literature assumes a simple model for the radio hardware energy dissipation where the transmitter dissipates energy to run the radio electronics and the power amplifier, and the receiver dissipates energy to run the radio electronics. For the experiments described here, both the free space (power loss) and the multipath fading (power loss) channel models were used, depending on the distance between the transmitter and receiver [28]. Power control can be used to invert this loss by appropriately setting the power amplifier - if the distance is less than a threshold, the free space (fs) model is used; otherwise, the multipath (mp) model is used. Thus, to transmit a k-bit message a distance, the radio expends: (16) E Tx   ( k , d ) = E Tx − elec   ( k ) + E Tx − amp   ( k , d ) = { kE elec + k ξ fs d 2 , d < d 0 kE elec + k ξ mp d 4 , d ≥ d 0and to receive this message, the radio expends: (17) E Rx   ( k ) = E Rx − elec   ( k ) = kE elec

The electronic energy, E_elec, depends on factors such as the digital coding, modulation, filtering, and spread of the signal, whereas the amplifier energy, ξ_fsd² or ξ_mpd⁴, depends on the distance to the receiver and the acceptable bit-error rate. For the experiments described in this paper, the communication energy parameters are set as: E_elec = 50 nJ/bit, ξ_fs = 10 pJ/bit/m², and ξ_mp = 0.0013 pJ/ bit/m⁴. Using the experimental results in [29], the energy for data aggregation is set as E_DA = 5 nJ/ bit/signal.

The first order radio model shows that we should reduce the communication of each sensor node as much as possible. In MSCWSNs-PC, without considering the following process of clustering routing, not only all sinks save power by constraining their radio range, but also all sensor nodes receive a smaller number of sink advertising messages, which greatly saves sensor node battery energy.

To reduce inter-cluster interference, each cluster in LEACH communicates using TDMA and direct-sequence spread spectrum (DSSS). Each cluster uses a unique spreading code; all the nodes in the cluster transmit their data to the cluster head using this spreading code and the cluster head filters all received energy using this spreading code. This is known as transmitter-based code assignment [27], since all transmitters within the cluster use the same code. In this paper, clustering interference is defined as the mean number of sinks a node senses. Wen a node wants to select a sink as its cluster head, the less sink node it hears, the less energy it needs to consume. Figure 17 shows that by using our algorithm, less sensor nodes need to decide which sink they should belong to. The reason is that since all sinks are broadcasting in a more smaller radio range by using MSCWSNs-PC, then less sensor nodes can receive the broadcast packets.

For our experiments in OPNET, let M = {1,2,3,4}, N = 28, and four source nodes are randomly deployed in a 100 m × 100 m rectangular region. Radio radius constrained at 20 m. In these experiments, the simulation period T is set from 0 to 10 minutes. The data rate created by each source node is 1,000 bits/s.

Figure 18 shows network load for different sink numbers. The more sinks deployed, the lower a network load is created. When more sink nodes are deployed, the source node has a chance to choose a nearer sink to transport its data packet to. This results in a significant decrease in the total communication hops, and results in a greatly lower load on the system.

In Figure 19, end-to-end delay of MSCWSNs-PC decreases as sink number increases. The performance of end-to-end delay when using four sink nodes always outperforms in terms of less sinks. In MSCWSNs-PC, more sink nodes result in shorter data transport paths and lower loads which have a significant impact on decreasing networks congestion. Thus, congestion is more likely to happen when less sinks are deployed.