Robust power control for IEEE wireless sensor networks with round-trip time-delay uncertainty

Transcription

1 WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. ; : Published online 21 April 9 in Wiley InterScience ( Robust power control for IEEE wireless sensor networks with round-trip time-delay uncertainty S. M. Mahdi Alavi,, M. J. Walsh and M. J. Hayes Wireless Access Research Centre, Department of Electronic and Computer Engineering, University of Limerick, Ireland Summary This paper presents a novel, practically implementable robust Power Control (PC) technique that is generally applicable to a variety of IEEE infrastructure and peer-to-peer wireless sensor networks (WSNs) where there is a round-trip time-delay uncertainty. In this methodology, robust stability and performance constraints are cast as a set of exclusion regions on the Nichols chart. The desired PC strategy is achieved through an iterative shaping of the system frequency response until these constraints are satisfied. A Smith Predictor (SP) is also adopted to mitigate the effects of time delay that occurs quite naturally in this type of problem. Such an approach is shown to be entirely appropriate for the discrete time controller design problem at hand. The designs are validated experimentally using a fully compliant testbed where mobility is introduced using autonomous robots. This testbed provides a good basis for a formal comparison of the new approach against a number of existing strategies. Copyright 9 John Wiley & Sons, Ltd. KEY WORDS: wireless sensor networks; power control; uncertain time-delay systems; loop-shaping technique 1. Introduction Wireless sensor networks (WSNs) play a key and increasing role in facilitating the collection, monitoring and control of data from remote locations, [1,2]. Although particular application spaces can pose specific challenges, for WSN deployment to be more effective it is imperative that the transmitted signal exhibits a certain minimum signal strength at the receiver so that information flow within the network can be maintained. This required level of received signal strength ensures that some floor level on outage probability can be guaranteed, the key quality of service (QoS) metric considered in this paper. Minimization of the outage probability is widely regarded as the principal enabler of improved network connectivity. Concurrently, since wireless sensor nodes generally possess limited (battery based) energy resources, some Correspondence to: Seyed Mohammad Mahdi Alavi, Wireless Access Research Centre, Department of Electronic and Computer Engineering, University of Limerick, Ireland. mahdi.s.alavi@ul.ie Copyright 9 John Wiley & Sons, Ltd.

2 812 S. M. M. ALAVI, M. J. WALSH AND M. J. HAYES optimization of energy consumption is often essential, particularly for mobile devices. This requirement leads to a constraint that the signal strength at the receiver not be higher than is necessary to achieve this same floor level on outage probability. Dynamic transmission power control (PC) is the most obvious means of addressing these interacting issues. Efficient PC design for wireless networks is constrained by a variety of factors. For example wireless radio channels are typically affected by exogenous, uncertain factors that have an adverse impact on system performance. Path loss, shadowing and fading effects as well as radio channel time delay can severely degrade performance and when mobility is introduced the problem inevitably becomes more difficult to solve, [3,4]. A large variety of WSN transmission PC strategies have already been proposed in the literature. A necessarily brief review is presented in the following. The interested reader is directed to Reference [5] for a more comprehensive survey. Several heuristic algorithms have been presented in References [6 8] that manage the transmission control protocol (TCP) and the network routing structure in order to minimize the transmission power. However, comprehensive information regarding the channel capacity and location of a network s wireless sensor nodes are required, often causing the algorithms that are proposed to be overly complex and practically difficult to implement. In Reference [9] the transmission power is adjusted as a function of some measure of the received signal strength. The proposed approach relies on the assumption that the radio channel gains between transceivers are the same in both directions (i.e. up and downlink) which is not valid for realistic problem scenarios. The PC algorithms proposed in Reference [] are based on packet-error-rate (PER) estimation that leads to a quite expensive computational burden, in particular for fading environments where the variance of the wireless channel gain is quite high and/or time varying. In References [11,12] the effect of hardware constraints that typically arise in practical power-controlled WSNs has been considered. Robust PC schemes have been proposed that fully address the saturation and quantization constraints within the system structure. However, the effectiveness of the proposed methodologies have only been tested for the scenarios that the communication link is assumed to be free of delay. As a concluding remark in relation to the existing literature on this topic, it is clear that there still exists a requirement for an easy to implement approach to PC that will work well in a realistic environment and that will also be robust to round-trip time-delay uncertainty. In this work, a modified PC structure is presented and formulated that provides intuitively appealing benefits from an engineering perspective and addresses the aforementioned issues. A frequency domain loop-shaping framework is proposed based on tracking the received signal strength indicator (RSSI) notwithstanding the existence of round-trip delay and radio channel uncertainties and also a bounded level of interference existing between sensor nodes which in this case is treated as an unknown output disturbance. The robust stability and performance constraints are shown to be equivalent to a set of exclusion regions for the system loop gain function plotted on the standard Nichols chart at any given frequency. A Smith predictor (SP) is added to the PC structure in order to mitigate the effect of round-trip time-delay. The design is shown to work based on worst-case operating conditions thereby, exact information in relation to the network operating conditions that obtain at any instant is not required for the paradigm at hand. A feature of the design methodology is that a large variety of existing PC schemes using different network topologies can be supported, (including both infrastructure and peerto-peer WSNs), and quantifiable improvements are demonstrated in terms of reduced overall outage probability and power consumption. Experimental results are presented that compare the new approach with a number of existing PC strategies using a fully compliant testbed where mobility is supported in a controlled fashion using autonomous robots. The paper is structured as follows. In Section 2, the system theoretic model is presented. In Section 3 a systematic design procedure is described for the problem at hand. Section 3.1 considers the appropriate SP design principle that is necessary. The design constraints, selection of robustness weighting functions, and finally the loop-function shaping method are described in Section 3.2. In Section 4 the benchmark example of a WSN infrastructure constructed using Moteiv s Tmote-Sky wireless modules is introduced. In particular this section discusses several technical issues that are necessary to consider when trying to implement PC in this paradigm. Experimental results are reported and the performance of the new Moteiv (which, it must be noted, has recently been rebranded as Sentilla Inc.) provides a wireless sensor platform for the nodes used in this study.

3 ROBUST POWER CONTROL FOR IEEE WIRELESS SENSOR NETWORKS 813 Fig. 1. Block diagram of the loglinear closed-loop PC structure in IEEE WSNs, based on RSSI measurement. methodology is compared with a selection of existing PC algorithms. 2. System Model and Problem Formulation Throughout this paper, the decibel value of a variable x is denoted by x, namely, x = log x. z represents the Z-transform operator. The relationship between z- domain and frequency domain (s-domain) operators is given by z = e jωt s, where T s is the system sampling time and ω is the frequency. Figure 1 shows an overview of the proposed powercontrolled wireless communications between a sensor node and a base station. In the IEEE WSN technology, the transceiver is typically an inexpensive off the shelf component that provides an RSSI value (in dbm) upon receipt of each data packet. Recent empirical evidence suggests that due to a stable radio now being a feature of even low cost devices, the RSSI value exhibits a highly linear behaviour in terms of transmission power, [11 13]. Hence, a closedloop loglinear PC algorithm based on local RSSI measurement is feasible. This work confirms this view and provides additional evidence that the RSSI value is a sufficiently good QoS measurement variable for improved transmission PC strategies that can robustly compensate for channel gain, noise and interference between sensor nodes. The relationship between the RSSI value and system parameters is given by r i (k) = p i (k) + D i (k) (1) where p i is the power is expended by the sensor node i to send the data. D i (k) = I i (k) + ρ + 3 where, I i represents channel gain and interference from the other users plus noise. ρ represents measurement offset. The scalar term 3 accounts for the conversion from dbm to db. k is time index. In the proposed framework, the actual RSSI of the sensor node i, r i (k), is measured at the base station and compared with a target value r t. The tracking error is then fed into the power controller block. According to the value of e i (k), the control signal is generated and forwarded to the power multiplier block. This block determines the power consumption law that is typically of the bilinear form p i (k) = p i (k 1) + u i (k) (2) where p i and u i denote the transmission power and control signal, respectively as illustrated in Figure 1. The integrator in Equation (2) naturally provides good tracking performance leading to reduced outage probability. A feature of commercial wireless devices is that transmission can only occur at a preset number of discrete power levels. This hardware limitation is modelled as a saturation/quantization constraint in Figure 1. Finally, the desired transmission power is propagated to the sensor node through the wireless medium. In Figure 1, d 1 and d 2 represent the unavoidable time delays, due to downlink and uplink communication, respectively, caused by this process. Figure 1 also shows how the model supports the robust analysis of noise effects (both thermal and measurement) and the interference from other users that are significant limitations in any practical network. The main objective in this paradigm is to design an appropriate power controller, C(z), that can successfully track r t with minimum required transmission power in such an uncertain environment. Figure 2 shows a simplified representation of the proposed closed-loop PC structure where the downlink and uplink delays are considered as a single roundtrip time-delay. The power controller consists of two components; a feedback controller, C(z) and a Smith Predictor (SP), S(z). For the problem at hand, it is assumed that the uncertain round-trip time-delay parameter, d = d 1 + d 2, can vary between (idealized)

4 814 S. M. M. ALAVI, M. J. WALSH AND M. J. HAYES Power Hardware Multiplier Constraint r t e i (k) C(z) u i (k) 1 p i (k) p si (k) 1 z 1 Link delay z d D i (k) r i (k) Smith Predictor S(z) Power controller,c(z) Fig. 2. Simplified loglinear RSSI-based PC structure for IEEE WSNs. and 2(worst case) sampling instants. The effects of channel uncertainty, noise, and interference from other sensor nodes are also denoted as the output disturbance signal, D i. In this scheme, the plant model is given by Remarks: z d G(z) =, d {, 1, 2} (3) 1 z 1 The proposed PC system can be a useful analysis paradigm for both infrastructure(star) and peer-topeer topologies. A loop similar to that in Figure 2 is implemented between each sensor node and that node which is acting as the base station/hop at any instant. From an engineering perspective, since noise is properly filtered in this scheme at the receiver, it is argued that the error signal e i (k) will be similar for both RSSI and signal-to-interference-noise ratio (SINR) based PC systems. Thus, the proposed SINR-based PC algorithms in the literature, for instance [14] and references therein, can be directly applied to the WSNs using an RSSI-based feedback measurement. 3. Design Procedure 3.1. Smith Predictor Design For time-delay systems (3), an SP is designed according to S(z) = 1 z d 1 z 1 (4) where d is the nominal time-delay value, [15]. There is a significant literature illustrating how SP has been shown to be sensitive to modelling error between d and d, [16]. The selection of d will therefore have important implications for performance. One option is to select d as a mean expected value of d. An alternative approach for the selection of d is to consider a worst-case scenario where d = max{d}, the maximum time delay. It is shown that the SP with d at mean value of d will result in unfeasible design bounds at a number of frequencies leading to difficulties in the loop-shaping process. On the other hand, the SP by using worst-case scenario, i.e. d = max{d}, results in feasible loop-shaping bounds that can be satisfied by a low-order feedback controller. Thus, S(z) is designed subject to the worst-case scenario: S(z) = 1 z 2 1 z 1 = z + 1 z (5) 3.2. Feedback Controller Design The proposed design methodology extends classical loop-shaping techniques based on the use of Quantitative Feedback Theory (QFT) to the WSN application space. Client-specified levels of desired performance are achieved over a region of parametric plant uncertainty determined a priori by the engineer. The desired specifications are cast as a set of design bounds dividing the Nichols chart into acceptable and unacceptable regions. C(z) is then obtained by adding appropriate poles and zeros so that the nominal loop function avoids these unacceptable regions, [17,18]. The earlier SP, Equation (5), leads to a modified uncertain plant given by G(z) = G(z) + S(z) = 1 z 2 + z d 1 z 1, d {, 1, 2} (6)

5 ROBUST POWER CONTROL FOR IEEE WIRELESS SENSOR NETWORKS 815 For the loop-shaping process, the nominal plant is selected as a plant with the longest time-delay, i.e. G (z) = z/(z 1). It is also assumed that an information flow of one data packet per second is required, dictating a system sampling time T s = 1 (sec) Formal statement of the desired specifications for power control problem In this technique, the robust stability is incorporated into gain and phase margins through the use of the following constraint: C G 1 + C G (z) µ, ω [,π/t s] (7) Typically, µ is chosen to be 1.5 thereby ensuring a phase and gain margin of 5 and 1.45, respectively. For robust performance, the following design constraint is used to ensure adequate tracking performance T L (z) C G 1 + C G (z) T U(z), ω [,π/t s ] (8) Equation (8) requires that the system (RSSI) output exhibits a complementary sensitivity that is in a predefined region specified between upper and lower bounds T U (z) and T L (z), respectively. T U (z) and T L (z) are typically defined by the engineer using timedomain concepts such as settling time and overshoot. Suppose that (i) the RSSI is required to settle around 6 (sec) t ss 24 (sec), and that (ii) a damping factor ξ =.5, is deemed appropriate to reduce outage probability to acceptable levels. The following transfer functions can be selected so as to define the desired tracking bounds with the aforementioned characteristics. T U (z) = T L (z) =.9945z z z z z z (9) In order to attenuate the effects of exogenous disturbance, it is sufficient to over-bound the transfer function from D i (k) to r i (k) with an appropriate disturbance rejection weight as follows: C G (z) W D(z), ω [,π/t s ] () where, W D represents a weighting function over the frequency range where the disturbance attenuation is likely to be of most significance. It is a feature of WSN that due to shadowing and fading effects the disturbance energy is typically concentrated at higher frequencies. Thus, an appropriate W D that exhibits good disturbance attenuation in this region of the spectrum is desirable. In the following, W D is selected as a first-order transfer function with crossover frequency around the desired performance bandwidth W D (z) =.7768 z.2231 (11) It is clear from the preceding system equation that if the control signal remains small, the transmission power is also reduced. A constraint on control effort can also be added in a similar fashion C(z) 1 + C G (z) W u(z), ω [,π/t s ] (12) where W u represents a weighting function on the required levels of control signal reduction. W u should be a transfer function with small gain, (less than 1), over a selection of frequencies that spans the aforementioned design bandwidth. However, some relaxations can be made on the frequencies where the plant exhibits low gain. Since the bodemagnitude of the integral bilinear PC law plant is a decreasing function, W u having magnitude response bigger than 1 at higher frequencies as given by Equation (13) is feasible for the problem at hand. W u (z) = z 1 z.1 (13) Loop-shaping technique For loop-shaping process, a finite set of design frequencies is firstly selected for each of the proposed design constraints. The solutions of Equations (7),

6 816 S. M. M. ALAVI, M. J. WALSH AND M. J. HAYES Intersection of Bounds 3 2(rad/s) 2.5(rad/s) Magnitude (db).2(rad/s) 3(rad/s) 1(rad/s) L(z) L(e.2T s ) L(e.5T s ) L(e T s ) L(e 2T s ) L(e 2.5T s ) L(e 3T s ).5(rad/s) Phase (degrees) Fig. 3. Illustration of the design bounds in Nichols chart. Note how L(z) is above the solid lines and below the dashed lines at each design frequency. The critical point is also avoided thereby ensuring robust stability. The worst-case scenario has been considered for this stage, d = 2. (8), () and (12) divide the Nichols chart into acceptable and unacceptable regions. The intersection of the bounds at each design frequency is the value that is taken for the design of C(z). Commercial MATLAB toolbox software [19] provides a convenient way of achieving this. Typical toolbox output is illustrated in Figure 3 for the design frequencies of ω ={.2,.5, 1, 2, 2.5, 3} (rad/s). C(z) is designed by adding appropriate poles and zeros to the nominal loop function so that it lies inside these acceptable regions described by the full (lower) and dashed (upper) constraint lines that are described at each frequency. Moreover the loop-function must not intersect the critical point at ( 18, db). A possible controller satisfying the related design bounds for this problem is given by C(z) =.51z(z +.5) z z (14) Therefore the desired PC law, (as per the proposed control structure of Figure 2), is given by C LS (z) = C(z) 1 + CS(z) =.33378z(z +.5) (z z ) (15) For robustness analysis, Figure 4(a) confirms that the closed-loop transfer function lies between T L (z) and T U (z) performance bounds as required. In addition, Figure 4(b) illustrates how the plant in relation to different values of the time-delay parameter, d, can meet the performance specifications. Remark: The selection of a large number of design frequencies will inevitably increase the design bounds that must be satisfied, thereby leading to conservatism and complex higher-order designs. Typically, the frequency array ω must be selected intuitively based on the required levels of system performance, the associated computational cost and engineering judgment Analysis of the Benefit of Employing a Smith Predictor The design bounds that obtain when the SP is absent from the design process are illustrated in Figure 5. In order to satisfy the desired constraints over the design frequencies.5 (rad/s) and 1 (rad/s), the use of a phase lead compensator would be required. Such a controller will lead to an oscillatory RSSI signal limit cycle around the target value that would in fact degrade the outage probability performance.

7 ROBUST POWER CONTROL FOR IEEE WIRELESS SENSOR NETWORKS 817 (a) 5 T U (z) 5 CG 1+CG (z) Magnitude (db) T L (z) Frequency (rad/sec) (b) Intersection of Bounds 3 2(rad/s) 2.5(rad/s) L 2 (z) L 1 (z) Magnitude (db).2(rad/s) 3(rad/s) 1(rad/s) L 2 (e 2.5T s ) L 2 (e.2t s ) L 2 (e.5t s ) L 2 (e T s ) L 2 (e 2T s ) L 1 (e.2t s ) L 1 (e.5t s ) L 1 (e T s ) L 1 (e 2T s ) L 1 (e 2.5T s ) L 1 (e 3T s ) 3.5(rad/s) L 2 (e 3T s ) Phase (degrees) Fig. 4. The robustness analysis. (a) The designed feedback controller (15) meets the tracking specification. (b) The design bounds are satisfied by the other existing loop-functions associated with d =, L 1 (z) and d = 1, L 2 (z). 3 1(rad/s) Intersection of Bounds 4. Practical Implementation and Discussion Magnitude (db) 3 4.5(rad/s).2(rad/s) L(e 2.5T s ) L(e 2T s ) L(z) L(e T s ) L(e.5T s ) 2(rad/s) 2.5(rad/s) 3(rad/s) L(e.2T s ) Phase (degrees) Fig. 5. Design bounds for the system without SP and L(z) = G (z). The design bounds in relation to.5 (rad/s) and 1 (rad/s) requires a phase lead compensator Use of Tmote-sky Wireless Nodes The Moteiv s Tmote-Sky, as shown in Figure 6(a), is an ultra low power IEEE compliant wireless module consisting of integrated sensors, transceiver, antenna, microcontroller and programming capabilities. With these facilities, Tmote-sky enables a wide range of network applications. Tmote-sky is typically powered by 2 AA batteries and is required Tmote-sky Datasheet is available at com/moteiv-transition.html

8 818 S. M. M. ALAVI, M. J. WALSH AND M. J. HAYES Fig. 6. (a) Tmote-Sky retrofitted to a fully autonomous MIABOT Pro miniature mobile robot. (b) The testbed, with two mobiles introduced in the system and three stationary nodes. to operate continuously for extended periods of time. As the technology is often deployed in remote and possibly hazardous environments, battery replacement may not be logistically viable, emphasizing the need for a dynamic power management scheme that can extend operational longevity Testbed Description The experimental setup is shown in Figure 6(b). It consists of five Tmote sensor nodes and one additional Tmote acting as a base station. The sensor nodes are programmed to send sensor data packets framed in the format [], using TinyOS Oscope application. The base station bridges packets over the USB/serial connection to a personal computer using a variation of the TOSBase application. # In Matlab, an application file compares the measured TinyOS is an open-source operating system designed for programming Moteiv WSNs. The software is available at: Each application is implemented as a set of modules written in nesc. The nesc language has a syntax like C programming, but supports concurrency, as well as mechanisms for structuring, naming, and linking together software components into robust network embedded systems. It is noted that a few applications and library components such as TOSBase (base station) and Oscope have already been prepared by the TinyOs community and can be used with only slight modifications for a variety of challenging applications. # An interface between Matlab and TinyOS has been established using TinyOS Matlab-tools written in Java. RSSI with the desired target value. Based on the aforementioned PC scheme, the power which is desired for the next data transmission is calculated. After the hardware limitations, (i.e. saturation and quantization constraints) are taken into account, the equivalent power level is sent to the sensor node where the radio frequency (RF) output power is adjusted accordingly. Two fully autonomous MIABOT Pro miniature mobile robots, ** as shown in Figure 6(a), are used to introduce tightly controlled mobility into the system that can be adjusted, removed and reintroduced as necessary. So that it can fit in a standard laboratory, the testbed is small in physical size, (m 2 ), excremental results show that the communication would normally be delay free in such conditions, [11,12]. The timedelay value has thus been set manually within the network for this study. Two sensors have been set to exhibit a one-step time delay, one sensor exhibits a delay in forward link and one in the reverse link. Two sensors have been set to exhibit a two-step timedelay and the last sensor is chosen to communicate as default Technical Implementation Notes Programmable power One particular feature of the Tmote-Sky node that facilitates its use in this study is the ability to adjust or program the RF output power by means of writing a **

9 ROBUST POWER CONTROL FOR IEEE WIRELESS SENSOR NETWORKS 819 Table I. Output power configuration for the CC24. Output power (dbm) power level value to the onboard CC24 transceiver. Table I shows the corresponding RF output power for different settings according to the CC24 datasheet. Following each subsequent PC iteration, the desired power for the next radio transmission is calculated, and then the equivalent power level must then be obtained and transmitted to the sensor node. To achieve this a linear(ized) relationship between power level and output power is established. Coupled with an incorporation of the saturation block that is an inevitable feature of such a transmission protocol, the power level for the next transmission is calculated according to the law 3 p i < 25; round(.5333(p i + ) + 11) 25 p i < ; p si = round(1.7143(p i + 3) + 23) p i ; 31 p i > (16) Figure 7 shows the real and linearized relationship between power level and RF power. The round command was employed to calculate an integer value for the power level. The difference between the real power and saturated-linearized power level (i.e. p i and p si, respectively) determines the amount of quantization error imposed on the system. Though, the smaller the error, the lower the variance around target RSSI, however, this quantization error was found to be practically negligible when compared with the variation due to fading and shadowing effects that naturally arise during the operation of this scenario, [21]. The CC24 is a single-chip 2.4GHz IEEE compliant transceiver utilizing direct sequence spread spectrum modulation/demodulation technique to code/decode the required data, [13] Linearized 5 Actual RF power (dbm) Fig. 7. Relationship between power level and RF output power for the Tmote-Sky Observations on the target received signal strength indicator In order to reconstruct the original transmitted message with a satisfactory level of PER, the received RSSI must satisfy a minimum threshold. Under the assumption that a PER of less than 1% is desired, r t should correspond to 55 dbm according to Reference [13] Benchmark Comparative Study System performance using the proposed loop-shaping PC strategy is now compared with two alternative, well cited, PC algorithms Power control technique using Linear Matrix Inequality (LMI) optimization problem In Reference [22] a convex optimization problem is presented as a set of LMI constraints and is used as a basis for PC synthesis. The output of the procedure is a set of controllers each satisfying the LMI constraints for a certain time-delay value. However, the scheduling of these candidate designs has not yet been addressed for a WSN with uncertain time-delay. An LMI controller is synthesized using this technique, taking the worst possible time delay (i.e. when d = 2), so that a reasonable comparison with the loop shaping strategy is possible. This process yields: C LMI (z) =.8932z 2 z z (17)

10 8 S. M. M. ALAVI, M. J. WALSH AND M. J. HAYES Power control technique using Genetic Algorithm (GA) In Reference [23], an alternative solution to the PC problem is presented that is based on the use of soft computing and in particular GA principles. An SP is also incorporated here to compensate for the effect of time delay. The design procedure relies on an assumption that the radio channel time-delay is fixed and known by the engineer. By trading off between quantization error and disturbance rejection, a set of controllers are output from the design procedure. In this comparison the quantization error is de-emphasized in the tradeoff exercise thereby producing a joint GA/SP PC law: C GA (z) = C(z) 1 + CS(z) =.33378z(z +.333)(z2.335z +.7) (z z )(z z ) (18) It should be noted that the higher order design yields an associated significant computational overhead that is not reflected in the assessment that follows; It will become a particularly significant problem if the system sampling time decreases Performance Analysis The following impartial performance analysis metrics are now considered for each algorithm: Tracking absolute error (TAE): Outage probability: E i (k) = r t r i (k) (19) O i (%) = number of times that r i < 57 db number of total iterations Power consumption: P i = () t p i (k) (21) k=1 57 db is arbitrarily selected as an a priori floor value below which performance is deemed unacceptable in terms of the ensuant PER. t represents the total number of samples for each experiment Testbed Scenarios for Performance Evaluation Consider the testbed introduced in Section 4.2. The following scenarios are adopted for the performance evaluation. In scenario 1, four sensor nodes are kept stationary and one node is defined to be mobile. For each of the proposed PC techniques, the testbed is run four times (for four randomly selected nodes locations). Having three PC strategies at hand, the total experiments for this scenario would be 12. Each experiment is (s) in duration. The RSSI, p i and p si are recorded during each experiment for the purpose of performance analysis. The aforementioned procedure is then repeated for scenario 2 where two mobile nodes and three stationary sensor nodes are introduced into the system. For consistency, the trajectories along which the mobile robots move remain the same for each experiment so that no location bias is incorporated into the analysis. Figure 8 shows a sample of the typical recorded data. It is also noted that LS, LMI and GA, respectively represent the results in relation to the proposed loop-shaping, LMI and gangetic algorithm PC techniques Average performance metrics taken over all existing nodes The RSSI TAE, outage probability, and power consumption is calculated for all nodes in each of the aforementioned scenarios. The average of the resultant data is the final metric taken for the comparison. Table II and Figure 9 illustrate the average taken over the TAE, the outage probability, and the power consumption denoted by Ẽ, Õ and P, respectively. The results can be summarized as follows: The RSSI TAE, outage probability, and power consumption are all proportional to number of mobile nodes. The availability of exact phase information in the loop-shaping procedure yields a minimally conservative design that exhibits the best system performance, i.e, power efficiency and outage probability. In particular, the use of an loop-shaping approach C LS (z) improves the power consumption by % when compared with the GA based law.

11 ROBUST POWER CONTROL FOR IEEE WIRELESS SENSOR NETWORKS 821 (a) RSSI (dbm) Actual power (dbm) RSSI (dbm) Actual power (dbm) (c) (e) RSSI (dbm) Actual power (dbm) (b) RSSI (dbm) Actual power (dbm) RSSI (dbm) Actual power (dbm) (d) (f) RSSI (dbm) Actual power (dbm) Fig. 8. A snapshot of resultant raw data for one-mobile and two-mobile scenarios. Thin lines correspond to the stationary nodes signals, and Thick lines correspond to the mobile nodes signals. (a) LS PC, One-mobile case. (b) LS PC, Two-mobile case. (c) LMI PC, One-mobile case. (d) LMI PC, Two-mobile case. (e) GA PC, One-mobile case. (f) GA PC, Two-mobile case.

12 822 S. M. M. ALAVI, M. J. WALSH AND M. J. HAYES Table II. Performance evaluation when all sensor nodes are considered. Table III. Performance evaluation when only mobile nodes are considered. PC (LS) PC (LMI) PC (GA) Ẽ (dbm) One-mobile case Two-mobile case Õ (%) One-mobile case Two-mobile case P (mw) One-mobile case Two-mobile case PC (LS) PC (LMI) PC (GA) Ẽ (dbm) One-mobile case Two-mobile case Õ (%) One-mobile case Two-mobile case P (mw) One-mobile case Two-mobile case Average performance metrics taken over mobile nodes It is also notable that there is significant algorithm performance variation when just the mobile nodes are considered. To this end, the related data is illustrated in Table III and in Figure. Use of a loopshaping strategy exhibits better performance than the other schemes and in particular displays a 6.9.2% improvement when compared to the GA control law. (a) 3 25 LS PC LMI PC GA PC (b) LS PC LMI PC GA PC E (dbm) 15 O (%) : One mobile case, 2: Two mobile case 1 2 1: One mobile case, 2: Two mobile case (c) 35 3 LS PC LMI PC GA PC 25 P (mw) : One mobile case, 2: Two mobile case Fig. 9. Average RSSI tracking absolute error, outage probability and power consumption, taken over all sensor nodes. (a) RSSI tracking absolute error. (b) Outage probability. (c) Power consumption.

13 ROBUST POWER CONTROL FOR IEEE WIRELESS SENSOR NETWORKS 823 (a) LS PC LMI PC GA PC (b) LS PC LMI PC GA PC 14 E (dbm) 12 8 O (%) : One mobile case, 2: Two mobile case 1 2 1: One mobile case, 2: Two mobile case (c) LS PC LMI PC GA PC P (mw) : One mobile case, 2: Two mobile case Fig.. Average RSSI tracking absolute error, outage probability and power consumption taken over mobile sensor nodes. (a) RSSI tracking absolute error. (b) Outage probability. (c) Power consumption. 5. Conclusions In this paper a novel PC technique has been presented that is generally applicable to WSNs that exhibit significant round-trip time-delay uncertainty. It has been shown that how the use of Smith predictor can significantly improve the feedback compensator design process for a practical sensor network that is a natural example of such a problem type. A loop shaping approach based around an assumption of worst case time delay works well without any recourse to scheduling of a vector of controllers being necessary. Significant improvements in robustness are achieved without reliable information regarding radio channel round trip delay uncertainty being required. Moreover, since phase information is utilized through the Nichols chart based loopshaping process in a minimally conservative fashion that is also intuitively appealing, significant benefits are derived by the engineer through the adoption of the proposed strategy. Significant improvements have been observed in relation to joint outage probability and power consumption. The resulting controller design procedure has been validated practically using a fully compliant experimental testbed that incorporates Moteiv s Tmote-Sky wireless nodes. Acknowledgments The support by Science Foundation Ireland under grant No. 5RFPCMS48 is acknowledged. The first author would like to extend his special thanks to Dr A. Karimi, Professor D. Bonvin, and Professor R. Longchamp, for

14 824 S. M. M. ALAVI, M. J. WALSH AND M. J. HAYES providing funding during his visit to the Automatic Control Laboratory, Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland. The many fruitful discussions that took place during this visit has added greatly to the quality of the final manuscript. Special thanks are also extended to the editor and anonymous reviewers for many fruitful comments to improve the quality of the work. References 1. Akyildiz IF, Su W, Sankarasubramaniam Y, Cayirci E. Wireless sensor networks: a survey. Computer Networks 2; 38: Jagannathan S. Wireless Ad hoc and Sensor Networks: Protocols, Performance and Control. CRC Press, Rappaport TS. Wireless Communications Principles and Practice (2nd edn). Prentice Hall, Goldsmith A. Wireless Communications. Cambridge University Press, Pantazis NA, Vergados DD. A Survey on power control issues in wireless sensor networks. IEEE Communications Surveys and Tutorials, 86 7, Liu J, Singh S. ATCP: TCP for mobile ad-hoc networks. IEEE Journal on Selected Area in Communications 1; 19(7): Gomez J, Campbell AT, Naghshineh M, Bisdikian C. Power aware routing in wireless packet networks. Proceedings of the 6th IEEE Workshop on Mobile Multimedia Communication, 1999; Das B, Bharghavan V. Routing in ad-hoc networks using minimum connected dominating sets. Proceedings of the IEEE Conference on Communications, 1997; Muqqattash A, Krunz MM. A distributed transmission power control protocol for mobile ad-hoc networks. IEEE Transactions on Mobile Computing 4; 3(2): Zurita Ares B, Fischione C, Speranzon A, Johansson KH. On power control for wireless sensor networks: system model, middleware component and experimental evaluation. Proceedings of the European Control Conferene, 7; Alavi SMM, Walsh MJ, Hayes MJ. Distributed power control technique for wireless sensor networks, based quantitative feedback theory. Proceedings of the IET Irish Signals and Systems Conference, Galway, Ireland, 8; Walsh MJ, Alavi SMM, Hayes MJ. A modified bumpless transfer technique for seamless handoff in adhoc wireless sensor networks. Proceedings of the IET Irish Signals and Systems Conference, Galway, Ireland, 8; GHz IEEE / ZigBee-Ready RF Transceiver (Rev. B), Texas Instruments. Avaliable at Koskie S, Gajic Z. Signal-to-interference-based power control for wireless networks: a survey, Dynamics of Continuous, Discrete and Impulsive Systems 6; 13(2): Smith OJM. Closer control of loops with dead time. Chemical Engineering Progress 1957; 53(5): Laughlin DL, Rivera DE, Morari M. Smith predictor design for robust performance. Int. J. Control 1987; 46(2): Horowitz I. Synthesis of Feedback Systems. Academic Press: New York, D Azzo JJ, Houpis CH. Linear Control System Analysis and Design. McGraw-Hill: New York, Borghesani C, Chait Y, Yaniv O. The QFT Frequency Domain Control Design Toolbox For Use with MATLAB. Terasoft Inc., 3.. IEEE Standard Wireless Medium Access Control (MAC) and Physical Layer (PHY) Specifications for Low-Rate Wireless Personal Area Networks (WPANs), Jakes W. Microwave Mobile Communications. IEEE Press, Lee BK, Chen YH, Chen BS. Robust H power control for CDMA cellular communication systems. IEEE Transactions on Signal Processing 6; 54(): Lee BK, Chen HW, Chen BS. Power control of cellular radio systems via robust Smith prediction filter. IEEE Transactions on Wireless Communications 4; 3(5): Authors Biographies Seyed Mohammad Mahdi Alavi received his Bachelor and Master degrees in Control Engineering from K.N. Toosi University of Technology in 1 and 3, respectively and Ph.D. from University of Limerick, Ireland in 9. He is currently a post doctorate researcher at Simon Fraser University, BC, Canada. His research interests include robust control theory (in particular Quantitative Feedback Theory) and fault detection and isolation technique with applications to wired/wireless networks as well as power systems. He received the best student award from K.N. Toosi University of Technology (1); Ph.D. scholarship from Science Foundation Ireland (May 6 October 8). He has held visiting positions at Centre for Embedded Software System, Aalborg University, Denmark (February April 7), and at Automatic Control Laboratory, EPFL, Switzerland (May October 7). Michael Walsh received a B.Eng. degree in Electronic Engineering in 1 from the University of Limerick. He is currently a Ph.D. candidate with the Wireless Access Research Centre and the Control Engineering Research Group at the University of Limerick, sponsored by the Embark Initiative s Postgraduate Research Scholarship Scheme under the Irish Research Council for Science, Engineering and Technology (IRCSET). His main research interests are centered around the control of systems with isolated memory-less non-linearlties, in particular the theory and application of Anti-Windup control. Other research interests include wireless communications and more specifically the application of systems science concepts to power aware Wireless Sensor Networks.

15 ROBUST POWER CONTROL FOR IEEE WIRELESS SENSOR NETWORKS 825 Martin Hayes has lectured at the University of Limerick (UL) since 1997, is course leader of the B.Sc. Electronics programme, and is a member of the Wireless Access Research Centre. He is the UL representative on the Irish Signals and Systems subcommittee of the Royal Irish Academy, and is a Steering committee member and previous Editor for the Irish Signals and Systems Conference. He holds a B.Eng. (1989) and M.Eng. (1992) from the University of Limerick as well as a Ph.D. from Dublin City University, (DCU, 1997). He has held a visiting Research fellowship at the University of Leicester and is also presently collaborating with researchers at the Universities of Sevilla in Spain. He has been an external examiner (Research) at the University of Leicester, NUI Maynooth, DCU and Dublin Institute of Technology and is currently an external examiner on engineering undergraduate programmes at both Dublin Institute of Technology and Limerick Institute of Technology.