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Showing papers on "Relay published in 2003"


Journal ArticleDOI
TL;DR: This work develops and analyzes space-time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network and demonstrates that these protocols achieve full spatial diversity in the number of cooperating terminals, not just theNumber of decoding relays, and can be used effectively for higher spectral efficiencies than repetition-based schemes.
Abstract: We develop and analyze space-time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network. The protocols exploit spatial diversity available among a collection of distributed terminals that relay messages for one another in such a manner that the destination terminal can average the fading, even though it is unknown a priori which terminals will be involved. In particular, a source initiates transmission to its destination, and many relays potentially receive the transmission. Those terminals that can fully decode the transmission utilize a space-time code to cooperatively relay to the destination. We demonstrate that these protocols achieve full spatial diversity in the number of cooperating terminals, not just the number of decoding relays, and can be used effectively for higher spectral efficiencies than repetition-based schemes. We discuss issues related to space-time code design for these protocols, emphasizing codes that readily allow for appealing distributed versions.

4,385 citations


Journal ArticleDOI
TL;DR: End-to-end performance of two-hop wireless communication systems with nonregenerative relays over flat Rayleigh-fading channels is presented and average bit-error rate expressions for binary differential phase-shift keying, as well as outage probability formulas for noise limited systems are derived.
Abstract: End-to-end performance of two-hop wireless communication systems with nonregenerative relays over flat Rayleigh-fading channels is presented. This is accomplished by deriving and applying some new closed-form expressions for the statistics of the harmonic mean of two independent exponential variates. It is shown that the presented results can either be exact or tight lower bounds on the performance of these systems depending on the choice of the relay gain. More specifically, average bit-error rate expressions for binary differential phase-shift keying, as well as outage probability formulas for noise limited systems are derived. Finally, comparisons between regenerative and nonregenerative systems are presented. Numerical results show that the former systems clearly outperform the latter ones for low average signal-to-noise-ratio (SNR). They also show that the two systems have similar performance at high average SNR.

1,388 citations


Journal ArticleDOI
TL;DR: This paper focuses on the multihop performance of a novel forwarding technique based on geographical location of the nodes involved and random selection of the relaying node via contention among receivers, and an idealized scheme (in which the best relay node is always chosen) is discussed.
Abstract: In this paper, we propose a novel forwarding technique based on geographical location of the nodes involved and random selection of the relaying node via contention among receivers. We focus on the multihop performance of such a solution, in terms of the average number of hops to reach a destination as a function of the distance and of the average number of available neighbors. An idealized scheme (in which the best relay node is always chosen) is discussed and its performance is evaluated by means of both simulation and analytical techniques. A practical scheme to select one of the best relays is shown to achieve performance very close to that of the ideal case. Some discussion about design issues for practical implementation is also given.

964 citations


Proceedings ArticleDOI
09 Jul 2003
TL;DR: This paper proposes a distributed and scalable acceptance algorithm called generous tit-for-tat (GTFT), which is used by the nodes to decide whether to accept or reject a relay request, and shows that GTFT results in a Nash equilibrium and proves that the system converges to the rational and optimal operating point.
Abstract: In wireless ad hoc networks, nodes communicate with far off destinations using intermediate nodes as relays. Since wireless nodes are energy constrained, it may not be in the best interest of a node to always accept relay requests. On the other hand, if all nodes decide not to expend energy in relaying, then network throughput will drop dramatically. Both these extreme scenarios (complete cooperation and complete noncooperation) are inimical to the interests of a user. In this paper we address the issue of user cooperation in ad hoc networks. We assume that nodes are rational, i.e., their actions are strictly determined by self interest, and that each node is associated with a minimum lifetime constraint. Given these lifetime constraints and the assumption of rational behavior, we are able to determine the optimal throughput that each node should receive. We define this to be the rational Pareto optimal operating point. We then propose a distributed and scalable acceptance algorithm called generous tit-for-tat (GTFT). The acceptance algorithm is used by the nodes to decide whether to accept or reject a relay request. We show that GTFT results in a Nash equilibrium and prove that the system converges to the rational and optimal operating point.

641 citations


Proceedings ArticleDOI
06 Apr 2003
TL;DR: Numerical results show that dual-hop wireless communication systems equipped with non-regenerative fixed gain relays have a comparable performance to non-Regenerative systems with variable gain relay and that relay saturation of these systems results in a minimal loss in performance.
Abstract: The paper presents a study on the end-to-end performance of dual-hop wireless communication systems equipped with non-regenerative fixed gain relays and operating over flat Rayleigh fading channels. More specifically, it first derives generic closed-form expressions for the outage probability and the average probability of error when the relays have arbitrary fixed gains. It then proposes a specific fixed gain relay that benefits from the knowledge of the first hop's average fading power and compares its performance with previously proposed relay gains that, in contrast, require knowledge of the instantaneous channel state information of the first hop. Finally, the paper investigates the effect of the relay saturation on the performance of the systems under consideration. Numerical results show that non-regenerative systems with fixed gain relays have a comparable performance to non-regenerative systems with variable gain relays. These results also show that relay saturation of these systems results in a minimal loss in performance.

595 citations


Journal ArticleDOI
TL;DR: An analytical framework is presented for the evaluation of the end-to-end outage probability of multihop wireless communication systems with nonregenerative relays over Nakagami fading channels and shows that regeneration is more crucial at low average SNR and for multihip systems with a large number of hops.
Abstract: We present a general analytical framework for the evaluation of the end-to-end outage probability of multihop wireless communication systems with nonregenerative relays over Nakagami fading channels. It is shown that the presented results can either be exact or tight lower bounds on the performance of these systems depending on the choice of the relay gain. More specifically, we obtain a closed-form expression for the moment generating function of the reciprocal of the end-to-end signal-to-noise ratio (SNR) and we then use this expression to calculate the outage probability via numerical inversion of the Laplace transform. Numerical examples show that regeneration is more crucial at low average SNR and for multihop systems with a large number of hops.

568 citations


Proceedings ArticleDOI
14 Sep 2003
TL;DR: This paper focuses on the topology control process for ANs and BSs, which constitute the upper tier of a two-tiered WSN, and proposes approaches to maximize the topological network lifetime of the WSN by arranging BS location and inter-AN relaying optimally.
Abstract: We consider a two-tiered Wireless Sensor Network (WSN) consisting of sensor clusters deployed around strategic locations and base-stations (BSs) whose locations are relatively flexible. Within a sensor cluster, there are many small sensor nodes (SNs) that capture, encode and transmit relevant information from the designated area, and there is at least one application node (AN) that receives raw data from these SNs, creates a comprehensive local-view, and forwards the composite bit-stream toward a BS. In practice, both SN and AN are battery-powered and energy-constrained, and their node lifetimes directly affect the network lifetime of WSNs. In this paper, we focus on the topology control process for ANs and BSs, which constitute the upper tier of a two-tiered WSN. We propose approaches to maximize the topological network lifetime of the WSN, by arranging BS location and inter-AN relaying optimally. Based on an algorithm in Computational Geometry, we derive the optimal BS locations under three topological lifetime definitions according to mission criticality. In addition, by studying the intrinsic properties of WSNs, we establish the upper and lower bounds of their maximal topological lifetime. When inter-AN relaying becomes feasible and favorable, we continue to develop an optimal parallel relay allocation to further prolong the topological lifetime of the WSN. An equivalent serialized relay schedule is also obtained, so that each AN only needs to have one relay destination at any time throughout the mission. The experimental performance evaluation demonstrates the efficacy of topology control as a vital process to maximize the network lifetime of WSNs.

547 citations


Journal ArticleDOI
TL;DR: A novel coding technique is proposed for the quasi-static fading relay channel, which indicates a combined diversity and coding gain, which is significant even for simple constituent codes.
Abstract: A novel coding technique is proposed for the quasi-static fading relay channel. The source broadcasts a recursive code to both relay and destination. The relay decodes, interleaves, and re-encodes the message prior to forwarding. Because the destination receives both codes in parallel, a distributed turbo code is embedded in the relay channel. Results indicate a combined diversity and coding gain, which is significant even for simple constituent codes.

411 citations


Proceedings ArticleDOI
06 Apr 2003
TL;DR: This work proposes an Alamouti based cooperative system with two relay stations and provides an approximate formula for the average symbol error probability of this system in a Rayleigh fading environment.
Abstract: Multiple antennas at the receiver and transmitter are often used to combat the effects of fading in wireless communication systems. However, implementing multiple antennas at mobile stations is impractical for most wireless applications due to the limited size of the mobile unit. We emulate spatial diversity using mobile relay stations, which cooperate by retransmitting the information received from a mobile station to a destination station. We propose an Alamouti based cooperative system with two relay stations and we provide an approximate formula for the average symbol error probability of this system in a Rayleigh fading environment.

166 citations


Proceedings ArticleDOI
01 Jan 2003
TL;DR: Simulation results show that the proposed code performs close to the information-theoretic bound on outage event probability of decode-and-forward relaying.
Abstract: A novel coding technique is proposed for the relay channel. The source broadcasts a recursive convolutional code to both relay and destination. After detecting the data broadcasted by the source, the relay interleaves and re-encodes the message prior to forwarding it to the destination. Because the destination receives both codes in parallel, a distributed turbo code is embedded in the relay channel. Simulation results show that the proposed code performs close to the information-theoretic bound on outage event probability of decode-and-forward relaying.

162 citations


Proceedings Article
20 Apr 2003
TL;DR: The capacities of the degraded cheap relay channel and the multi-hop net- work with cheap nodes are derived from the direct application of the upper bounds derived in (7).
Abstract: We consider the communication problem in a multi-hop relay network where the intermediate relay nodes cannot transmit and receive at the same time. The motivation for this assumption comes from the fact that current radios operate in TDD mode when the transmitting and receiving frequencies are the same. We label such a node radio as a cheap radio and the corresponding node of the network as a cheap node. In this paper we derive the capacities of the degraded cheap relay channel and the multi-hop net- work with cheap nodes. The proof of the achievability parts in coding theorems are presented based on the jointly typical sequences, while the proof of the con- verses are derived from the direct application of the upper bounds derived in (7).

Patent
15 Apr 2003
TL;DR: In this article, the relay system (10) obtains voltage and current values from a power line and uses a first sampling element to sample the voltage and currents at selected intervals of time.
Abstract: The relay system (10) obtains voltage and current values from a power line and uses a first sampling element to sample the voltage and current values at selected intervals of time. The resulting sampled signals are used for power system-wide protection, control, monitoring and metering. The sampled signals are then resampled at a rate which is a selected multiple of the power system frequency. The results of the resampling are used by processing circuitry for protection functions including fault determinations.

Patent
14 Jul 2003
TL;DR: In this article, the authors proposed a multi-hop transmission scheme that utilizes intelligent relays within a conventional cellular system having at least one base station, one or more relays, and user equipment elements.
Abstract: A multi-hop relaying method and apparatus used in a cellular network. The multi-hop transmission scheme utilizes intelligent relays within a conventional cellular system having at least one base station, one or more intelligent relays, and user equipment elements. The method includes selecting the strongest pilot signal from among the base stations and intelligent relays, reporting such to the base station, distributing an active user list to the relays along with scheduling and routing information via a relay control channel, and transmitting data according to a respective active user based upon the pilot signal strength to maximize coverage and capacity over the cellular system.

01 Jan 2003
TL;DR: The optimal weighting parameters for coherent combining based non-regenerative relaying are derived under aggregate relay power constraint and it is illustrated that the resulting SNR is substantially enhanced compared to direct communication and that SNR improves with increasing relay station density.
Abstract: Communication schemes exploiting cooperating relay nodes can enable significant SNR and diversity order enhancements. In this paper, a communicating pair of nodes with support from an arbitrary num ...

Proceedings ArticleDOI
02 Apr 2003
TL;DR: In this article, a thermally-actuated bistable MEMS relay with a transient thermal actuator is presented, which achieves a minimum total resistance of 60 n/spl Omega/ and a maximum current carrying capacity of 3 A. In the off state, this relay stands off more than 200 V.
Abstract: This paper reports the design, fabrication and testing of a thermally-actuated bistable MEMS relay. Mechanical bistability ensures zero actuation power in both the on and off states, and permits actuation with a transient thermal actuator. In the off state, this relay stands off more than 200 V. In the on state, it exhibits a minimum total resistance of 60 n/spl Omega/ and a maximum current carrying capacity of 3 A. It switches with a maximum 5 Hz rate.

Journal Article
TL;DR: The study shows that with R relays, a diversity factor around R/2 can be achieved, i.e., the averaged bit error rate is in the order of 1/SNR/sup R/ 2/ as opposed to 1/ SNR for a single (regenerative) relay system.
Abstract: We first provide an overview of some of the latest developments in wireless communications using multiple transmitters and multiple receivers. We point out the importance of SNR control in fast random fading environments. For applications where large antenna arrays are not suitable, we introduce the concept of wireless antennas or wireless relays that are distributed between a source and a destination. We propose Hurwitz-Radon space-time code for the wireless relays. Each relay receives a noisy baseband signal simultaneously from the source. The baseband signals (symbols) are not decoded into information bits at the (non-regenerative) relays, but rearranged (i.e., space-time modulated) in their orders, amplitudes and phases according to the Hurwitz-Radon code. The relays do not exchange symbols with each other, but forward the modified sequences of symbols in parallel to the destination. Our study shows that with R relays, a diversity factor around R/2 can be achieved, i.e., the averaged bit error rate is in the order of 1/SNRR2/ as opposed to 1/SNR for a single (regenerative) relay system. More than 10 dB power saving, from the baseline of a single relay system, is possible with eight relays. Issues such as channel estimation, symbol synchronization, medium access protocols and signal processing hardware are also discussed.

01 Jul 2003
TL;DR: A current project that uses mobile autonomous communication relay nodes to overcome the problem of low-bandwidth digital radio link between a mobile robot and its remote control station degrades quickly as the robot penetrates the interior of a building or becomes shielded by intervening terrain.
Abstract: The high-bandwidth digital radio link between a mobile robot and its remote control station degrades quickly as the robot penetrates the interior of a building or becomes shielded by intervening terrain. This paper describes a current project that uses mobile autonomous communication relay nodes to overcome this problem. Each node is a small slave robot equipped with sonar, ladar, and 802.11b-based ad hoc networking radio. The relay robots follow the lead robot and automatically stop where needed to maintain a solid communication network between the lead robot and the remote operator. With their onboard external sensors, they also act as rearguards to secure areas already explored by the lead robot. As the lead robot advances and RF shortcuts are detected, relay nodes that become unnecessary will catch up to the lead robot and be reused, using maps generated by the lead robot. All relay deployment and redeployment functions occur without the operator's awareness.

Journal ArticleDOI
TL;DR: Simulation results clearly indicate that, by incorporating the shape information, improved autotuning can be achieved in a straightforward manner, and possible dead-time compensation and higher-order compensation can also be devised when necessary.
Abstract: Since the introduction of the relay feedback test by Astrom and Hagglund (Automatica 1984, 20, 645-651), autotuning of PID controller has received much attention, and many commercial autotuners have also been designed accordingly. Without knowledge of the model structure, most of these relay feedback autotuners use Ziegler-Nichols-type tuning rules to set controller parameters. This can lead to poor performance in some cases, because no single tuning rule can work well for all model structures over the entire range of parameter values. Luyben points out that additional information can be obtained from relay feedback tests, namely, the shape of the response (Ind. Eng. Chem. Res. 2001, 40 (20), 4391-4402). In this work, relay feedback tests are conducted on processes with different orders and a wide range of dead-time-to-time-constant ratios. On the basis of the shape of the response from the relay feedback tests, these processes can be broadly classified into three major categories (model structures). Procedures are given to find parameters for the corresponding model structures, and then different tuning rules are employed to find appropriate PI controller settings. The procedures are tested against linear systems with and without noise. Simulation results clearly indicate that, by incorporating the shape information, improved autotuning can be achieved in a straightforward manner. Moreover, possible dead-time compensation and higher-order compensation can also be devised when necessary. It should be emphasized that the improvement is obtained from the conventional relay feedback test and no additional testing is required.

Journal ArticleDOI
TL;DR: Good tuning performance according to the specified bandwidth and phase margin can be obtained and the limitation of the standard relay auto-tuning technique using a version of Ziegler-Nichols formula can be eliminated.

Proceedings ArticleDOI
01 Jan 2003
TL;DR: This paper provides a further extension to generate a smaller forward node set without additional cost based on MPR and confirms the effectiveness of this approach through a simulation study.
Abstract: Multipoint relays (MPR) (A. Qayyum et al., 2002) provide a localized and optimized way of determining a small forward node set for broadcasting messages in an ad hoc network. Using 2-hop neighborhood information, each node determines a small set of forward neighbors to relay messages. Selected forward nodes form a connected dominating set (CDS) to ensure full coverage. Recently, Adjih, Jacquet, and Viennot [Ref. 1] proposed a novel localized algorithm to construct a small forward node set based on MPR. In this paper, we provide a further extension to generate a smaller forward node set without additional cost. The effectiveness of our approach is confirmed through a simulation study.

Proceedings ArticleDOI
01 Oct 2003
TL;DR: In this paper, the authors proposed the concept of wireless antennas or wireless relays that are distributed between a source and a destination, where relays do not exchange symbols with each other, but forward the modified sequences of symbols in parallel to the destination.
Abstract: We first provide an overview of some of the latest developments in wireless communications using multiple transmitters and multiple receivers. We point out the importance of SNR control in fast random fading environments. For applications where large antenna arrays are not suitable, we introduce the concept of wireless antennas or wireless relays that are distributed between a source and a destination. We propose Hurwitz-Radon space-time code for the wireless relays. Each relay receives a noisy baseband signal simultaneously from the source. The baseband signals (symbols) are not decoded into information bits at the (non-regenerative) relays, but rearranged (i.e., space-time modulated) in their orders, amplitudes and phases according to the Hurwitz-Radon code. The relays do not exchange symbols with each other, but forward the modified sequences of symbols in parallel to the destination. Our study shows that with R relays, a diversity factor around R/2 can be achieved, i.e., the averaged bit error rate is in the order of 1/SNR/sup R/2/ as opposed to 1/SNR for a single (regenerative) relay system. More than 10 dB power saving, from the baseline of a single relay system, is possible with eight relays. Issues such as channel estimation, symbol synchronization, medium access protocols and signal processing hardware are also discussed.

Patent
21 May 2003
TL;DR: In this article, a mobile communication system capable of deciding a communication path that can realize a multihop high-speed communication is presented, which consists of a mobile station (10), one or more relay stations (30) and a base station (20).
Abstract: A mobile communication system capable of deciding a communication path that can realize a multihop high-speed communication. A mobile communication system (1), which comprises a mobile station (10), one or more relay stations (30) and a base station (20), performs a packet transmission from the mobile station (10) to the base station (20) via one or more relay stations (30) or via no relay stations. The mobile communication system (1) has a communication path deciding part for deciding, based on the interference levels of the signals received by the base station (20) and by the relay stations (30) constituting the communication paths between the transmission and reception stations, a communication path that exhibits the highest communication speed or a communication path that satisfies a required line quality.

Patent
31 Dec 2003
TL;DR: In this paper, the authors propose a method, device, and system in which radio links between relays and users are optimized separately from the links between relay and base stations and in which multiple simultaneous data streams between relay nodes and base nodes are created.
Abstract: A method, device, and system in which radio links between relays and users are optimized separately from the links between relays and base stations and in which multiple simultaneous data streams between relays and base stations are created. The system includes transceivers of at least three kinds with two kinds of radio interfaces. The first kind of transceiver, a base station (BS), is connected to the core network with a link of wire line quality. The second kind, a relay station (RS), is connected to the BS with a first radio interface, and to the third kind, the user equipment (UE), with a second radio interface. The first and second radio interfaces can operate, at least in part, using the same frequency bandwidth. The UE can also connect directly to the BS using the second radio interface if the BS is closer than any RS.

Proceedings ArticleDOI
01 Dec 2003
TL;DR: A switching criterion is presented based on which the source terminal may opt to forego relay-assisted communication and communicate with the destination terminal directly, based on the cut-off rate of the effective channel - the physical channel in conjunction with finite constellation and maximum-likelihood (ML) decoding.
Abstract: Cooperative diversity is a transmission technique where multiple users pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. We examine space-time signal design for a simple amplify-and-forward relay channel. We show that the code design criteria for the relay case consist of the traditional rank and determinant criteria as well as appropriate power control rules. While proper signal design and power control can indeed achieve full spatial diversity gain, the potential benefit of relay-assisted communication over direct communication depends strongly on the channel conditions. In particular, we present a switching criterion based on which the source terminal may opt to forego relay-assisted communication and communicate with the destination terminal directly. The criterion is based on the cut-off rate of the effective channel - the physical channel in conjunction with finite constellation and maximum-likelihood (ML) decoding.

Patent
05 Sep 2003
TL;DR: In this article, routing, scheduling, and power control methods for single and multi-hop wireless networks are discussed. But the authors focus on single-hop networks, where source and destination nodes may communicate directly or through relay nodes.
Abstract: The invention concerns routing, scheduling, and power control methods for single and multi-hop wireless networks. A multi-hop network is one in which source and destination nodes may communicate directly or through relay nodes. Nodes in single hop networks communicate without use of relay nodes. Embodiments of the invention may produce an optimal schedule to provide for the best-case goal for a given parameter. In a preferred embodiment, total power is the parameter and total power is minimized for the network. In another preferred embodiment, data throughput is the parameter, and throughput is maximized for the network.

Patent
James Mark Naden1, Fiona Wilson1
06 Jun 2003
TL;DR: In this paper, the decision about which relays are included in which communication paths in the system is distributed to the relay equipments of the system, thus reducing the signalling overhead as compared with link state protocols which are typically used for routing in such multi-hop systems.
Abstract: A multi-hop wireless, for example cellular, communications system is provided comprising a source equipment which may be one of a base station or an end user terminal for transmitting signals towards a destination equipment which may be the other of a base station or an end user terminal via at least one relay equipment. The relay equipment receives a plurality of signals transmitted from one or more source equipments of the system and from this plurality of signals selects a signal to relay. In this way the decision about which relays are included in which communication paths in the system is distributed to the relay equipments of the system, thus reducing the signalling overhead as compared with link state protocols which are typically used for routing in such multi-hop systems.

Proceedings Article
01 Jan 2003
TL;DR: This study uses Hurwitz-Radon matrices to construct a space-time code for parallel wireless mobile relays that are located anywhere between a source and a destination and shows that with R relays, an order of diversity around R/2 can be achieved, i.e., the averaged bit error rate is in the order of 1/SNR/sup R/ 2/ as opposed to 1/ SNR for a single relay system.
Abstract: We use Hurwitz-Radon matrices to construct a space-time code for parallel wireless mobile relays that are located anywhere between a source and a destination. Each relay receives a sequence of symbols (i.e., baseband signals corrupted by fading and noise) simultaneously from the source. These symbols are not decoded into information bits at the relays but are rearranged (i.e., space-time modulated) in their orders, amplitudes and phases according to the Hurwitz-Radon code. The relays do not exchange symbols with each other but forward the modified sequences of symbols in parallel to the destination. Our study shows that with R relays, an order of diversity around R/2 can be achieved, i.e., the averaged bit error rate is in the order of 1/SNR/sup R/2/ as opposed to 1/SNR for a single (regenerative) relay system. More than 10 dB power saving, from the baseline of the single relay system, can be achieved with eight (non-regenerative) relays.

Proceedings ArticleDOI
20 Mar 2003
TL;DR: This paper illustrates the potential transmit energy savings that are possible by using macrodiversity-combining approaches by the analysis and simulation of an idealized system and discusses practical issues that must be considered before integrating macrod diversity-combined strategies into actual embedded networks.
Abstract: Embedded networks of sensors and actuators must operate at extremely low power and use inexpensive single-antenna transceivers. The economics of such systems preclude the use of complex signal processing or antenna arrays at any one device. However, the same economics allows the coverage area to be blanketed with a high density of devices, which results in a rich spatial diversity. This spatial diversity can be exploited by forming a virtual antenna array, which combines observations made at multiple receivers. This paper illustrates the potential transmit energy savings that are possible by using such macrodiversity-combining approaches by the analysis and simulation of an idealized system. It concludes by discussing practical issues that must be considered before integrating macrodiversity-combining strategies into actual embedded networks.

Journal ArticleDOI
TL;DR: This paper derives necessary and sufficient conditions for well-posedness in the sense of Filippov of linear systems of relative degree one and two in closed loop with relay feedback and shows that this intuitively clear condition is not true for systems with relative degree larger than two.

Journal ArticleDOI
TL;DR: The asymmetrical relay feedback method is modified to get improved parameters estimates of a first order plus time delay transfer function model and gives closed loop ISE values similar to that of the actual system.