MIMO Enabled Efficient Mapping of Data in WiMAX Networks

Transcription

1 MIMO Enabled Efficient Mapping of Data in WiMAX Network Penumarthi Phani Krihna, R. Saravana Manickam, and C. Siva Ram Murthy Department of Computer Science and Engineering Indian Intitute of Technology Madra, Chennai Abtract. MIMO technique upported by IEEE network improve either throughput or reliability in the network. But thee MIMO technique do not alway perform optimally, epecially in the preence of high mobility. In thi paper, we propoe a cro layered mapping technique that exploit multiple antenna available at each MS. An optional error correction mechanim i propoed at the receiver to correct erroneouly received ignal. Finally, uing extenive imulation we how that the propoed technique achieve higher throughput compared to the exiting technique while providing the ame reliability. We alo how that the propoed technique can be a tand alone technique and adaptive witching of MIMO technique i not required. Keyword: WiMAX, IEEE , MIMO, Kalman Filter. 1 Introduction Worldwide interoperability for Microwave Acce (WiMAX) i the commercial verion of the IEEE tandard [2] targeted to provide Wirele Broadband connectivity with data rate upported up to everal hundred Mbp and covering ditance up to everal km. WiMAX ue Orthogonal Frequency Diviion Multiple Acce (OFDMA) technology at the phyical layer in order to mitigate multi path interference. Thi improve the reliability of the tranmitted data and the throughput of the network. WiMAX upport a variety of technique uch a Adaptive Modulation and Coding, Multiple Input Multiple Output (MIMO) to improve the achieved throughput of the network. WiMAX, in order to utilize the available MIMO technique, upport up to 4 antenna at each Mobile Station (MS) and up to 8 antenna at the Bae Station (BS). It alo upport Adaptive MIMO technique depending on the channel quality between an MS and the BS, and improve the quality of the data tranmitted. Some of the MIMO technique that are comparable to the propoed technique are explained here. Spatial Multiplexing i a MIMO technique in which everal tream of data (which i minimum of the number of antenna available at the tranmitter and the receiver) can be tranmitted imultaneouly uing multiple antenna. A 2 2 Spatial Multiplexing cheme i hown in Figure 1. For a fixed L. Bononi et al. (Ed.): ICDCN 2012, LNCS 7129, pp , c Springer-Verlag Berlin Heidelberg 2012

2 398 P. Phani Krihna, R. Saravana Manickam, and C. Siva Ram Murthy Channel + AWGN Noie MS BS Fig. 1. MIMO Technique: Spatial Multiplexing number of allocated lot, the effective throughput achieved uing multiple (two) antenna at an MS i theoretically twice the throughput achieved uing a ingle antenna. Spatial Diverity technique are upported to improve reliability of the tranmitted data. Tranmit Diverity i a technique in which the ame data (with different tranmiion characteritic) i tranmitted on more than one antenna imultaneouly. An example of Tranmit Diverity technique (Alamouti Coding [1]) i hown in Figure 2. Receiver Diverity i a technique in which a ignal i received acro multiple antenna, and one of the receiver combining technique among Maximum Ratio Combining, Selection Combining and Equal Gain Combining [3] i ued to maximize the Signal to Noie Ratio (SNR) of the required tranmitted ignal. Since SNR of the required ignal i maximized, error in the ignal are reduced. Thu the reliability of the tranmitted data i improved by uing multiple antenna at the receiver Channel + AWGN Noie MS BS * 2 1 * 3 * * 4 Fig. 2. MIMO Technique: Spatial Diverity (Alamouti) An interim concept, Path Diverity [7] i ued to improve the lo reilience in Wirele Local Area Network (WLAN) by enabling multiple Acce Point (AP) to receive the data tranmitted by a ingle client. A frame recombining cheme i ued at each AP to recover original frame from a et of poibly erroneou frame, thu improving the reliability of the tranmitted frame. Currently, MAC Protocol Data Unit (MPDU ) in WiMAX network are cheduled for each frame baed on the number of OFDM lot and the MIMO technique allocated to each MS. Thee MIMO technique are adaptively aigned to each MS depending on the channel quality. The reliability of the tranmitted data and the achieved throughput of the network are highly dependent on the MIMO technique ued. MIMO technique are adaptively aigned to each MS baed on the channel condition, condition number and Quality of Service (QoS) requirement of each MS.

3 MIMO Enabled Efficient Mapping of Data in WiMAX Network 399 The problem that we tudy in thi paper can be termed a Can we propoe a MIMO technique that can maximize the achievable throughput with out compromiing the reliability of tranmitted data? The reliability of tranmitted data hould be ame a that of diverity technique, but the throughput hould be maximized. However, adaptive witching of exiting MIMO technique [12] i a completely different problem, and i not tudied in thi paper. Due to high variation in the channel, adaptive MIMO witching doe not alway provide optimal performance in high mobility region. In thi cenario, providing a MIMO technique that i alway optimal i a challenge that we tudy in thi paper. In thi paper, we deign a tranmiion technique conidering the channel condition and improve the performance of the network. A thi i a time invariant MIMO technique that guarantee reliability value equal to that of diverity technique and throughput comparable to that of multiplexing technique, the propoed technique need not be adaptive in nature. We achieve thi by propoing an optional error correction mechanim at the receiver. The advantage of the propoed technique i that the choice of an appropriate MIMO technique to be ued at each MS i reduced to the baic choice of whether to ue multiple antenna or not for the tranmiion. The ret of the paper i organized a follow. In Section 2 we provide the aumption made and continue with decription of the propoed technique in detail. The technique i evaluated in Section 3. We conclude the paper and provide drawback of the propoed technique in Section 4. In the Appendix, we provide a critical analyi of the aumption made in the paper. 2 Propoed Technique 2.1 Aumption Following are the aumption made in thi work: The channel gain of the tranmitted tream acro an antenna remain contant for all the m OFDM lot in a ingle frame, between each MS and the BS. The tranmiion of ignal through a channel can be repreented mathematically a y = h x + n (1) where y i the received ignal for the tranmitted ignal x with the channel gain a h and a contant Gauian noie n of mean 0. Since the channel gain remain contant for a ingle frame between an MS and the BS, we aume that Equation 1 hold for all the OFDM lot tranmitted at an MS i.e., i [1,m], y [i] = h x [i] + n where i repreent the OFDM lot. The value of h i independent of i, for all OFDM lot tranmitted in a ingle frame. The channel gain i independent of the frequency at which data i tranmitted, and the channel i aumed to be Additive White Gauian in nature.

4 400 P. Phani Krihna, R. Saravana Manickam, and C. Siva Ram Murthy For each frame (typically of 5 m duration), a typical WiMAX MS, feed back the Channel Quality Indicator (CQI) attained in it previou frame to the BS. Since each MS ue everal OFDM lot for tranmiion, and an MS tranmit only one CQI value, we conider that all the OFDM lot in a ingle frame will have contant channel quality. When an MS tranmit data acro two antenna, each tream obtain different SNR value at the BS [8]. In a deployed cellular network, it can be deduced that the difference in the SNR value of the ignal from two antenna will differ by at leat 3 db. The difference i alo dependent on SNR level. A the SNR value increae, o doe the difference. When the SNR value of an MS i cloe to the accepted threhold value at the BS, it can be aumed that one tream of data i received with SNR threhold (nonerroneou), and the other tream with SNR<threhold (erroneou). It i at thi SNR region we propoe the technique. However, receiver combining technique can be ued to receive data tranmitted from an antenna. Thee combining technique [3] are ued before the propoed technique i utilized. The propoed technique work on the ignal that are egregated by the exiting combining technique, for each tranmitting antenna eparately. 2.2 Propoed Technique at the Tranmitter Alamouti coding [1] i one of the frequently ued antenna technique to improve the reliability of the data tranmitted. When an MS i equipped with ingle antenna, Alamouti coding technique ue time (or frequency) lot for tranmitting data redundantly. When equipped with multiple antenna, each antenna tranmit data acro all the OFDM lot, and receiver ue combining technique to retrieve the tranmitted data. The propoed technique i decribed a follow: When an MS i allocated n ofdm lot to tranmit in a ingle frame, MS tranmit variant of ame data acro both antenna in t ofdm lot. The technique i enabled only when one tream i received with SNR higher than the threhold and other tream i received with SNR lower than the threhold from an MS. The redundant data (in form of ignal) in t ofdm lot acro both the antenna will be ued by the propoed error correction mechanim at the BS. The data tranmitted at an MS in 4 OFDM lot acro multiple antenna with t ofdm = 2 i hown in Figure 3. The firt two OFDM lot acro both the antenna tranmit variant of ame data. Different data i tranmitted in remaining OFDM lot. We derive the optimal t ofdm value when the error detection and correction mechanim i utilized at the BS. For the following analyi, we follow the notation that each OFDM lot comprie of two OFDM ymbol. In an IEEE network, the packet error ratio of a Protocol Data Unit (PDU) tranmitted uing OFDM ymbol i given a p pdu =1 (1 p ofdm ) n ofdm (2)

5 MIMO Enabled Efficient Mapping of Data in WiMAX Network Channel + AWGN Noie MS BS * 2 1 * 5 6 Fig. 3. Data Tranmitted in the Propoed Technique where p ofdm denote the probability of receiving an erroneou OFDM ymbol and n ofdm i the number of OFDM ymbol required to tranmit the PDU [6]. When a PDU can be tranmitted in a ingle frame uing n ofdm ymbol acro two antenna, the packet error probability of PDU in Eq. (2) can be modified a p pdu =1 [(1 p ofdm1 ) k 1 (1 p ofdm2 ) k 2 ] (3) where k 1 and k 2 are the number of OFDM ymbol tranmitted, p ofdm1 and p ofdm2 denote the probability of receiving an erroneou OFDM ymbol tranmitted from antenna 1 and 2, repectively. Sufficient condition being k 1 + k 2 = n ofdm. With out lo of generality, we aume that the data tranmitted from a ingle antenna will receive equal interference for all the OFDM lot ued at that antenna (Aumption 1). In a ingle frame (of 5 m duration), the probability of an error occurring in k i OFDM ymbol tranmitted from an antenna i ame a error occurring in a ingle OFDM ymbol. Baed on thi aumption, Eq. (3) can be modified a p pdu =1 [(1 p ofdm1 ) (1 p ofdm2 )] (4) Eq. (4) aume that the receiver (BS) doe not incorporate any error correction mechanim. By enabling an appropriate error correction mechanim at the BS and providing t ofdm ymbol redundancy in the data being tranmitted from both antenna, Eq. (4) can be modified a p pdu = XY (1 P(χ 1 = k 1 t ofdm ν 2 = k 2 )) + X Y (1 P(χ 2 = k 2 t ofdm ν 1 = k 1 )) + X Y where X =(1 p ofdm1 ),Y =(1 p ofdm2 ), X =(p ofdm1 ) and Y =(p ofdm2 ) (5) where X and Y denote the probability of receiving the ignal from antenna 1 and 2 without error, while X and Y i the probability of receiving ignal with error. P(χ 1 = k 1 t ofdm ν 2 = k 2 ) i the probability of correcting the erroneouly received k 1 OFDM ymbol tranmitted from antenna 1 when k 2 OFDM ymbol from antenna 2 are received without error. Similarly, P(χ 2 = k 2 t ofdm ν 1 = k 1 ) can be defined. Thi correction probability i dependent on the correction mechanim ued at the BS.

6 402 P. Phani Krihna, R. Saravana Manickam, and C. Siva Ram Murthy 2.3 Propoed Technique at the Receiver Alamouti coding [1] tranmit data uch that both original and conjugate form of the data are tranmitted acro different antenna imultaneouly. Thi technique i independent of any phyical layer technology. Our propoed technique aume OFDM technology at the phyical layer. The error ignal determined from the redundant data in t ofdm OFDM lot i ued for correcting the data in the remaining OFDM lot of the erroneou tream [Theorem 2 in Appendix]. We determine the error ignal that differentiate the ignal of erroneou tream and non-erroneou tream in the firt t ofdm lot. The error ignal i the ignal when convolved with an erroneou tream of ignal, will improve the SNR of the tream. Some of the plauible filter for propoing an error correction and detection mechanim are analyzed a follow. Weiner filter [5,13] i one of the tationary filter that tatitically determine the effective channel tate, and thu improve the SNR of the received ignal by at leat 2 db [5]. The diadvantage of Weiner filter i that, it aume the underlying proce to be Wide Sene Stationary. In the propoed technique, the input data need not be tationary and Weiner filter i not applicable. Matched filter efficiently compare a compound ignal with an ingredient ignal and maximize the SNR of the compound ignal with repect to the ingredient ignal, and i ued for packet recognition [10]. However, the expreion to etimate error uing Matched filter i dependent on the input ignal i.e., Matched filter provide different etimate for different ingredient ignal. Hence, the error etimated in one OFDM lot can not be ued for other OFDM lot and Matched Filter i not applicable. Kalman filter [5,13,14] efficiently etimate the noie in the received ignal by meauring the noie from the previouly received ignal, and i adaptive in nature. For each iteration, Kalman filter update the etimated value and etimate the value accurately, tabilizing with time. A variation of Kalman filter applied at ub-carrier level [4] conider uing of OFDM ymbol for tranmitting data. The per ub-carrier Kalman update recurively etimate for a et of ub-carrier in a ingle time lot. Several iteration are poible for each OFDM ymbol, and the etimated value are accurate after 40 iteration (Obervation 1 in Appendix). Hence, per ub-carrier Kalman filter i apt for error detection in our propoed technique and we ue Kalman filter to efficiently etimate the difference between the erroneou and non-erroneou tream. Detail of Kalman filter parameter are tabulated in Table 1. The flow diagram for decoding the ignal received at two antenna of the BS i hown in Figure 4. The SNR of each ignal i checked for acceptance baed on the threhold value. When one of the tream i received with SNR Threhold and the other tream i received with SNR<Threhold, the propoed technique i utilized. When both the ignal are received with SNR below the Threhold, both ignal are rejected.

7 MIMO Enabled Efficient Mapping of Data in WiMAX Network 403 Table 1. Mapping of Kalman Filter Parameter at the Receiver Parameter Decription Relevance Parameter in the Technique x State Vector Etimate Error Etimate H Obervation Matrix Data in Non-erroneou Stream Z Obervation Vector Data in Erroneou Stream A State Tranition Matrix Identity Matrix B Input Matrix Null Matrix u Input Control Vector Null Matrix vandw Gauian Noie Gauian Noie Antenna 1 RF SNR >T 1 Ye SNR 1>T and SNR 2<T No SNR >T 1 No Reject Signal No Ye Ye Ue Propoed Technique ADC Filter Demodulator Decoder No Ye Ye Antenna 2 RF SNR >T 2 Ye SNR 2>T and SNR 1<T No SNR >T 2 No Reject Signal Fig. 4. Signal Flow at the Receiver The error correction mechanim i triggered only when one of the tream i received with error and the other i received without error (SNR<Threhold). Auming that data i tranmitted redundantly in t ofdm OFDM lot at each antenna, data in the firt OFDM lot at each antenna i given a input to the Kalman filter. Each OFDM lot i plit into everal ub-carrier (48 in WiMAX), and Kalman filter i ued to etimate the error for each ub-carrier, a explained in Figure 5. A the number of ub-carrier in one OFDM lot (48) i greater than 40, the etimated value converge and we can etimate the error for the remaining ub-carrier. Thu, error in the erroneou tream compared to nonerroneou tream i etimated. The error determined in firt OFDM lot remain contant, and can be ued to correctdata in the remaining OFDM lot [Theorem 2 in Appendix]. The data in remaining OFDM lot of the erroneou tream i convolved with the error ignal, and data i corrected [Theorem 1 in Appendix]. An MS utilize multiple antenna only when the number of lot allocated i higher than a threhold value (8 in imulation), which i dependent on the SNR of the received ignal. The optimal number of OFDM lot t ofdm,inwhich data i to be tranmitted redundantly acro different antenna i determined a below. The etimated error i accurate after 40 iteration [Obervation 1 in Appendix]. Since 48 ub-carrier available in an OFDM lot provide iteration 40, the error etimated uing the firt OFDM lot i ufficient to determine

8 404 P. Phani Krihna, R. Saravana Manickam, and C. Siva Ram Murthy Information Stream 1 2 m 48 Kalman Filter Etimate h 1 h 2 h 3 h 4 h 5 OFDM ymbol ub carrier Information Stream h 47 h 48 m 48 Fig. 5. Propoed Error Detection Mechanim at the Receiver the error efficiently. Hence, an optimal redundancy of data in t ofdm =1OFDM lot acro different antenna at an MS i required for the propoed technique to improve performance of the network. 3 Evaluating the Propoed Technique We ue tandard n-2 imulator with a WiMAX patch provided by NIST [9] for evaluating the propoed technique. We conducted imulation at 3.5 GHz carrier frequency with a bandwidth of 7 MHz, and each OFDM ymbol contitute μ and ue QPSK 3/4 modulation technique. Each MS and the BS i equipped with two antenna. A Contant Bit Rate (CBR) traffic i generated at each MS with a contant packet ize of 1500 byte. Wecomparethepropoed technique with Alamouti technique and a technique that ue ingle antenna, by meauring the throughput and reliability of the data tranmitted in the network. We alo aume that for a ingle OFDMA frame of 5m, data tranmitted acro each antenna will have contant channel coefficient and noie term at each receiving antenna. A hown in Figure 6, the throughput of the network increae until the number of MS reach a value of 20, a ufficient traffic i induced in the network. The throughput in the Alamouti coding technique i cloe to the throughput of ingle antenna technique even though it ue 2 antenna, becaue the entire data i tranmitted redundantly on the other antenna. However, ince the reliability i high for the data tranmitted uing Alamouti technique, throughput i lightly higher in Alamouti technique compared to ingle antenna technique. Since, the number of redundant OFDM lot in the propoed technique i only 1, an improvement in the throughput of the network i viible.

9 MIMO Enabled Efficient Mapping of Data in WiMAX Network e+06 3e+06 Throughput (Mbp) 2.5e+06 2e e+06 Alamouti Propoed SingleAntenna 1e Number of MS Fig. 6. Throughput of the Network Veru Number of MS in the Network A can be een in Figure 7, the Alamouti technique maintain the highet reliability value while the ingle antenna technique maintain the lowet. For the imulation, reliability i the ratio of number of packet received uccefully to the number of packet tranmitted. Thi i becaue the data i entirely replicated at other antenna alo. The reliability of the tranmitted data in the propoed technique matche with Alamouti technique when the number of MS in the network i le than 20, and maintain value in between the value of Alamouti and ingle antenna technique. Thi improvement in reliability i due to the uage of filtering at the receiver and elimination of error in the erroneouly received ignal. However, the propoed technique work only when one SNR<Threhold and another SNR Threhold. Hence, the value of reliability i not alway ame a Alamouti technique Reliability Alamouti Propoed SingleAntenna Number of MS Fig. 7. Reliability of the Tranmitted Data Veru Number of MS in the Network

10 406 P. Phani Krihna, R. Saravana Manickam, and C. Siva Ram Murthy 4 Concluion In thi paper, we propoed a tranmiion technique acro multiple antenna that exploit the uage of OFDM technology in WiMAX network. We alo proved that by tranmitting redundant data in OFDM lot (t ofdm =1lot)at different antenna of an MS and uing efficient error correction mechanim at the receiver (BS), the reliability of the tranmitted data i improved. While other technique that improve the reliability have coniderable reduction in achievable throughput, the propoed technique maintain the reliability by reducing the throughput marginally compared to multiplexing technique. We ue extenive imulation and how that our propoed mechanim perform better than other MIMO technique. The tranmiion technique propoed in thi paper aume that irrepective of the ignal proceing technique over an exiting ignal, the domain of the noie term in the proceed ignal remain in the ame domain a the preproceed (exiting) ignal. However, thi aumption i highly idealitic in nature and i conidered practically impoible. Solving the propoed problem when thi aumption i relaxed (cloe to realitic condition) remain a a challenge and can be conidered a future work. Acknowledgement. Thi work wa upported by the Department of Science and Technology, New Delhi, India. Appendix Theorem 1. In any network with a frame ize of 5 m uing OFDM ymbol for tranmiion, when two tream I 1 and I 2 tranmitted from a ingle terminal (MS) are received at two antenna of another terminal (BS), we can correct one erroneou ignal if the other ignal i received without error. Proof. The channel gain for a tream of data tranmitted from an antenna in a 5 m frame i contant [2] irrepective of the fading ditribution. Let tream I 1(2) ha a channel gain of h 1(2) with Gauian noie a n 1(2). Here, n 1(2) i the Circularly Symmetric Gauian Random Variable taken from (0,N σ 2), where N σ 2 i average noie value < 1. Let I 1 tream i received without error (SNR Threhold) and I 2 tream i received with error (SNR<Threhold). Let tream I 1 i tranmitted with ignal d 1,d 2,d 3 and tream I 2 i tranmitted with ignal d 1,d 4,d 5 acro 3 OFDM lot. The tranmiion of ignal acro the channel can be written a 1 1 = h 1 d 1 + n 1 (6) 2 1 = h 2 d 1 + n 2 (7)

11 MIMO Enabled Efficient Mapping of Data in WiMAX Network 407 Calculating d 1 from Eq. (6) and ubtituting in Eq. (7), 2 1 = h n, (8) where h = h 2 /h 1 and n = n 2 n 1 h 2 /h 1. Hence, by convolving the erroneou tream (I 2 ) ignal with h 1 =(h 2 /h 1 ) 1, the channel gain i hown to be ame a that of tream I 1. It i to be noted that the noie alo i improved by the ame factor. However, ince noie term n 1(2) i the Circularly Symmetric Gauian variable, the noie value remain in (0, 1). Hence, the power of noie i improved marginally compared to the channel gain. Since the channel gain i improved with marginal change in power of the noie, the SNR of the tream I 2 increae. Alo, the channel gain in I 2 i improved to that of I 1 with minor variation in noie. Hence, the error in tream I 2 i corrected. Theorem 2. The error (h in Theorem 1) that we determine for erroneou tream I 2 uing the firt OFDM lot remain contant for all the remaining OFDM lot, and can be utilized to improve the quality of the received ignal. Proof. Following from Eq. (7), we can determine 2 4 with data tranmitted a d 4 to be 2 4 = h 2 d 4 + n 2 (9) Now, convolving 2 4 with h 1 =(h 2 /h 1 ) 1 give 2 4 h 1 =(h 2 d 4 + n 2 ) (h 1 /h 2 )=h 1 d 4 + n 2 h 1 /h 2 (10) Since the channel gain i improved to h 1, the quality of the received ignal i improved. Alo, the value of h i achieved only from the firt OFDM lot and the ame h i ued to improve the quality of the remaining OFDM lot. Hence, the quality of the received ignal i improved by determining the h from the firt OFDM lot and applying for the remaining OFDM lot. Obervation 1. The value of the etimate from the Kalman filter converge after 40 iteration (etimation). We generate the plot uing MATLAB, by tranmitting integer a the correctly and wrongly received ignal and etimated the value of error ignal. A we know that the data i tranmitted in form of contellation for each modulation type, we denote that the data in each contellation (bit) can be repreented a integer. In a contellation, the probability of converting adjacent point i high compared to other [11]. Thu, we aume that we get different integer for different contellation. The approximate error percentage i a plotted in Figure 8. A can be een, the initial etimate contitute an error etimate of up to 30%, and a the number of etimate cro 40, the error percentage remain table at 1% 5%.

12 408 P. Phani Krihna, R. Saravana Manickam, and C. Siva Ram Murthy Percentage of Error Number of Etimate Fig. 8. Reliability of the Tranmitted Data Veru Number of MS in the Network Reference 1. Alamouti, S.: A imple tranmit diverity technique for wirele communication. IEEE Journal on Selected Area in Communication 16(8), (1998) 2. Board, I.S.S.: IEEE Standard for Local and Metropolitan Area Network Part 16: Air Interface for Broadband Wirele Acce Sytem. IEEE Std (Reviion of IEEE Std ) pp (May 2009) 3. Brennan, D.: Linear diverity combining technique. Proceeding of the IEEE 91(2), (2003) 4. Chen, W.: Time- Frequency- Selective Channel Etimation of OFDM Sytem. Ph.D. thei, Drexel Univerity, Pennylvania, USA (2005) 5. Haye, M.H.: Statitical Digital Signal Proceing and Modeling. Wiley (1996) 6. Hoymann, C.: Analyi and performance evaluation of the OFDM-baed metropolitan area network IEEE Computer Network 49(3), (2005) 7. Miu, A., Balakrihnan, H., Kokal, C.E.: Multi-radio diverity in wirele network. Wirele Network 13(6), (2007) 8. Moberg, P., Oeiran, A., Skillermark, P.: Cot comparion between SISO and MIMO deployment in future wide area cellular network. In: Proceeding of IEEE Vehicular Technology Conference, pp. 1 5 (2009) 9. NIST: IEEE module for NS-2 (February 2009), Nychi, G., Hottelier, T., Yang, Z., Sehan, S., Steenkite, P.: Enabling MAC protocol implementation on oftware-defined radio. In: Proceeding of USENIX Sympoium on Networked Sytem Deign and Implementation, pp (2009) 11. Sen, S., Gilani, S., Srinath, S., Schmitt, S., Banerjee, S.: Deign and implementation of an approximate communication ytem for wirele media application. In: Proceeding of the ACM Special Interet Group on Data Communication, pp (2010) 12. Tran, M., Hall, D., Nix, A., Doufexi, A., Beach, M.: Mobile WiMAX downlink performance analyi with adaptive MIMO witching. In: Proceeding of IEEE Mobile WiMAX Sympoium, pp (2009) 13. Treichler, J.R., Johnon Jr. C.R., Larimore, M.J.: Theory and Deign of Adaptive Filter. Wiley-Intercience (1987) 14. Welch, G., Bihop, G.: An Introduction to the Kalman Filter. Tech. rep., Univerity of North Carolina, Chapel Hill, NC, USA (1995)