Pub Date : 2005-09-01DOI: 10.1109/GLOCOM.2005.1577643
M. Yajima, Takumi Hasegawa
Phased array antennas have primarily been used for narrowband systems such as radar. However, in recent years, these systems have been increasingly used for wideband applications, such as satellite communication. In this paper, we describe the beam shift principle of a wideband linear phased array antenna with reduced true-time-delay devices, as well as a simple formula for calculating the beam pointing error. The results obtained from the application of the formula were in concurrence with the simulation results. We also propose a simple method for compensating for the pointing error, and report the simulation results.
{"title":"Beam pointing error of wideband phased array antennas with reduced true-time-delay devices","authors":"M. Yajima, Takumi Hasegawa","doi":"10.1109/GLOCOM.2005.1577643","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1577643","url":null,"abstract":"Phased array antennas have primarily been used for narrowband systems such as radar. However, in recent years, these systems have been increasingly used for wideband applications, such as satellite communication. In this paper, we describe the beam shift principle of a wideband linear phased array antenna with reduced true-time-delay devices, as well as a simple formula for calculating the beam pointing error. The results obtained from the application of the formula were in concurrence with the simulation results. We also propose a simple method for compensating for the pointing error, and report the simulation results.","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114104704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-07-01DOI: 10.1109/GLOCOM.2005.1578070
Yuanbin Guo, Jianzhong Zhang, D. McCain, Joseph R. Cavallaro
In this paper, a streamlined MIMO Kalman equalizer architecture is proposed to extract the commonality in the data path by jointly considering the displacement structure of the transition matrix and the block-Toeplitz structure of the channel matrix. Finally, an iterative conjugate-gradient based algorithm is proposed to avoid the inverse of the Hermitian symmetric innovation correlation matrix in Kalman gain processor. The proposed architecture not only reduces the numerical complexity to O(F log F) per chip, but also facilitates the parallel and pipelined VLSI implementation in real-time processing
{"title":"Displacement MIMO Kalman equalizer for CDMA downlink in fast fading channels","authors":"Yuanbin Guo, Jianzhong Zhang, D. McCain, Joseph R. Cavallaro","doi":"10.1109/GLOCOM.2005.1578070","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1578070","url":null,"abstract":"In this paper, a streamlined MIMO Kalman equalizer architecture is proposed to extract the commonality in the data path by jointly considering the displacement structure of the transition matrix and the block-Toeplitz structure of the channel matrix. Finally, an iterative conjugate-gradient based algorithm is proposed to avoid the inverse of the Hermitian symmetric innovation correlation matrix in Kalman gain processor. The proposed architecture not only reduces the numerical complexity to O(F log F) per chip, but also facilitates the parallel and pipelined VLSI implementation in real-time processing","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122810658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-04-01DOI: 10.1109/GLOCOM.2005.1578084
Hee Goo Han, S. Oh, Seung Joon Lee, D. Kwon
We analyze the computational complexity of sphere decoding (SD) for maximum likelihood detection (MLD) according to initial radius selection schemes, and also propose an efficient initial radius reduction scheme that reduces further the initial radius. As the initial radius for SD, we use the Euclidean distance between the received signal vector and the lattice vector corresponding to a suboptimum initial estimate. The proposed initial radius reduction scheme selects a new lattice vector closer to the received signal vector than the initial lattice vector in order to reduce the initial radius further. From our analyses, the reduction in the overall complexity due to further reduction of initial radius gets more significant as the SNR decreases. The ZF-DFE scheme in a combination with the proposed radius reduction scheme has the fewest computations over practical SNR range for communications, and its computations are less than that of the vertical Bell-labs layered space-time (V-BLAST) detection scheme with optimal ordering, even at low SNR values achieving an uncoded bit error rate (BER) of 0.1
{"title":"Computational complexities of sphere decoding according to initial radius selection schemes and an efficient initial radius reduction scheme","authors":"Hee Goo Han, S. Oh, Seung Joon Lee, D. Kwon","doi":"10.1109/GLOCOM.2005.1578084","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1578084","url":null,"abstract":"We analyze the computational complexity of sphere decoding (SD) for maximum likelihood detection (MLD) according to initial radius selection schemes, and also propose an efficient initial radius reduction scheme that reduces further the initial radius. As the initial radius for SD, we use the Euclidean distance between the received signal vector and the lattice vector corresponding to a suboptimum initial estimate. The proposed initial radius reduction scheme selects a new lattice vector closer to the received signal vector than the initial lattice vector in order to reduce the initial radius further. From our analyses, the reduction in the overall complexity due to further reduction of initial radius gets more significant as the SNR decreases. The ZF-DFE scheme in a combination with the proposed radius reduction scheme has the fewest computations over practical SNR range for communications, and its computations are less than that of the vertical Bell-labs layered space-time (V-BLAST) detection scheme with optimal ordering, even at low SNR values achieving an uncoded bit error rate (BER) of 0.1","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131112752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-03-13DOI: 10.1109/GLOCOM.2005.1578034
Huan Liu, F. Tobagi
WDM/SONET provides a natural migration path to support traffic growth. In WDM/SONET, each wavelength is a separate SONET ring and each ring can be set to one of several line speeds. The line speed should be high if there is enough traffic to realize the economy of scale, otherwise, it should be low to reduce the cost. Despite of the advantages, there are no general tools and methodologies available to help network designers enjoy the benefits of multiple line speeds. For the first time, we propose a comprehensive approach to solve the traffic grooming problem, which includes both novel, complete ILP formulations that can be used to solve small size problems exactly and an efficient heuristic algorithm that can be used to solve large problems quickly. Using the tools we developed, we study the trade-offs of shortest path routing, study the cost benefits of traffic switching, compare UPSR and BLSR, and show that multiple line speeds can significantly reduce cost
{"title":"Traffic grooming in WDM/SONET BLSR rings with multiple line speeds","authors":"Huan Liu, F. Tobagi","doi":"10.1109/GLOCOM.2005.1578034","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1578034","url":null,"abstract":"WDM/SONET provides a natural migration path to support traffic growth. In WDM/SONET, each wavelength is a separate SONET ring and each ring can be set to one of several line speeds. The line speed should be high if there is enough traffic to realize the economy of scale, otherwise, it should be low to reduce the cost. Despite of the advantages, there are no general tools and methodologies available to help network designers enjoy the benefits of multiple line speeds. For the first time, we propose a comprehensive approach to solve the traffic grooming problem, which includes both novel, complete ILP formulations that can be used to solve small size problems exactly and an efficient heuristic algorithm that can be used to solve large problems quickly. Using the tools we developed, we study the trade-offs of shortest path routing, study the cost benefits of traffic switching, compare UPSR and BLSR, and show that multiple line speeds can significantly reduce cost","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123853895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-03-01DOI: 10.1109/GLOCOM.2005.1577756
L. Marchal, P. Primet, Y. Robert, J. Zeng
While grid computing reaches further to geographically separated clusters, data warehouses, and disks, it poses demanding requirements on end-to-end performance guarantee. Its pre-defined destinations and service criteria ease the performance control; however, expensive resources and equipments used by grid applications determine that optimal resource sharing, especially at network access points, is critical. From the resource reservation perspective, this article looks at communication resources shared by grid sites. Two resource request scenarios have been identified, aiming at optimizing the request accept rate and resource utilization. The optimization problems, proven NP-complete, are then solved by heuristic algorithms. Simulation results, aside from showing satisfying results, illustrate the pros and cons of each algorithm
{"title":"Optimizing network resource sharing in grids","authors":"L. Marchal, P. Primet, Y. Robert, J. Zeng","doi":"10.1109/GLOCOM.2005.1577756","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1577756","url":null,"abstract":"While grid computing reaches further to geographically separated clusters, data warehouses, and disks, it poses demanding requirements on end-to-end performance guarantee. Its pre-defined destinations and service criteria ease the performance control; however, expensive resources and equipments used by grid applications determine that optimal resource sharing, especially at network access points, is critical. From the resource reservation perspective, this article looks at communication resources shared by grid sites. Two resource request scenarios have been identified, aiming at optimizing the request accept rate and resource utilization. The optimization problems, proven NP-complete, are then solved by heuristic algorithms. Simulation results, aside from showing satisfying results, illustrate the pros and cons of each algorithm","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123255612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1109/GLOCOM.2005.1577462
A. Roy, J. Doherty
Locally Optimum (LO) detection offers a means of reliable signal detection under high noise conditions. This technique is applied to remove first order autoregressive narrowband interference from a spread spectrum system. A new expression for output signal-to-interference ratio (SIR) is derived and compared with simulation results. A comparison of the LO detector performance and adaptive Wiener filtering based on the output SIR is presented to highlight the strengths of this technique. Further, it is shown that LOD technique is not overly sensitive to model parameter estimation error.
{"title":"Locally optimum detection performance analysis for narrowband interference rejection in spread spectrum communications","authors":"A. Roy, J. Doherty","doi":"10.1109/GLOCOM.2005.1577462","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1577462","url":null,"abstract":"Locally Optimum (LO) detection offers a means of reliable signal detection under high noise conditions. This technique is applied to remove first order autoregressive narrowband interference from a spread spectrum system. A new expression for output signal-to-interference ratio (SIR) is derived and compared with simulation results. A comparison of the LO detector performance and adaptive Wiener filtering based on the output SIR is presented to highlight the strengths of this technique. Further, it is shown that LOD technique is not overly sensitive to model parameter estimation error.","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115132563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1109/GLOCOM.2005.1578097
I. Bahceci, G. Al-Regib, Y. Altunbasak
Parallel distributed detection for wireless sensor networks is studied in this paper. The network consists of a set of local sensors and a fusion center. Each local sensor makes a binary (single-bit) or M-ary (multi-bit) decision and passes it to the fusion center where a final decision is made. The links between the local sensors and the fusion center are subject to fading and additive noise resulting in corruption of the transmitted decisions. We analyze the performance of the decision fusion based on likelihood ratio tests and derive false alarm and detection probabilities. Based on the theoretical probability expressions, we design optimal decision rules for the local sensors and the fusion center. Finally, we illustrate the performance of the parallel fusion by numerical examples
{"title":"Parallel distributed detection for wireless sensor networks: performance analysis and design","authors":"I. Bahceci, G. Al-Regib, Y. Altunbasak","doi":"10.1109/GLOCOM.2005.1578097","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1578097","url":null,"abstract":"Parallel distributed detection for wireless sensor networks is studied in this paper. The network consists of a set of local sensors and a fusion center. Each local sensor makes a binary (single-bit) or M-ary (multi-bit) decision and passes it to the fusion center where a final decision is made. The links between the local sensors and the fusion center are subject to fading and additive noise resulting in corruption of the transmitted decisions. We analyze the performance of the decision fusion based on likelihood ratio tests and derive false alarm and detection probabilities. Based on the theoretical probability expressions, we design optimal decision rules for the local sensors and the fusion center. Finally, we illustrate the performance of the parallel fusion by numerical examples","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115493750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1109/GLOCOM.2005.1578457
H. Bai, D. Lija, Mohammed Atiquzzaman
The throughput degradation of transport control protocol (TCP) over lossy links due to the coexistence of congestion losses and link corruption losses is very similar to the degradation of processor performance due to control hazards in CPU design. First, two types of loss events in networks with lossy links can be considered as two possibilities of a branching result (correct speculation vs. incorrect speculation) in a CPU. Secondly, both problems result in performance degradations in their application environments, i.e., penalties (in clock cycles) in a processor, and throughput degradation (in bit per second) in TCP networks. This has motivated us to apply speculative techniques (i.e., speculating on the outcome of branch predictions), used to overcome control dependencies in a processor, to TCP improvements when lossy links are involved in TCP connections. The objective of this paper is to propose a protocol-level speculation based TCP modification to improve its throughput over lossy links. Simulation results show that, compared to other prior research, our proposed algorithm significantly improves TCP throughput in a network with satellite links
{"title":"Applying speculative technique to improve TCP throughput over lossy links","authors":"H. Bai, D. Lija, Mohammed Atiquzzaman","doi":"10.1109/GLOCOM.2005.1578457","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1578457","url":null,"abstract":"The throughput degradation of transport control protocol (TCP) over lossy links due to the coexistence of congestion losses and link corruption losses is very similar to the degradation of processor performance due to control hazards in CPU design. First, two types of loss events in networks with lossy links can be considered as two possibilities of a branching result (correct speculation vs. incorrect speculation) in a CPU. Secondly, both problems result in performance degradations in their application environments, i.e., penalties (in clock cycles) in a processor, and throughput degradation (in bit per second) in TCP networks. This has motivated us to apply speculative techniques (i.e., speculating on the outcome of branch predictions), used to overcome control dependencies in a processor, to TCP improvements when lossy links are involved in TCP connections. The objective of this paper is to propose a protocol-level speculation based TCP modification to improve its throughput over lossy links. Simulation results show that, compared to other prior research, our proposed algorithm significantly improves TCP throughput in a network with satellite links","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116803044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1109/GLOCOM.2005.1578216
Lillian L. Dai, V. Chan
Many wireless network studies pertain to the derivation of throughput bounds and cross-layer optimization for energy conservation. From a practical perspective, often a network must meet the competing objective of attaining high throughput while conserving energy for prolonged operation. The tradeoff between these two important network metrics has not been adequately addressed in the literature. A further deficiency in existing research lies in the suppression of non-distance-dependent processing energy in energy models, which can lead erroneously to routing on paths with large number of hops. We model processing energy explicitly, and show that for a particular implementation of wireless network, the average path power is a monotonically increasing, piecewise linear function of throughput. Furthermore, we quantify a network region size threshold such that in a small region relative to the threshold, direct transmission routing is both energy conserving and throughput achieving. For larger regions, path power optimal routing may not achieve the maximum throughput. Higher throughput may be achieved with suboptimal routing schemes that lead to higher marginal power increase as the throughput increases
{"title":"Energy and throughput tradeoff in wireless networks with processing energy considerations","authors":"Lillian L. Dai, V. Chan","doi":"10.1109/GLOCOM.2005.1578216","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1578216","url":null,"abstract":"Many wireless network studies pertain to the derivation of throughput bounds and cross-layer optimization for energy conservation. From a practical perspective, often a network must meet the competing objective of attaining high throughput while conserving energy for prolonged operation. The tradeoff between these two important network metrics has not been adequately addressed in the literature. A further deficiency in existing research lies in the suppression of non-distance-dependent processing energy in energy models, which can lead erroneously to routing on paths with large number of hops. We model processing energy explicitly, and show that for a particular implementation of wireless network, the average path power is a monotonically increasing, piecewise linear function of throughput. Furthermore, we quantify a network region size threshold such that in a small region relative to the threshold, direct transmission routing is both energy conserving and throughput achieving. For larger regions, path power optimal routing may not achieve the maximum throughput. Higher throughput may be achieved with suboptimal routing schemes that lead to higher marginal power increase as the throughput increases","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116974108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1109/GLOCOM.2005.1577635
A. Urra, E. Calle, J. Marzo
This paper focuses on QoS routing with protection in an MPLS network over an optical layer. In this multi-layer scenario each layer deploys its own fault management methods. A partially protected optical layer is proposed and the rest of the network is protected at the MPLS layer. New protection schemes that avoid protection duplications are proposed. Moreover, this paper also introduces a new traffic classification based on the level of reliability. The failure impact is evaluated in terms of recovery time depending on the traffic class. The proposed schemes also include a novel variation of minimum interference routing and shared segment backup computation. A complete set of experiments proves that the proposed schemes are more efficient as compared to the previous ones, in terms of resources used to protect the network, failure impact and the request rejection ratio.
{"title":"Enhanced multi-layer protection in multi-service GMPLS networks","authors":"A. Urra, E. Calle, J. Marzo","doi":"10.1109/GLOCOM.2005.1577635","DOIUrl":"https://doi.org/10.1109/GLOCOM.2005.1577635","url":null,"abstract":"This paper focuses on QoS routing with protection in an MPLS network over an optical layer. In this multi-layer scenario each layer deploys its own fault management methods. A partially protected optical layer is proposed and the rest of the network is protected at the MPLS layer. New protection schemes that avoid protection duplications are proposed. Moreover, this paper also introduces a new traffic classification based on the level of reliability. The failure impact is evaluated in terms of recovery time depending on the traffic class. The proposed schemes also include a novel variation of minimum interference routing and shared segment backup computation. A complete set of experiments proves that the proposed schemes are more efficient as compared to the previous ones, in terms of resources used to protect the network, failure impact and the request rejection ratio.","PeriodicalId":319736,"journal":{"name":"GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117130276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}