Enhancement of IEEE 802.15.4 MAC layer to combat correlated channel errors

Enhancement of IEEE 802.15.4 MAC layer to Combat Correlated Channel ErrorsJasvinder Singh & Dirk PeschNimbus Centre for Embedded System ResearchCork Institute of TechnologyCork, Ireland{jasvinder.singh, dirk.pesch}@cit.ieAbstract- In indoor environment, the IEEE 802.15.4 low-rate, low-power packet transmissions experience statistical correlation between channel errors due to interference and multipath fading. The 802.15.4 MAC layer implements an ARQ (Automatic Repeat-Request) mechanism for error recovery. In this work, we investigate the impact of correlated errors on the ARQ mechanism. The MAC layer back-off strategy employs a uniform random distribution to choose back-off values; which often reduces retransmission resolution time when packets confront collisions or transmission errors. We therefore propose the application of non-uniform (skewed) distribution which improves the system performance. Furthermore, an adaptive back off strategy, fast EI-slow ED is developed for IEEE 802.15.4 MAC protocol to combat channel errors in time varying conditions. A detailed comparative analysis is presented employing accurate models of wireless channel and MAC protocol. Numerical results indicate that proposed scheme performs better, especially in worst channel conditions, when long duration error bursts are more frequent.Keywords-IEEE802.15.4; MAC; fading; skewed distributionI.I NTRODUCTIONThe IEEE802.15.4 standard [1] is increasingly being usedin various critical applications [2] to implement energy efficient low-rate, low-power wireless personal area networks (LR-WPANs). In these application environments, the quality of low-power communication is severely affected by multi-path fading and external interferences dueto devices or machineries operating in same frequency band. As a result, packet transmissions more often encounter temporally correlated channel errors. The standard does not facilitate any error correction schemes at lower link/physical layer; it incorporates error detection codes at the receiver asa part of MAC layer ARQ (Automatic Retransmission Request) mechanism to examine the received packet integrity and erroneous packets are requested to be retransmitted. The wireless channel irregularities have a significant influence on communication energy consumption, and it has been ignored in most of existing state-of-the-art low-power protocols. In present work, we examine 802.15.4 MAC protocol to ensure reliable data transport against correlated channel errors being modelled using first order Markovian approximation [3]. The transition probabilities are derived from physical channel parameters, e.g. Doppler frequency, data rate, fading margin, etc [4]. It is observed that MAC layer CSMA/CA (carrier sense multiple access/collision avoidance) algorithm doesn’t perform well for parameters settings allowed in standard. Therefore, we suggest some improvements in back-off procedure. After getting transmission error, probability of larger resolution in retransmission time is achieved by drawing random back-off units from the window with non-uniform distribution (left or negatively skewed) instead of uniform derivates. The rationale is to defer retransmission by pulling large back-off value to curb the impact of stochastic burst errors. This mechanism is efficient from energy management perspective of battery operated nodes as temporarily bad link quality may result in excessive energy expenditure due to unnecessary transmissions. The Kumarswamy distribution [5] (similar to Beta distribution) has been employed to approximate the desired shapes of non-uniform distributions as it offers simplified closed form distribution function. Later, an adaptive back-off procedure (fast EI-slow ED) is proposed; the BW size (back- off window) is adjusted by taking into account the history of previously transmitted packets. The comparative analysis is presented with other strategies using IEEE 802.15.4 MAC protocol. Numerical results reveal that proposed scheme offers better trade-off in terms of packet deliveries, energy consumption and delay when long duration error bursts are frequent.In next section, we discuss the related work. Section III gives the overview of IEEE802.15.4 standard. In Section IV, Markov channel model is explained. The numerical evaluations are presented in Section V along with results. Section VI introduces proposed back off mechanism and comparative analysis with other schemes. In the final section, we conclude the paper with discussion.II.R ELATED W ORKThe IEEE 802.15.4 is the de-facto standard for LR-WPAN based sensor network applications. The suitability of IEEE802.15.4 MAC protocol, especially with a focus on transmissions over noisy wireless medium has never been worked out extensively. Many efforts have been undertaken focusing on different aspects [6]-[10]. In [6], impact of network node densities has been discussed with conclusion of achieving desired reliability using MAC parameters values not allowed by 802.15.4. To minimize packet collisions, a novel non-persistent CSMA/p* protocol is proposed [7] that employs unique non-uniform probability distribution to select the contention slots. Similarly, IEEE802.15.4 MAC layer parameter values are proposed to978-1-4577-0351-5/11/$26.00 ©2011 IEEEdifferentiate packet transmission frequencies of network nodes [8]. The Memorized Back-off Scheme (MBS) with Exponential Weighted Moving Average (EWMA) is suggested [9] that works well for smaller range of parameters values and becomes inefficient otherwise. An adaptive back exponent algorithm [10] is aimed to improve performance against packet collisions. Most of the above work assumes error free transmissions without any noise or interference. Recently, the empirical study [11] using IEEE 802.15.4 standard has concluded that the assumption of an ideal error-free wireless channel is not always true and low power transmissions often encounter correlated channel errors. The IEEE802.11 MAC protocol for wireless local area network (WLAN) has been evaluated extensively against the fading and noisy environment [12]-[13]. The work [12] focuses on the influence of retry limits; while double increment-double decrement [DIDD] back-off algorithm is proposed in [13]. In present work, IEEE 802.15.4MAC performance is analyzed when correlated packet errors (burst errors) are apparent due to interference and other obstacles between the communicating nodes.III. IEEE802.15.4 MAC O VERVIEWThe IEEE802.15.4 MAC layer supports two operating modes: beacon-enabled mode (slotted CSMA/CA) and non beacon-enabled mode (unslotted CSMA/CA). In this work,we use non beacon-enabled version due to low overheadsassociated with it. The time axis is discretized into back-off units, each with duration of aUnitBackoffPeriod (320µsec) [1]. The back-off exponent (BE ) parameter is boundedbetween macMinBE (default=3, range: 0-7), macMaxBE (default=5, range: 3-8). During transmission, random numberof complete aUnitBackoffPeriods are selected between 0 and 2 1, where 2 1 represents BW size to determine the channel access time. The random back-off period is pulled from uniform distribution, where probabilityof all values in the interval being selected is equal. In ARQ scheme, the corrective actions (packet retransmissions) depend upon the macMaxFrameRetries parameter, (default=3, range: 0-7). Beyond this limit, MAC layer drops the packet. Each retransmission is attempted when acknowledgement is not received within macAckWaitDuration (~ 864 us ). In present work, we assume zero packets collision probability to study the impact of channel errors, which is realistic case for time slotted system when same frequency band is time shared among several nodes. At any instant, only one node is in dialogue with sink node over fading channel which is valid, if nodes are deployed between several obstacles. According to default MAC CSMA/CA procedure, on transmission error, the retransmission of same packet occurs after 2.24ms (assuming minimum value of back-off parameter, BE = macMinBE = 3)[1]. In case of larger value, i.e. BE = 5 or 8, resolution of retransmission time becomes 9.9ms and 81.6ms respectively. In real-world scenario, channel temporarily becomes bad for random durations (coherence time) on the scale of few hundred milliseconds [11][14]. Therefore, attempt for packetretransmissions might again suffer from poor channel conditions, if inappropriate retransmission resolution time is selected. Therefore, new strategy related to back-off procedure is proposed to ensure transmission reliability in energy-constrained sensor network.IV. C HANNEL M ODELThe wireless links are highly non-deterministic due to link burstiness [11]. The channel models that generate independent and identical distributed (iid ) errors, don’t represent the realistic scenario. We have considered the channel model that explicitly accounts for statistically correlated packet errors. The packet level errors can be modelled as first order Gilbert-Elliot (GE) Markov chain [3, 4], with two states, e.g. “good” (no packet error) and “bad” (packet error). The state transition probability matrix for the Markov process is given by;(1) Where p 00 and p 01 represents the probabilities that j th packet transmission is successful, if (j-1)th packet transmission was successful or unsuccessful, respectively. The steady state packet error probability (P e ) is given as;(2) The transition matrix of the Markov model is derived from physical channel and transmission parameters, for e.g.channel Doppler frequency (f d ), data rate, fading margin (G). The average packet error rate (PER) is given by; 1 ⁄ (3) The transition probability matrix parameter, p 00 is given by;1, , ⁄ (4) Where ⁄ , and 2 is the Gaussian correlation coefficient of two samples of the complex amplitude of a fading channel taken at time distance T . . is the Bessel function of first kind and zero order [2],and .,. is the Marcum Q function. ,(5) Where H 0 is modified Bessel function of first kind and zero-th order. We apply Markov model at IEEE802.15.4 packet level (127 bytes) with 250Kbps data rate. The channel state changes from good to bad, or vice versa and a particular state (good/bad) remains same for one time slot which corresponds to round-trip time (RTT ≈ 4.8ms )* assuming negligible propagation and processing delays. Therefore, the sequence of channel values experienced by packet transmissions can be seen as a sampled version of continuous channel taken at RTT distance. The states transition rate and states duration depends on the degree of temporal correlation, which is related to f d , for e.g. f dvalue <10 Hz aretypical of slow moving pedestrians. The packet errors in such scenarios tend to be more bursty. The large values of f d (80 Hz) are typical of fast moving vehicular users and packet errors are nearly independent in such scenarios. For the given parameters G , f d and T , transition matrix (M ) of the Markov process is derived. For further details, please refer [4]. *The round trip time (RTT) includes the time duration for transmittinga IEEE802.15.4 data frame (127 bytes of MAC protocol data unit + 6-byte packet overhead (Preamble and Start of Frame Delimiter [SHR], and Frame Length [PHR]) plus the duration in which the acknowledgment of thatframe (11 bytes) is received. Therefore, RTT is obtained by adding the dataframe transmission time (4.256ms), device turnaround time (0.192ms) and acknowledgement frame receiving time (0.352ms) [1].V.P ERFORMANCE E VALUATIONFor performance evaluations, OPNET-Modeler tool [15] is used due to availability of IEEE 802.15.4 MAC library. We assume zero packets collision probability to study the impact of channel errors, which is realistic case for time slotted system when same frequency band is time shared among several nodes [16]. At any instant, only one node is in dialogue with sink node over fading channel which is valid, if nodes are deployed between several obstacles. The sending node is always backlogged with the new packet to be transmitted. Each collected data point is averaged over 25 simulation tests using different random seed over 105 packets. The performance emulations are carried out based on three metrics. First, packet reception ratio (PRR), measures the network reliability; defined by the ratio of number of unique packets received to total number of packets transmitted. Second, Energy-Tax, the average energy consumption for each successfully delivered packet; is calculated as total transmission energy divided by energy consumption of successful packets. Third, average packet delay, measures the network responsiveness; average time of the packet measured from the beginning of its first transmission to the time, it is received successfully.A.IEEE802.15.4 MAC PerformanceFirst, the different parameter settings related to back-off mechanism, for e.g. BW size (BE), maximum number of retransmissions (macMax-FrameRetries) is applied. The battery operated nodes generally operate at lower noise margins and in dynamic channel conditions, a small variation in signal-to-noise ratio often turns good link to poor link [11]. As per channel model, the degree of correlation among random errors depends upon the product f d T (normalized Doppler bandwidth). Smaller f d T increases the long duration probability of the particular state or vice- versa. The impact of different degrees of correlated channel errors on PRR and Energy-Tax is studied, assuming G = 2.5dB (P e≈0.4) for different BE (range 3-8) allowed in standard keeping default settings of other parameters (Fig.1 a,b). The MAC protocol with default settings of BE (3-5) is not able to handle burst errors. At particular f d, large BE value enhances PRR along with significant reduction in Energy-Tax metric. However, performance degrades at lower f d values due to long duration bad channel states. For channel with uncorrelated errors (f d =80Hz), performance remains constant. The effect of macMaxFrameRetries parameter on PRR at different BW sizes is also studied at f d T = 0.024 (f d =5Hz) (Fig.1c). At BE=3(default), larger macMax-FrameRetries parameter value doesn’t improve PRR significantly due to lower retransmission resolution time (not shown). Therefore, window sizes, BE=5 and 7 are selected. More retransmissions improve packet delivery but it isn’t an appropriate strategy to ensure reliability in energy constrained sensor network. Therefore, we propose to improve the performance by limiting macMaxFrameRetries parameter to the default value (=3) in following sections. B.Skewed DistributionAfter packet transmission, the sending node waits for macAcknowledgewait (0.864ms) time duration for acknowledgement. In case of no acknowledgement, random back-off value is selected from the pool of uniformly distributed values in a particular window interval (BE=3 to 8). As, the probability of all values in the interval being selected is equal in case of uniform distribution, that often leads to poor retransmission resolution time with more frequent retransmission attempts during temporarily bad channel state. The reasons are twofold; first, the inappropriate window size and the other is contribution of uniform distribution towards it. Selecting the back-off value from the uniform distribution yields the effect of reduced window size, even at larger window sizes. Leaving the decision of window size adjustment for next section; here we focus on non-uniform distributions as they offer greater control over probabilistic weight adjustment of the back-off values in tails and at the centre of the generated distribution. For non-uniform distribution (skewed) of random back-off units, we employ kumaraswamy distribution as it is much simpler to use due to simple closed-form of both probability density and cumulative distribution function. For detailed information, please refer [5]. The double-bounded probability density function (DB-PDF) has following form;1 (6), (7) The cumulative distribution function (cdf) is defined by;1 1 (8)Where λ > 0, >0 are shape parameters. Depending on λ and , DB-PDF can take any shapes to approximate single modal distributions. Beside uniform distribution, five different shape distributions are considered which are characterized by statistical properties such as mean, mode and shape parameters. Two symmetrical distributions (sym1, sym2) have same mean (=0.5) and mode (=0.5) but different shape parameters (λ=1.63, =1.8) and (λ=2.87, =5.0) respectively. For non-uniform skewed left/right (negatively/positively skewed), the probability of obtaining values in the right/left of the interval increases due to high mass of the distribution. Therefore, right skewed distribution (mean=0.32, mode=0.25,λ=1.71, =5.0) generates random values most likely from lower half interval. The left skewed1 (mean=0.65, mode=0.75,λ=3.14, =2.0) and left skewed2 (mean=0.82, mode=0.90, λ=7.35, =2.0) produce the most likely values in upper-half interval. The two left skewed distributions have been considered to see the influence of more weights of the higher values in the interval. All these distributions (Fig. 2) are employed in CSMA/CA back-off procedure corresponding to back-off windows (BE=5,7). The performance results are shown for channel f d T=0.024 (Fig.3). Both types of the symmetrical distributions don’t offer any improvement like uniform distribution. The probability of the values being selected from the middle of window is very high. The left skewed distributions probabilistically yield greater retransmission resolution time. Consequently, higher PRR with lower(a)(b) (c)Figure 1. Impact of f d on PRR (a), Energy-Tax (b), G=2.5dB, macMaxFrameRetries=3, Impact of macMaxFrameRetries on PRR (c), f d T=0.024Energy-Tax is achieved. Moreover, they also eliminate the problem of reduced window size as back-off values are stochastically selected from specific interval inside the window. The effect is more pronounced, if the weight of higher values of the window interval is increased but it comes at the expense of small increment in average delay (~10 ms) if larger size BW is considered (Fig.3c).Figure 2: DB-PDF for Different Values of λ and , Mean and Mode VI. P ROPOSED B ACKOFF M ECHANISMThe wireless channel dynamics is generally unpredictable.Therefore, an adaptive back-off strategy is required to adaptto changing conditions. Comparatively, fewer efforts havebeen undertaken in context of IEEE802.15.4 MAC ascompared to IEEE802.11 in non-ideal environmentconditions. We propose fastEI-slowED (fast-Exponential-Increase slow-Exponential-Decrease) back-off mechanismfor IEEE802.15.4 MAC layer. The fastEI-slowED is avariant of Exponential Increase-Exponential Decrease(EIED) back-off procedure; suggested for distributed co-ordinated function of IEEE 802.11 to deal with differenttraffic load conditions [18]. But here, our focus is to ensurereliable data transport against correlated random errors. Thebasic EIED mechanism for IEEE802.11 is as follows;BW=min [α.BW, BW max ]if No-Ack BW=max [BW/β, BW min ] if Ack In case of no acknowledgment, BW size is multiplied by factor α for next transmission; while on receiving acknowledgement, it is reduced by β. The performance of EIED is highly affected by the choice of α and β. Moreover, it also suffers from the dominant usage of greater BW size as window size increases quickly in case of transmission failures and decreases gradually on successful transmission. In our proposed fast EI-slow ED strategy, instead of changing BW size during retransmission attempts of the same packet, the skewness of distribution is altered to increase the probability of larger retransmission resolution time. For newpacket, BW is adjusted based on the history of previously transmitted two packets as during experiments it is observed that retaining memory larger than two packets does not affect the performance. In case of packet failure after all attempts, the BW is step-up by the factor α (after two consecutivepacket drops, α = 4 while after single drop, α=2). The number of transmission efforts not only yields an idea aboutthe state of the channel but also its longevity. Therefore, aftersuccessful packet delivery, the reduction factor β isdetermined based on transmission attempts made for previous packet. The fastEI-slowED mechanism is shown inFig. 4, where N l is number of transmission attempts forsuccessful packet delivery, N max is maximum allowed attempts, defined by macMaxFrameRetries +1. The thresholdBE th (real value) indicates the stage at which current windowsize is reduced to integer BE value as BE may have any real value during BW size reduction. If current BE value is lessthan or equal to BE th , it is step down to integer BE value. Formore insight, the behaviour of proposed scheme is presented(Fig.5). The number of stages experienced by the node to getwindow size reduced by factor 2 with corresponding windowsizes at each stage is shown assuming successfultransmission at n th attempt (≤macMaxFrameRetries ). Fig.5adisplays stages counts incurred at different macMax-FrameRetries parameter values. At particular macMax-FrameRetries value (>1), larger value of n th attemptincreases the stages count due to reduced BW size. On theother hand, window size gets reduced by a large amountwhen n th attempt value is small (i.e. n=1). At any stage, theBW size (Fig.5b, normalized on scale) depends upon thevalue of n. The successful transmissions at every 1st attemptresults in 31% size reduction in consecutive stages; whilesuccessful transmission at every 3rd attempt yields the 26%size reduction respectively. Therefore, it indicates that our approach offers sufficient nonlinearities in adjusting BW size to efficiently adapt to the irregularities of wireless medium in addition to flexibility in selecting any range of parameters0.10.20.30.40.50.60.70.80.91345678P a c k e t R e c e p t i o n R a t i o (P R R )BEfd =1.0 Hz fd=2.5 Hz fd=5.0 Hz fd=10 Hz fd=80 Hz0246810121416182022345678E n e r g y T a xBEfd=1.0 Hz fd=2.5 Hz fd=5.0 Hz fd=10 Hz fd=80 Hz0.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.7P a c k e t R e c e p t i o n R a t i o (P R R )Error Probability (P e )No ReTx,BE=5No ReTx,BE=73 Retx,BE=53 ReTx,BE=77 Retx,BE=57 ReTx,BE=7Normalized Variable P r o b a b i l i t y D e n s i t y F u n c t i o n (P D F )Figure 3: Impact of Non-Uniform Distributions on Performance Metrics (a,b,c) f d T=0.024(BEmin, BEmax, macMaxFrameRetries ). Furthermore, it can easily be integrated in IEEE 802.15.4 MAC without any significant modification in the communication procedure.A. Comparative EvaluationsThe fastEI-slowED scheme is analyzed for BE parameter settings allowed in IEEE802.15.4 MAC (BE min = 3 to BE max = 8) keeping macMaxFrameRetries at default value (=3). During 3 retransmission attempts of the same packet, non-uniform distribution mean is shifted towards higher values (for e.g. 0.65, 0.75, 0.90) that increases the probability of larger retransmission resolution time with increase in attempts. For comparisons, three other back- off schemes are considered; simple binary exponential back-off(BEB) which is inherently being used in 802.11, Double Increment-Double Decrement (DIDD) [13], and the memorized back-off scheme with exponential weighted moving average (EWMA) [18]. In BEB, BW size is doubled for each retry until packet is successfully transmitted or maximum allowed retry attempts is reached. After successful transmission, window size is reset to minimum (BE min =3). In case of DIDD scheme proposed for 802.11 MAC to deal with burst or correlated errors; window size increases like BEB during retransmission attempt but steps-Figure 4. fastEI-slowED Back-off Scheme Flow Diagram(a) (b)Figure 5: Effect of Transmission Attempts on Window Size Reduction (by factor 2); (a) Stages Counts at Consecutive Successful Retransmission at n th attempt (b) Window Sizes ( Normalized value) at Each Stage for Different n th Attempt Values (macMaxFrameRetries =3)down by factor of 2 after successful packet delivery. In case of EWMA back-off procedure proposed to adapt to dynamic traffic load conditions; BW size used for last few packets transmissions is applied to predict window size for current transmission [18]. The 802.15.4 MAC parameters settings is applied for comparative evaluations; for e.g BE parameter values (BE min =3 to BE max =8), macMaxFrameRetries =3. At channel f d T=0.024, legacy BEB scheme doesn’t perform well as compared to other schemes at different P e , while EWMA scheme outperforms in terms of PRR when P e <0.5 (Fig.6a). Although, fastEI-slowED (skewed) offers packet delivery lower than DIDD when P e < 0.3, but it is more than 90%. At lower fading margin (P e ≥ 0.3), correlated errors occur more frequently; our approach starts performing well. Similar trend is observed for Energy-Tax metric (Fig.6b). The EWMA scheme outperforms ( in terms of PRR and Energy-Tax) but exhibits very high average packet delay (Fig.6c) due to rapid increase and gradual decrease in BW size, resulting in dominant usage of large BW size. The average packet delay for our approach is higher than DIDD, which is due to better adaptation to combat long duration error bursts to avoid energy intensive retransmissions. In Fig. 7, fine-grain view of BW sizes (each data point averaged over 5 values) adopted by back-off schemes are shown. Both (fastEI-slowED , DIDD) strategies adapt well to channel dynamics. At low fading margin, our approach adapts to higher window sizes while DIDD scheme exhibits oscillatory behaviour resulting in comparatively lower PRR and more Energy-Tax . The results conclude that fastEI-slowED back-off mechanism adapts well to channel dynamics and is more energy efficient due to less retransmission attempts, especially when long duration error bursts are dominant.00.10.20.30.40.50.60.70.80.9100.10.20.30.40.50.60.7P a c k e t R e c e p t i o n R a t i o (P R R )Error Probability (P e )BE=5,Uni,Sym1,Sym2BE=5,Right Skewed BE=5,Left Skewed1BE=5,Left Skewed2BE=7,Uni,Sym1,Sym2BE=7,Right Skewed BE=7,Left Skewed1 BE=7,Left Skewed2024681012141600.10.20.30.40.50.60.7E n e r g y T a xError Probability (P e )BE=5,Uni,Sym1,Sym2BE=5,Right Skewed BE=5,Left Skewed1BE=5,Left Skewed2BE=7,Uni,Sym1,Sym2BE=7,Right Skewed BE=7,Left Skewed1 BE=7,Left Skewed2-5.55E-170.0050.010.0150.020.0250.030.0350.040.0450.050.0550.060.0650.0700.10.20.30.40.50.60.7A v e r a g e P a c k e t D e l a y (S e c )Error Probability (P e )BE=5,Uni,Sym1,Sym2BE=5,Right Skewed BE=5,Left Skewed1BE=5,Left Skewed2BE=7,Uni,Sym1,Sym2BE=7,Right Skewed BE=7,Left Skewed1 BE=7,Left Skewed232222223322224332253336437481234567macMaxFrameRetriesn=1n=2n=3n=4n=5n=6n=7n=1n=2n=300.10.20.30.40.50.60.70.80.91st2nd3rd4rthW i n d o w S i z e (2x )Stage Number n=1n=2n=3(a)(b) (c)Figure 6. Comparative Performance of Back-off Strategies (a,b,c) f d T=0.024Figure 7. Back-off Window Sizes Against Channel Dynamics (f d =5Hz )VII. C ONCLUSIONWe have studied the IEEE802.15.4 MAC protocol performance in noisy wireless environment where statistical correlation exists between channel errors. The MAC layer back-off procedure is investigated for different set of parameter settings. The application of simple non-uniform distribution (left skewed) not only improves the performance but also offers flexibility for selecting back-off values stochastically without changing the default structure of CSMA/CA algorithm. The proposed fastEI-slowED back-off mechanism adapts well to wireless channel dynamics. In future work, we will increase the robustness of our scheme in the network conditions where packet collisions are also inherent in addition to channel errors. A CKNOWLEDGMENTThe authors acknowledge the support of the Irish Higher Education Authority under the Program for Research in Third Level Institutions (PRTLI) cycle 4 funded NEMBES program in funding the reported work.R EFERENCES[1] IEEE Std. 802.15.4 – 2003, “Standard for Telecommunications andInformation Exchange Between Systems– Local Area Metropolitan Area Networks – Specific Requirements - Wireless Medium AccessControl (MAC) and Physical Layer (PHY) Specifications for Low Rate Wireless Personal Area Networks (WPAN)”; /15/pub/TG4.html[2] A. Willig, “Recent and Emerging Topics in Wireless Industrial Communications: a Selection”, IEEE Transactions on Industrial Informatics, Vol. 4, May 2008.[3] H.S. Wang, “On verifying the first-order Markovian assumption for a Rayleigh fading channel model”, in Proc. ICUPC’94, pp. 160-164, San Diego, CA, Sep. 1994.[4] M. Zorzi, R. R. Rao, and L. B. Milstein, “On the accuracy of a first-order Markov model for data transmission on fading channels,” in Proc. IEEE ICUPC’95, Nov. 1995, pp. 211–215[5]P. Kumaraswamy, A generalized probability density function for double bounded random processes, J. Hydrol. (46) (1980) 79–88.[6] G. Anastasi, M. Conti, and M. Di Francesco, “The MAC unreliability problem in IEEE 802.15.4 wireless sensor networks,” in Proc. MSWIM 2009, 26-30 October 2009.[7]Y.C. Tay, K.Jamieson, H. Balakrishnan, “Collision-minimizing CSMA and Its Applications to Wireless Sensor Networks”, IEEE Journal on Selected Areas in Communications, Volume: 22, Issue: 6, Pages: 1048 – 1057, Aug. 2004.[8] J.-G. Ko, Y.-H. Cho, and H. Kim. “Performance evaluation of IEEE 802.15.4 MAC with different backoff ranges in wireless sensor networks”, in Proc. of .IEEE ICCS 2006, Singapore, Oct. 2006.[9] Ai-Chun Pang, Hsueh-Wen Tseng, "Dynamic Backoff for Wireless Personal Networks," IEEE GLOBECOM'04, 2004[10] V. P. Rao and D. Marandin, "Adaptive Backoff Exponent Algorithm for Zigbee (IEEE 802.15.4)," in NEW2AN, St.Petersburg, Russia, Sept 2006, pp. 501-516.[11] Srinivasan, K., Dutta, P., Tavakoli, A., and Levis, P. “An empirical study of low-power wireless”, pp 1-49, ACM Trans. Sen. Netw. 6, (Feb. 2010).[12]P. Chatzimisios, A. C. Boucouvalas and V. Vitsas,“ Performance analysis of IEEE 802.11 DCF in presence of transmission errors”, in Proceedings of the IEEE International Conference on Communications (ICC 2004), vol. 7, pp. 3854–3858, June 2004.[13] Chatzimisios, P., Vitsas, V., Boucouvalas, A.C, “Revisit of fading channel characteristics in IEEE 802.11 WLANs: independent andburst transmission errors”, PIMRC'06, Helsinki,11-14 Sept. 2006[14] Theodore S. Rappaport, Wireless communications: Principals and Practice (2nd Edition), Prentice Hall, Upper Saddle River, NU, 2001 [15] OPNET, "OPNET Simulator, v15”, .[16] M.Singh, V.K.Prasanna, ”A Hierarchical Model for Distributed Collaborative Computation in Wireless Sensor Networks”, in Proceedings of IPDPS ,22-26 april, 2003, Nice , France.[17]N.-O. Song, B.-J. Kwak, J. Song, and L. E. Miller, “Enhancement of IEEE 802.11 distributed coordination function with exponential increase exponential decrease backoff algorithm”, in Proceedings of the 57th IEEE VTC, vol. 4, pp. 2775 – 2778, Apr. 2003.[18]Ai-Chun Pang and Hsueh-Wen Tseng, “Dynamic backoff for wireless personal networks,” in Proc. IEEE GLOBECOM, vol. 3, pp. 1580−1584, Nov. 2004.0.40.450.50.550.60.650.70.750.80.850.90.9510.10.20.30.40.50.60.7P a c k e t Re c e p t i o n R a t i o (P R R )Error Probability (P e )fastEI-slowED (Skewed)fastEI-slowED (Uniform)EWMA DIDD BEB11.522.533.544.555.566.577.588.50.10.20.30.40.50.60.7E n e r g y T a xError Probability (P e)fastEI-slowED(Skewed)fastEI-slowED(Uniform)EWMA DIDD BEB0.010.020.030.040.050.060.070.080.090.10.110.10.20.30.40.50.60.7A v e r a g e P a c k e t D e l a y (S e c )Error Probability (P e )fastEI-slowED(Skewed)fastEI-slowED(Uniform)EWMA DIDD BEBB a c k -o f f E x p o n e n t (B E )Time (sec)。