Wireless system for improving performance and prolonging battery lifetime of node by energy harvesting

Abstract

In wireless system, radio frequency (RF) energy harvesting addresses the problem of limited battery lifetime in wireless nodes. In this invention, a wireless system for improving performance and prolonging battery life time of node, a battery assisted relay (2) framework is introduced. In this battery assisted relay framework, the energy harvested (EH) relay (2) augments the harvested energy with energy drawn from the battery (10) so as to prolong the battery life. Thus the following optimizations become relevant (i) maximizing throughput performance by using fixed small amount of battery energy in every signaling interval, (ii) minimizing battery energy consumption with predefined throughput performance requirement by optimizing a fixed charging time and energy together (best statistically optimum fixed charging time and energy drawn are determined), (iii) minimizing battery energy consumption by allowing channel-dependent energy harvesting duration, and (iv) minimizing battery energy consumption by drawing energy from the battery dependent on channel values. The suggested method and system can increase throughput as well as battery lifetimes, and are thus of practical value.

Claims

1. A wireless system for improving performance and prolonging battery lifetime of a node by energy harvesting, the wireless system comprising: at least a source node configured to provide RF signals; at least a destination node configured to receive the RF signals transmitted from the source node; a relay in communication with the source node and the destination node, where the source node is configured for communicating with the destination node via the relay for a Time “T”, where the Time “T” has a first signaling phase, a second signaling phase, and a third signaling phase, the relay comprising: an energy harvesting unit comprising an energy storage element, configured for harvesting an energy from the source node in the first signaling phase and storing the energy in the energy storage element; an information processing unit configured for decoding the RF signal received from the source node in the second signaling phase and transferring the decoded RF signal to the destination node; a battery energy control unit having a battery, configured for controlling an amount of energy to be withdrawn from the battery; a central controlling unit in communication with the energy harvesting unit, the battery energy control unit, and the information processing unit, configured for optimizing a fraction of Time “T” apportioned to the first signaling phase for optimizing harvested energy stored via the energy harvesting unit and for transferring the decoded RF signal from the information processing unit to the destination node in the third signaling phase with (i) the harvested energy from the energy harvesting unit augmented with (ii) energy withdrawn from the battery via the battery energy control unit.

2. The system of claim 1, wherein the battery energy control unit extracts the energy from the battery as specified by the central controlling unit.

3. The system of claim 1, wherein the relay uses a Time switching relay (TSR) protocol.

4. The system of claim 1, wherein the relay comprises a switching circuit for switching the relay from the energy harvesting unit to the information processing unit, after harvesting the energy from the source.

5. The system of claim 1, wherein the energy harvesting unit comprises a matching circuit and 3 stage voltage multiplier.

6. The system of claim 1, wherein the energy storage element comprises a super capacitor.

7. The system of claim 1, wherein the central controlling unit optimizes the fraction of Time “T” so that the harvested energy is optimally stored within the Energy storage element.

8. A method for improving performance and prolonging battery lifetime of a node by energy harvesting in wireless system, the method comprising: providing an RF signal by a source node; receiving the RF signal from the source node by a destination node; configuring a relay in such a way so that the relay communicates with the source node and the destination node, and configuring the source node in such a way such that the source node communicates with the destination node via the relay for a Time “T”, the Time “T” having a first signaling phase, a second signaling phase and a third signaling phase, and the relay comprising: an energy harvesting unit, an information processing unit, a battery control unit, and a central controlling unit; via the energy harvesting unit, harvesting energy from the source node RF signal and storing the harvested energy in a storage element in the first signaling phase by an energy harvesting unit; via the information processing unit, decoding the RF signal from the source node by an information processing unit in the second signaling phase; via the battery control unit, controlling an amount of energy to be extracted from a battery by a battery control unit; and via the central controlling unit, optimizing a fraction of the time “T” apportioned to the first signaling phase for optimizing harvested energy by the central controlling unit, the central controlling unit in communication with the energy harvesting unit, the information processing unit, and the battery control unit for transferring the decoded RF signal from the information processing unit to the destination node by augmenting (i) the harvested energy from the energy harvesting unit with (ii) the battery energy from the battery control unit in the third signaling phase.

Description

BRIEF DESCRIPTION OF ACCOMPANYING DRAWINGS

(1) FIG. 1: illustrates the block diagram of relay which shows usage of harvested energy and variable amount of battery energy E.sub.b with the central controlling unit.

(2) FIG. 2: illustrates two-hop system with battery-assisted energy harvesting relay.

(3) FIG. 3: illustrates the Time-switching relaying protocol of two-hop network.

(4) FIG. 4: illustrates the representation of time-switching relaying protocol implementation at relay.

(5) FIG. 5: illustrates the variation of throughput with TSR parameter. It shows there exist an optimum TSR parameter value which maximizes throughput.

(6) FIG. 6: illustrates the throughput variation with source signal-to-noise ratio (SNR). It shows that optimum TSR parameter improves throughput as compared to fixed TSR parameter value for fixed E.sub.b.

(7) FIG. 7: illustrates the energy required for target throughput versus TSR parameter. It shows that there exist an optimum TSR parameter value which minimizes the required relay battery energy E.sub.b for target throughput requirement.

(8) FIG. 8: illustrates the source-user sensor network with energy harvesting users.

(9) FIG. 9: illustrates the protocol of source downlink energy transfer, and user uplink information transfer with harvested energy and battery energy E.sub.b.

(10) FIG. 10: illustrates the power-splitting relaying protocol of two-hop network.

(11) FIG. 11: illustrates the representation of power-splitting relaying protocol implementation at relay.

DETAILED DESCRIPTION OF INVENTION

(12) Provided below is a non-limiting exemplary embodiment of the present invention with described reference of the accompanying drawings.

(13) FIG. 1 illustrates the block diagram of the (Energy Harvesting) EH relay (2). The sensors have a wireless energy harvesting circuit, which is supplemented by a battery (10) from which variable amount of energy E.sub.b can be drawn as shown in FIG. 1. The amount of energy E.sub.b drawn from battery (10) is controlled through a central controlling unit (11). The energy storage element (5) like super capacitor of energy harvesting unit (4) is connected to battery (10) and central controlling unit (11), so that the augment battery energy extraction is controlled for desired performance. In a typical energy harvesting circuit, the fraction of time spent on energy harvesting (time-switching parameter), or fraction of signal energy diverted for energy harvesting (power-splitting parameter) determine the performance of a communication link with energy harvesting nodes. This invention shows how battery (10) energy and energy harvesting parameter can be controlled effectively to maximize throughput, or minimize battery energy consumption for given throughput requirement. As shown in FIG. 1, the relay (2) consists of four major units viz. (i) the central controlling unit (11), (ii) the energy harvesting unit (4), (iii) the battery energy controlling unit (9), and (iv) the information processing unit (8). The description mentioned here is specifically for time-switching, though similar hardware can be used for power-splitting type of energy harvesting circuits. The central controlling unit (11) performs the job of specifying the energy harvesting time through the parameter “α” and the energy “E.sub.b” to be drawn from the battery (10). The signalling interval is denoted by T. The energy harvesting duration is αT. During this interval, the central controlling unit (11) provides timing waveforms that enables the circuit to switch between energy harvesting (4) and information processing (8). The central controlling unit (11) has information about average channel characteristics, harvested energy in the super capacitor (5), and optionally (when available) channel state information. This unit also indicates to the battery energy controlling circuit (9) the amount of energy E.sub.b to be drawn from the battery (10) in every signalling interval. The second unit is the energy harvesting unit (4) which harvests energy from the received RF signal from the antenna of source node (1) for αT time i.e. first signalling phase. The energy harvesting unit (4) consists of a matching circuit, a 3 stage voltage multiplier, and an energy storage element (5) like super capacitor. The harvested energy is temporarily stored in super-capacitor (5) and can be used for transmission in the next signalling phase. The battery energy controlling unit (9) extracts energy from battery as specified by the central controlling unit (11). The extracted battery energy is added to the harvested energy and the sum energy is used to transmit in the next signalling phase. The information processing unit (8) decodes the information using received signal from the antenna for (1−α)T/2 duration i.e. second signalling phase. Upon successful decoding, the relay (2) uses harvested energy from energy harvesting unit and battery energy from energy control unit for transmission of decoded message to destination in the next or third signalling phase. This invention relates to specifying the energy harvesting duration and the battery energy to be drawn. In this invention the central controlling unit (11) optimizes the fraction of Time “T” i.e first signalling phase so that optimum amount of energy can be harvested from the RF signal and optimally stored within the super capacitor (5) or energy storage element In this invention, in some situations, channel estimation units might be available, and the second hop channel knowledge can be used to save considerable amount of battery energy.

(14) In present invention, the two-hop transmission facilitated by a node with energy harvesting capabilities. In present invention the node serving as a relay (2) possesses a battery (10) from which (possibly variable) amount of energy can be drawn as depicted in FIG. 2. Transmission takes place in three phases as depicted using time-switching relaying (TSR) protocol as shown in FIG. 3. In the first energy harvesting phase of αT duration, the source (1) transmits energy to the sensor serving as a relay (2), which harvests the energy Q.sub.r=P.sub.s∥h.sub.1∥.sup.2aηT. Here ‘P.sub.s’ source power, ‘α’ denotes TSR parameter, ‘η’ denotes efficiency of energy harvesting unit, ‘T’ denotes the time duration, ∥⋅∥ denotes l.sub.2 norm and ‘h.sub.1’ denotes channel between source (1) and relay (2). In the second slot of (1-α)T/2 duration, the source (1) transmits information symbols to the node serving as a relay (2). In the third time-slot also of duration (1-α)T/2), the node serving as a relay (2) communicates the symbols to the destination node (3) using the harvested energy Q.sub.r and E.sub.b energy from the battery (10). The relay (3) draws (possibly variable) amount of energy from the battery using the central controlling unit (11) and battery energy control unit (9) as shown in FIG. 4. In present invention We are interested in a) choosing fixed energy harvesting time (through α) to maximize throughput for fixed E.sub.b, or b) choosing fixed α and minimum possible fixed E.sub.b to attain some desired throughput, and c) minimizing battery (10) energy consumption E.sub.b while allowing it to depend on channel values. The implementation of proposed invention is explained in two scenarios in two scenarios (i) two-hop network (ii) uplink transmission by nodes. The detailed explanation of each scenario as follows.

(15) (I) Two-Hop Network:

(16) Referring to FIG. 2 shows the system with multi antenna source (1) communicates with the destination node (3) with help of energy harvesting (EH) relay (2). The relay (2) has limited battery energy (10) which is to be used along the harvested energy to improve the system performance while prolonging battery lifetime. When using the standard TSR protocol of FIG. 3, the relay (2) harvests energy for fraction of time (αT). In the second phase of (1−α) T/2 duration, the relay (2) receives information from source and decodes it. In third phase of (1−α) T/2 time, the relay (2) forward the successfully decoded information to the destination (we assume a decode-and-forward (DF) relay (2), though similar optimizations can be performed for amplify-and-forward (AF) relays as well). For forwarding information, the relay (2) uses harvested energy along with variable amount of battery energy E.sub.b as shown in FIG. 4. The destination node (3) decodes the received information.

(17) Referring to FIG. 5 shows the variation of system throughput with TSR parameter. It shows that there exists an optimum TSR parameter value which maximizes the throughput for different battery energy values. It also shows that using more battery energy improves the throughput. Optimum TSR parameter depends on system parameters, and a closed form expression for optimum TSR parameter can be found as follows. For information transmission rate ‘R’, outage P.sub.out characterizes performance using signal-to-noise ratio (SNR) at relay Γ.sub.r and SNR at destination Γ.sub.d as [2]:

(18) $\begin{array}{cc}\begin{array}{c}{P}_{\mathrm{out}}=\mathrm{Pr}\left\{{\rho }_{s}X<{\gamma }_{\mathrm{th}}\right\}+\mathrm{Pr}\left\{{\rho }_{s}X>{\gamma }_{\mathrm{th}},\left(\frac{2\alpha {\mathrm{\eta \rho }}_{s}X}{\left(1-\alpha \right)}+\frac{2E_b/{\sigma }^2}{\left(1-\alpha \right)T}\right)Y<{\gamma }_{\mathrm{th}}\right\}\\ =1-\frac{{\lambda }_x^{N_x}}{\Gamma \left(N_s\right)}{\int }_{\frac{{\gamma }_{\mathrm{th}}}{{\rho }_s}}^{\infty }{x}^{N_s-1}\exp \left(-{\lambda }_{x}x-\frac{\left(1-\alpha \right){\lambda }_y{\gamma }_{\mathrm{th}}}{2\alpha \eta {\rho }_{s}x+2E_b/\left(T{\sigma }^2\right)}\right)\mathrm{dx}.\end{array}& \left(1\right)\end{array}$

(19) In above expression ‘ρ.sub.s’ indicates SNR of source, ‘α ’ denotes TSR parameter, ‘η’ denotes EH circuit efficiency, ‘E.sub.b’ denotes relay battery energy per time-slot, ‘ T’ denotes time-slot, ‘σ.sup.2’ denotes noise variance and ‘γ.sub.th=2.sup.R−1’ denotes threshold. In above expression, ‘ X’ denotes channel between source-relay and ‘Y’ denotes channel between relay-destination. We use the high signal-to-noise (SNR) approximation of outage for finding α*. The high SNR approximation of outage for two-hop network with decode-and-forward relay can be written as [2]:

(20) $\begin{array}{cc}{P}_{\mathrm{out}};\frac{\left(1-\alpha \right){\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}}{\left[2\alpha \eta {\gamma }_{\mathrm{th}}+2E_b/\left(T{\sigma }^2\right)\right]{\lambda }_x+\left(N_s-1\right)2\alpha {\mathrm{\eta \rho }}_s}& \left(2\right)\end{array}$

(21) Here λ.sub.x=(d.sub.1).sup.3 and λ.sub.y=(d.sub.2).sup.3. Here ‘d.sub.1’ denotes distance of source-relay, ‘ d.sub.2’ denotes distance between relay and the destination, ‘ N.sub.s’ is number of source terminal antennas and ‘ρ.sub.s’ denotes source SNR (P.sub.s/σ.sup.2).

(22) (a) Throughput maximization for fixed E.sub.b:

(23) The throughput of the system is given by:
τ=(1−α)(1−P.sub.out)R/2  (3)

(24) The optimum TSR parameter can be found as:

(25) $\begin{array}{cc}{\alpha }^{*}=\underset{\alpha }{\arg \max }\tau =\underset{\alpha }{\arg \max }\left(1-\alpha \right)\left(1-P_{\mathrm{out}}\right)R/2& \left(4\right)\end{array}$
It can be observed from FIG. 5 that ‘ τ’ is concave with ‘ α ’. Using (2) in (3) and

(26) $\frac{\partial \tau }{\partial \alpha }=0,$
we can found ‘α*’ of (4). We can found α* as [2]:

(27) ${\alpha }^{*}=\frac{-b+\sqrt{b^2-4\mathrm{ac}}}{2a}$$\mathrm{With}$$a={\left[2{\lambda }_x\eta {\gamma }_{\mathrm{th}}+2\eta {\rho }_s\left(N_s-1\right)\right]}^2+{\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}\left[2{\lambda }_x\eta {\gamma }_{\mathrm{th}}+2\eta {\rho }_s\left(N_s-1\right)\right],b=\left(2{\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}+2\left[2{\lambda }_x\eta {\gamma }_{\mathrm{th}}+2\eta {\rho }_s\left(N_s-1\right)\right]\right)\left(\frac{2{\lambda }_x{E}_b}{T{\sigma }^2}\right)\mathrm{and}$$c={\left(\frac{2{\lambda }_x{E}_b}{T{\sigma }^2}\right)}^2-2{\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}\left(\frac{2{\lambda }_x{E}_b}{T{\sigma }^2}\right)-{\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}\left[2{\lambda }_x\eta {\gamma }_{\mathrm{th}}+2\eta {\rho }_s\left(N_s-1\right)\right].$

(28) FIG. 6 depicts the throughput with fixed TSR parameter and optimum TSR parameter α*. The throughput with optimum TSR parameter ‘ α*’ is higher than that with any other fixed TSR parameter for any given ‘E.sub.b’ which shows the importance of optimum TSR parameter. It shows that proposed hybrid usage of battery energy and harvesting energy is effective as compared to conventional techniques used in literature (i) only battery energy based technique which corresponds to ‘α=0’ (ii) only energy harvesting based technique which corresponds to E.sub.b=0′ [1]. It also shows that throughput with the expression for ‘α*’ provided above matches closely with throughput with exact ‘α*’ (it can be found numerically as in FIG. 5). It can be seen that the throughput increases as the relay battery energy ‘ E.sub.b’ increases.

(29) (b) Minimization of Battery Energy Consumption with Statistical Channel Knowledge:

(30) FIG. 7 shows the battery energy required for desired throughput (or target throughput in quality-of-service based applications) performance with variation of TSR parameter. It is important to note that there is optimum TSR parameter value which minimizes the relay battery energy requirement. We can obtain the relation between the desired target throughput and required battery energy by equating the throughput in (3) to target throughput as follows [2]:

(31) $\begin{array}{cc}\left(1-\alpha \right)\left(1-P_{\mathrm{out}}\right)R/2={\tau }_{\mathrm{tr}}.& \left(5\right)\\ \left(1-\alpha \right)\frac{R}{2}\frac{{\lambda }_x^{N_s}}{\Gamma \left(N_s\right)}{\int }_{\frac{{\gamma }_{\mathrm{th}}}{{\rho }_s}}^{\infty }{x}^{N_s-1}\exp \left(-{\lambda }_{x}x-\frac{\left(1-\alpha \right){\lambda }_y{\gamma }_{\mathrm{th}}}{2\alpha \eta {\rho }_{s}x+2E_b/\left(T{\sigma }^2\right)}\right)\mathrm{dx}={\tau }_{\mathrm{tr}}.& \end{array}$

(32) The above expression can be obtained using ‘P.sub.out’ in (1). Here ‘τ.sub.tr’ indicates target throughput. Using high signal-to-noise (SNR) outage expression of outage (2), we can write above expression as:

(33) $\begin{array}{cc}\left(1-\alpha \right)\frac{R}{2}\left(1-\frac{\left(1-\alpha \right){\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}}{\left[2\alpha \eta {\gamma }_{\mathrm{th}}+2E_b/\left(T{\sigma }^2\right)\right]{\lambda }_x+\left(N_s-1\right)2\mathrm{\alpha \eta }{\rho }_s}\right)\cong {\tau }_{\mathrm{tr}}.& \left(6\right)\\ E_b=\frac{T{\sigma }^2}{2{\lambda }_x}\left(\frac{{\left(1-\alpha \right)}^2{\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}}{\left(1-2{\tau }_{\mathrm{tr}}/R\right)-\alpha }-\left(N_s-1\right)2\alpha \eta {\rho }_s-2\alpha {\mathrm{\eta \lambda }}_x{\gamma }_{\mathrm{th}}\right).& \end{array}$

(34) The above expression of battery energy for target throughput can be obtained trivially. We can obtain the optimum TSR parameter ‘α.sub.b’ that minimizes relay battery energy consumption as:

(35) $\begin{array}{cc}{\alpha }_b=\underset{\alpha }{\arg \min }{E}_b& \left(7\right)\end{array}$

(36) We can found expression for ‘α.sub.b’ using

(37) $\frac{\partial E_b}{\partial \alpha }=0\mathrm{as}\text{:}$

(38) 0$\begin{array}{cc}{\alpha }_b=\left(1-\frac{2{\tau }_{\mathrm{tr}}}{R}\right)-\frac{\sqrt{b_1^2-4a_1{c}_1}}{2a_1}.& \left(8\right)\\ \mathrm{Here}{a}_1={\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}+\left[2{\lambda }_x\eta {\gamma }_{\mathrm{th}}+2\eta {\rho }_s\left(N_s-1\right)\right],& \\ b_1=2\left(1-\frac{2{\tau }_{\mathrm{tr}}}{R}\right)-\left[{\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}+2{\lambda }_x\eta {\gamma }_{\mathrm{th}}+2\eta {\rho }_s\left(N_s-1\right)\right]\mathrm{and}& \\ c_1={\left(1-\frac{2{\tau }_{\mathrm{tr}}}{R}\right)}^2\left[-2\eta {\rho }_s\left(N_s-1\right)-2{\lambda }_x\eta {\gamma }_{\mathrm{th}}\right]+{\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}-2{\lambda }_x{\lambda }_y{\gamma }_{\mathrm{th}}\left(1-\frac{2{\tau }_{\mathrm{tr}}}{R}\right).& \end{array}$

(39) We note that the α.sub.b gives the minimum energy consumption (which is depend only on statistical system parameters but not on channel state information (CSI) to achieve the target throughput, and denote it by E.sub.b.sup.nc. We note that E.sub.b.sup.nc is the battery energy consumption without CSI at the relay.

(40) (c) Exploiting Channel Knowledge to Minimize Battery Energy Consumption:

(41) The energy consumption at the relay can be further minimized if the relay to destination CSI is available at relay. Using (1), we can write the battery energy required for successful transmission as:

(42) $E_b^{\mathrm{req}}=\frac{T}{2}\left[\frac{{\gamma }_{\mathrm{th}}{\sigma }^2\left(1-\alpha \right)}{Y}-2\mathrm{\alpha \eta }{P}_{s}X\right].$
With the CSI available, we devise a mechanism to minimize the energy consumption at relay with target throughput requirement as [2]:

(43) $E_b=\{\begin{array}{cc}\max \left(E_b^{\mathrm{req}},0\right)& \mathrm{if}{E}_b^{\mathrm{req}}<E_b^{\mathrm{nc}}\\ 0& \mathrm{if}{E}_b^{\mathrm{req}}>E_b^{\mathrm{nc}}\end{array}$

(44) Here E.sub.b.sup.req is CSI based relay energy required for successful decoding at the destination. The above condition ensures target throughput and minimizes relay energy consumption substantially due to CSI availability. In above scenario the relay does not transmit when E.sub.b.sup.req>E.sub.b.sup.nc, and transmits with required energy max(E.sub.b.sup.req,0) when E.sub.b.sup.req<E.sub.b.sup.nc. We can observe energy consumption for different schemes with target throughput requirement in Table 1. It can be observed that the energy consumption is minimum with CSI availability and optimum TSR parameter α.sub.b. The average battery energy consumed E.sub.b,avg.sup.req for target throughput τ.sub.tr, with CSI availability can be found as [2]:

(45) $E_{b,\mathrm{avg}}^{\mathrm{req}}={\int }_{\frac{{\gamma }_{\mathrm{th}}}{{\rho }_s}}^{\infty }\frac{{\lambda }_y{\gamma }_{\mathrm{th}}\left(1-{\alpha }_b\right)T{\sigma }^2}{2\Gamma \left(n_s\right)}{\lambda }_x^{N_s}{x}^{N_s}{e}^{-{\lambda }_{x}x}\left[E_1\left(\frac{{\lambda }_y{\gamma }_{\mathrm{th}}\left(1-{\alpha }_b\right)T{\sigma }^2}{2E_b^{\mathrm{nc}}+2{\alpha }_b\eta {\rho }_{s}T{\sigma }^{2}x}\right)-E_1\left(\frac{{\lambda }_y{\gamma }_{\mathrm{th}}\left(1-{\alpha }_b\right)}{2{\alpha }_b\eta {\rho }_{s}x}\right)\right]\mathrm{dx}+{\int }_{\frac{{\gamma }_{\mathrm{th}}}{{\rho }_s}}^{\infty }\frac{{\lambda }_y{\gamma }_{\mathrm{th}}\left(1-{\alpha }_b\right)T{\sigma }^2}{2\Gamma \left(n_s\right)}{\lambda }_x^{N_s}{x}^{N_s}{e}^{-{\lambda }_{x}x}[\exp \left(\frac{{\lambda }_y{\gamma }_{\mathrm{th}}\left(1-{\alpha }_b\right)}{2{\alpha }_b\eta {\rho }_{s}x}\right)-\exp \left(\frac{{\lambda }_y{\gamma }_{\mathrm{th}}\left(1-{\alpha }_b\right)T{\sigma }^2}{2E_b^{\mathrm{nc}}+2{\alpha }_b\eta {\rho }_{s}T{\sigma }^{2}x}\right)]\mathrm{dx}$
Here E.sub.1 (⋅) indicates exponential integral function.

(46) We can analyze the two-hop system for power-splitting relaying (PSR) protocol with help of the FIG. 10 and FIG. 11. We note optimum PSR parameter for maximizing the throughput β.sub.τ, and optimum PSR parameter β.sub.b for minimizing energy consumption for target throughput.

(47) TABLE-US-00001 TABLE 1 The energy consumption at relay for different conditions with target throughput requirement [2]. Battery energy Battery energy required with required with Battery Energy optimum TSR optimum TSR Target required with parameter α.sub.b - parameter α.sub.b - throughput fixed α α = 0.25 without CSI with CSI 1.2 407 339 28 1.5 674 636 81 2 1451 1367 295
(II) Uplink Transmission by Sensors:

(48) Referring to FIG. 8 shows the sensors (users) communicate with base station (source) with the help of harvested energy and battery energy. The selected sensor (for communication with source) harvest energy for fraction of time αT as shown in FIG. 9. The sensor uses harvested energy Qu=P.sub.s|h.sub.u|.sup.2αηT along with the battery energy E.sub.b for transmission. Here ‘h.sub.u’ denotes the channel between source and sensor. The sensor sends its information to source using available power:

(49) $P_u=\frac{Q_u}{\left(1-\alpha \right)T}+\frac{E_b}{\left(1-\alpha \right)T}=\frac{P_s{.Math.h_u.Math.}^2\mathrm{\alpha \eta }}{\left(1-\alpha \right)}+\frac{E_b}{\left(1-\alpha \right)T}.$
The received signal-to-noise ratio at source can be written as:

(50) ${\Gamma }_s=\frac{P_u{.Math.h_u.Math.}^2}{{\sigma }^2}=\frac{P_s{.Math.h_u.Math.}^4\mathrm{\alpha \eta }}{\left(1-\alpha \right){\sigma }^2}+\frac{E_b{.Math.h_u.Math.}^2}{\left(1-\alpha \right){\sigma }^{2}T}.$

(51) For information transmission rate ‘R’ and outage P.sub.out, the throughput of the uplink system can be defined as:
τ=(1−α)(1−P.sub.out)R

(52) The high SNR approximation of outage in above expression can be written as:

(53) $\begin{array}{cc}{P}_{\mathrm{out}}•\frac{{\left(-\frac{{\lambda }_s{E}_b}{2\alpha \eta P_s{\sigma }^{2}T}+{\lambda }_x\sqrt{{\left(\frac{E_b}{2\alpha \eta P_s{\sigma }^{2}T}\right)}^2+\frac{y_{\mathrm{th}}\left(1-\alpha \right)}{\mathrm{\alpha \eta }{P}_s}}\right)}^{N_s}}{N_s!}.& \left(9\right)\end{array}$
Here Δ.sub.x=d.sup.3. Here ‘η’ denotes EH circuit efficiency, ‘E.sub.b’ denotes relay battery energy, ‘σ.sup.2’ is noise variance, ‘ N.sub.s’ is number of source terminal antennas, ‘σ.sup.2’ is noise variance and ‘d’ denotes the distance between source and sensor. The optimum TSR parameter can be found as:

(54) ${\alpha }^{*}=\underset{\alpha }{\arg \max }\tau =\underset{\alpha }{\arg \max }\left(1-\alpha \right)\left(1-P_{\mathrm{out}}\right)R.$
We further investigate the minimization of required battery energy for desired target throughput by equating system throughput to target throughput ‘ τ.sub.tr’ as:
(1−α)(1−P.sub.out)R=τ.sub.tr

(55) We can use P.sub.out in (9) and obtain expression for E.sub.b. We can minimize the required energy for target throughput τ.sub.tr requirement by optimizing TSR parameter as:

(56) ${\alpha }_b=\underset{\alpha }{\arg \max }{E}_b$

(57) Using the above expression we can obtain the optimum TSR parameter for minimizing the required battery energy E.sub.b for target throughput in similar fashion discussed in two-hop network.

(58) While aspects of the present invention have been particularly shown and described, it will be understood by those skilled in the art that various additional embodiments may be contemplated by modification of the disclosed device without departing from the scope of what is disclosed. Such embodiments should be understood to fall within the scope of the present invention as determined based upon claims and any equivalents thereof.