STiCMAC: A MAC Protocol for Robust Space-Time Coding in Cooperative Wireless LANs

Relay-assisted cooperative wireless communication has been shown to have significant performance gains over the legacy direct transmission scheme. Compared with single relay based cooperation schemes, utilizing multiple relays further improves the reliability and rate of transmissions. Distributed space-time coding (DSTC), as one of the schemes to utilize multiple relays, requires tight coordination between relays and does not perform well in a distributed environment with mobility. In this paper, a cooperative medium access control (MAC) layer protocol, called \emph{STiCMAC}, is designed to allow multiple relays to transmit at the same time in an IEEE 802.11 network. The transmission is based on a novel DSTC scheme called \emph{randomized distributed space-time coding} (\emph{R-DSTC}), which requires minimum coordination. Unlike conventional cooperation schemes that pick nodes with good links, \emph{STiCMAC} picks a \emph{transmission mode} that could most improve the end-to-end data rate. Any station that correctly receives from the source can act as a relay and participate in forwarding. The MAC protocol is implemented in a fully decentralized manner and is able to opportunistically recruit relays on the fly, thus making it \emph{robust} to channel variations and user mobility. Simulation results show that the network capacity and delay performance are greatly improved, especially in a mobile environment.

fading environment. While utilizing multiple relays at the PHY layer greatly improves the reliability of transmissions, it remains unclear how such techniques can be employed to deliver significant network capacity gains for a loosely synchronized network such as the IEEE 802.11.
In this paper, we design a robust MAC layer protocol called STiCMAC (Space-Time coding for Cooperative MAC), which is compliant with the IEEE 802.11 standard and enables R-DSTC based cooperation. STiCMAC allows one to harvest cooperative diversity from multiple nodes in a decentralized manner. In this scheme, if a data packet from the source needs to be relayed, all potential relays listen to the transmission from the source and try to decode. Assuming error detection mechanisms such as cyclic redundancy check (CRC) are employed at the relays, only relays that successfully decode the packet forward to the destination in unison using R-DSTC. In order to do so, the handshaking procedure defined by the IEEE 802.11 standard is extended to allow relays be recruited in an opportunistic manner while ensuring that the transmissions from multiple relays are collision free.
The main contribution of this paper is that it fundamentally changes the way cooperation is established.
Instead of picking nodes with fast links or finding a fast path in the network, our scheme picks a transmission mode (modulation, channel coding and STC) that could most improve the end-to-end rate on the average. Relays decide to participate or not to participate independently based on whether they receive the packet or not. In fact, neither the source or destination station need to know who the relays are or where they are located. STiCMAC is an optimized PHY/MAC cross-layer scheme that can be implemented in a fully decentralized manner and is able to opportunistically recruit relays on the fly at minimum signaling cost for an infrastructure-based IEEE 802.11 network. We evaluate the system performance of STiCMAC, and employ cross-layer optimization to find suitable transmission parameters, i.e., per-hop rates and STC dimension, that maximize the end-to-end rate.
Optimization of transmission parameters is performed assuming either a complete knowledge of average channel statistics for both hops, or simply considering the number of stations in each WLAN cell. We call these two approaches STiCMAC with channel statistics (STiCMAC-CS) and STiCMAC with user count (STiCMAC-UC) respectively. We investigate the aggregated network throughput and the average delay for all stations in both a static and mobile environment. Our results suggest that both STiCMAC-CS and STiCMAC-UC have similar performance, especially for a large number of users. This outcome strongly supports our argument that the proposed scheme does not need a priori knowledge of channel conditions, as opposed to DSTC. Additionally, simulation results show that both types of STiCMAC significantly outperform DSTC in terms of throughput and delay, due to lower signaling cost, and also outperform CoopMAC and direct transmission due to increased diversity. While the performance of DSTC and CoopMAC significantly decreases under mobility, STiCMAC is more robust, and in particular STiCMAC-UC shows minimal performance degradation in a mobile environment. Finally, we conduct a study of the interference propagated to neighboring wireless LANs for all transmission schemes. Simulation results show that, for the same traffic load, the average interference generated by STiCMAC is similar to DSTC, and much less than CoopMAC and direct transmission.
A related work [8] proposes a MAC layer protocol that deploys DSTC in an ad hoc network to assist network layer routing. This allows cooperative transmissions from multiple relays, however, its performance and practicality for a mobile network are still limited due to the limitations of DSTC outlined above. Opportunistic routing [9] is a routing protocol for ad hoc networks that allows one node closest to the destination to forward in case multiple nodes receive from the previous hop. Compared with STiCMAC, which operates in MAC/PHY cross-layer, opportunistic routing operates in the network layer. The other difference is that STiCMAC allows an end-to-end multihop transmission within a single channel access and queuing is not necessary at the relays. STiCMAC also allows signals from multiple relays to be combined coherently in the PHY layer. Another use of the term "opportunistic" appears in the cooperative communications literature in [10], however, the notion there is to select relays based on instantaneous channel state. Generic MAC protocols for R-DSTC are designed in [11], [12], where transmission parameters are optimized given the bit error rate, assuming no channel coding is employed.
Without forward error correction coding, those schemes can cause error propagation by allow relays to forward even if erroneous packets are received. These papers mostly focus on the PHY layer characteristics that enable the use of randomized codes in realistic wireless networks, and do not explicitly investigate MAC layer details. STiCMAC is the first protocol derived from the IEEE 802.11 where practical MAC layer aspects of randomized cooperation are addressed.
We note that synchronization is an important issue for all transmission schemes that allow multiple stations to transmit at the same time on the same frequency. As demonstrated in [13], symbol level synchronization in DSTC based transmission is feasible on a software defined radio platform with commercially available IEEE 802.11 components and a customized FPGA. Thus we believe necessary synchronization for R-DSTC, which is more robust to synchronization errors than DSTC [14], can also be implemented.
The rest of this paper is outlined as follows. Section II introduces the PHY layer background for R-DSTC. In Section III, we present the STiCMAC protocol in detail. Section IV develops two opportunistic rate adaptation schemes for STiCMAC to optimize the transmission parameters. Section V presents the simulation results and the performance evaluation. Finally, in Section VI, we present conclusions.

II. R-DSTC PHYSICAL LAYER DESCRIPTION
An STC is designed to operate over several antennas at the same transmitter station. In contrast, DSTC employs an STC over multiple relays in a distributed manner. When these relays cooperatively forward a signal, each relay corresponds to a specific antenna element of the underlying STC, and transmits a predefined STC encoded stream. The advantage of DSTC lies in its capability to form a virtual MIMO system by using these relays and producing diversity gain, even if each station is only equipped with one antenna. The performance of DSTC and the diversity gain obtained has been studied in [3].
R-DSTC is introduced and examined in [5] as a novel form of DSTC. Like conventional DSTC, R-DSTC is deployed in a cooperative scenario with multiple relays along with a source and destination pair and operates over two hops. Although R-DSTC can be employed using relays with multiple antennas, we assume that each station is only equipped with a single antenna. The scenario with multiple antennas per station can be easily extended from the single-antenna case. Fig. 1 shows a single-antenna relay that employs a regular single-input and single output (SISO) decoder to decode the information sent by the source station in the first hop. Provided the information is decoded correctly, as determined by checking the CRC field, the relay is responsible for re-encoding the information bits and passing them to an STC encoder. Suppose the underlying space-time codeword has a dimension L × K, where L is the number of antennas and K is the block length transmitted by each antenna. The STC encoder generates an output of L parallel streams, each stream corresponding to an antenna. Unlike a regular DSTC where the jth relay simply transmits the stream j, in a R-DSTC system the jth relay transmits a linear weighted combination of all L streams. The weights of the L streams at the jth relay are denoted by a vector w j = [w j1 w j2 . . . w jL ]. Each element in w j is an independently generated random variable with zero mean and variance 1/L. As described in [5], a complex Gaussian distribution is adopted for the distribution of the weights since it has desirable properties in terms of PHY layer error rates. Assuming n relays simultaneously transmit in the second hop, the vector w j , where j = 1, 2, . . . n, represents the random weights at relay j and R = [w 1 , w 2 , . . . , w n ] T is the weight matrix for all these n relays. The destination station is assumed to have one antenna and is able to decode the received signal with a conventional STC decoder.
The physical layer fundamentals of R-DSTC is described in detail in [5], where it is shown that R-DSTC comes very close to the performance of DSTC in terms of PHY layer properties and can provide the full diversity order of L with at least L relays. A major advantage of the R-DSTC technique over DSTC lies in the fact that the source station does not need to specifically select its relays as well as to assign antenna indices to each relay. In R-DSTC, the source and destination remain unaware of which stations act as relays and which random weight vector has been used in relays. These features enable R-DSTC to be a fully decentralized scheme in a cooperative environment.

III. STIC MAC: A ROBUST COOPERATIVE MAC LAYER FRAMEWORK
While R-DSTC has been mainly studied in the PHY layer, an efficient MAC layer protocol is essential in order to enable its use in a real environment and to translate its PHY layer benefits to performance gain in the upper layers. This section presents a robust MAC layer protocol, called Space-Time coding in Cooperative MAC (STiCMAC), in support of R-DSTC in an IEEE 802.11 WLAN environment. In this paper, we consider a WLAN operating in the infrastructure mode, where an access point (AP) works as a central unit. The proposed MAC protocol is mainly composed of two parts: (1) a three-way handshake, which includes relay recruiting and acknowledgements; (2) cooperative two-hop data transmission. The three-way handshaking takes care of all signaling among the source, destination and relays. During the handshaking procedure, relays are recruited simultaneously and opportunistically according to each relay's instantaneous channel conditions, while no other stations, except for the selected relays, needs to know these channel conditions. Cooperative two-hop data transmission occurs when relays receive the necessary transmission parameters. The details of STiCMAC are explained in the rest of this section.

A. Wireless LAN Medium Access Control Overview
In the IEEE 802.11 WLAN standard [15], Distributed Coordination Function (DCF) is the mandatory MAC protocol. Since DCF is contention based, stations employ carrier sensing multiple access/collision avoidance (CSMA/CA) algorithm to resolve collisions. Under this scheme, each station can starts a packet transmission only if it senses the channel to be free. However, due to sensing range limitations, two stations could be sending to a common receiver simultaneously. This phenomena is referred to as the hidden node problem. In order to avoid such scenarios, virtual carrier sensing is employed, by means of the Request-to-Send (RTS) and Clear-To-Send (CTS) frames. These two control frames broadcast the duration for the upcoming data transmission so that stations that do not participate in this transmission withhold their own transmissions until the end of the ongoing packet transmission. In this paper, we focus on the DCF mode with RTS/CTS messaging and develop a cross-layer framework for a distributed cooperative system based on IEEE 802.11. STiCMAC with RTS/CTS turned off is presented in the appendix of this paper.

B. Protocol Design for R-DSTC in WLANs
In this subsection, we introduce the STiCMAC protocol that enables R-DSTC in an infrastructure-based WLAN under DCF mode. STiCMAC enables relay discovery and concurrent cooperative transmissions from all relays to the destination. Without loss of generality we consider that the source of a transmission is a station while the destination is the AP. A symmetric scheme with the same characteristics can be applied for the downlink transmission (from the AP to the stations).
In order to enable all relays to forward a packet in unison, the MAC layer needs to provide critical parameters for the cooperative transmission. The required transmission include the transmission rates for both hops, and the underlying space-time code for the second hop. Let us denote r 1 as the first-hop rate, r 2 as the second-hop rate, and L as the STC dimension. We assume that R-DSTC uses a class of underlying orthogonal STC's parameterized by the code dimension L. A proper joint selection of these parameters can optimize the MAC layer performance. Details of such an optimization will be provided in Section IV. Additionally, the MAC layer must also provide timing information for both hops, as a data packet undergoes a two-hop transmission. In STiCMAC, a three-way handshaking procedure is initiated by the source to disseminate these transmission parameters, followed by the data transmission. Fig. 2 illustrates how STiCMAC works for a single packet transmission, which consists of the following steps: a. The Three Way Handshaking Phase 1) The source station initiates the handshaking by transmitting a RTS frame at the base rate in compliance with the IEEE 802.11 protocol. The RTS frame reserves the channel for subsequent signaling and data messages. The source continues with the transmission of the second control frame, called Helper-Recruiting (HR) frame, a short inter-frame spacing (SIFS) period after the transmission of the RTS frame. This HR frame is transmitted at the chosen first-hop rate r 1 using a corresponding physical layer modulation level and channel coding rate. Only those stations that have a channel strong enough to decode the HR message are likely to receive the subsequent data packet correctly at the same rate. Thus, all stations receiving the HR frame correctly are recruited as relays for the current data packet forwarding. Since recruiting of the relays is conducted on the fly, this procedure is fully decentralized. The exact set of recruited relays may vary from packet to packet due to channel variations or mobility, enabling fully opportunistic use of relays. The HR frame contains the underlying STC dimension L and the hop-2 rate r 2 , which is characterized by a modulation scheme and channel coding rate.
2) A SIFS time after the HR frame, the recruited relays send in unison the helper-to-send (HTS) frame using R-DSTC. The transmission is at the second-hop rate r 2 , using an STC of size L. The HTS message is jointly transmitted by all relays that successfully decoded the HR message from the source station. Since a single STC is employed by all the relays, only a single HTS message is received and decoded by the destination station without causing a collision. The HTS frame is employed for the following reasons. Firstly, it is used as an acknowledgement to the source station that one or more relays have been recruited. Secondly, the destination station, as long as it receives the HTS frame correctly, can verify that those relays can indeed support a rate r 2 transmission to the destination, even though it doesn't explicitly know which stations act as relays. Thirdly, HTS frame helps to alert the hidden terminals around the relays and avoid a possible collision.
3) The destination responds with a CTS frame, which signals the end of the three-way handshaking among all participants. The above handshaking procedure reduces the likelihood of a data packet collision which is especially in the case of a long data packet.

b. Data Transmission Phase
1) In the data transmission stage, the source station proceeds with sending the data frame over the first hop, at rate r 1 . We call this frame Data-S frame.
2) The recruited relays cooperatively transmit the data frame over the second hop, at rate r 2 . We denote this frame as Data-R. The transmission employs an STC dimension of L.
3) The destination station finishes the procedure by sending back to the sender an Acknowledgement (ACK) message in order to confirm that the data packet is successfully received.
The above protocol is backward compatible with standard IEEE 802.11 WLAN protocol since RTS/CTS follows the same format as defined in standard WiFi. Legacy stations can read the Duration field and set their Network Allocation Vector (NAV), which indicates how long the surrounding nodes must defer from accessing the channel. Thus legacy stations can co-exist with STiCMAC stations, even though they cannot participate in the cooperative transmissions. The newly introduced HR and HTS messages do lead to some additional overhead, which is evaluated in Section V.

IV. RATE ADAPTATION
Rate adaptation refers to the adjustment of the values of the transmission parameters, e.g., for STiCMAC, the first hop rate r 1 , second hop rate r 2 and STC dimension L, based on the network conditions. In this section, we develop a rate adaptation mechanism to maximize the end-to-end user rate while meeting an acceptable error probability. Our rate adaptation scheme is subject to an end-to-end packet error rate (PER) threshold γ, before MAC layer retransmissions are initiated. The selection of γ affects the system performance. A high γ leads to too many retransmissions due to high packet loss at the MAC layer, while a low γ leads to an under-utilized bandwidth since the communication link could support higher modulation and coding rates. Rate adaptation also requires calibration in the physical layer [16] for a practical system. Considering that the main focus of this paper is the MAC protocol design, we do not address this issue in detail and assume that all stations have been calibrated.
We assume each station supports a set of transmission rates r ∈ {R 0 , R 1 , . . . , R p }, where R 0 is the base rate at which the stations exchange control information, i.e., RTS/CTS, and R 0 < R 1 < · · · < R p .
A given r is identified by the modulation level M r and the channel coding level C r . In addition, we denote the STC code rate as R c . We assume an additive white Gaussian noise (AWGN) channel with independent slow Rayleigh fading between each pair of stations and between the stations and the AP.
Each fading level is assumed to be longer than a packet duration. All stations have a symbol energy of E s and the power spectral density of noise signal is N 0 /2.
In order to present our rate adaptation scheme, we first formulate the PHY layer error rates, i.e.
per-hop bit error rate (BER), per-hop PER and end-to-end PER performance. Along with R-DSTC, we also calculate for comparison the PHY layer error rates for the direct transmission scheme, the two-hop single-relay (CoopMAC) scheme and the DSTC scheme.
The BER and PER for a direct connection between stations i and j are respectively denoted as P ij b (r, h ij ) and P ij p (r, h ij ) for a fixed rate r and instantaneous channel gain h ij between stations i and j. Let us denote i = s when station i is the source and j = d when station j is the destination.
Assuming the instantaneous channel gain vector from all relays to the destination is denoted as h (2) , where . . ], the BER and PER between relays and the destination for DSTC with space-time codeword dimension L are denoted by P DST C b,hop2 (r, L, h (2) ) and P DST C p,hop2 (r, L, h (2) ), respectively. Similarly, when the instantaneous channel gain vector h (2) weighted by the instantaneous random matrix R is defined as h (2) R, the BER and PER between relays and the destination for R-DSTC with space-time for a given r. When these instantaneous PHY layer error rates are averaged over channel fading levels, the average BER and PER rates can be obtained accordingly. Table I lists all parameters and notation used in this section. Based upon the analysis of PHY layer error rates, rate adaptation optimizes the transmission parameters for all transmission strategies with an objective to maximize the end-to-end rate for each station while ensure an end-to-end PER bounded by γ.

A. R-DSTC PHY Layer Per-hop BER Performance
In the suggested two-hop framework, note that the BER for the first hop between the source and a potential relay can be computed using the direct link formulation. We denote the second hop between all the relays and the destination as the cooperative R-DSTC link. This subsection formulates the BER performance for both links.

1) BER performance for a direct link:
In a direct link with an instantaneous channel gain h ij along with rate r (corresponding to modulation level M r , assuming square modulation) between stations i and j, the symbol error rate is given by with where If Gray coding is used in the constellation, the approximate BER is When station i is the source and station j is a relay, Eq. (3) describes the instantaneous BER performance from the source to a relay, since each relay decodes the source signal independently.
Additionally, Eq. (3) gives the per-hop BER performance for a CoopMAC system [6] for both hops, when a single relay is employed without combining the first and second hop signal at the receiver.
2) BER performance for the cooperative R-DSTC link: Assuming n relays, i.e., stations 1 . . . n, successfully decode the source signal, each relay forwards the signal over the cooperative R-DSTC link. Suppose the STC used by the relays has a dimension of L × K [17]. During symbol interval m, m = 1, 2, · · · , K, the forwarded signal from relay j is given by where j = 1, 2, · · · , n, and w j is the random vector at relay j, as described in Section II. Here, X(m) is the mth column of the STC. The received signal at the destination, during the mth symbol interval is given by, where w(m) denotes the AWGN at the mth symbol, and Z(m) = [z 1 (m) z 2 (m) . . . z n (m)] T . Hence, the destination station observes a space-time coded signal with equivalent channel gain vector h (2) R. The destination only needs to estimate h (2) R for STC decoding. By using the orthogonality of the underlying STC [17], the BER of the cooperative R-DSTC link using rate r, L and a fixed h (2) R , denoted by (r, L, h (2) , R), can be computed by replacing h ij with h (2) R in Eq. (3).
Note that for an orthogonal DSTC with a space time codeword dimension L, each of the L relays is assigned an antenna index. Hence, there is no randomization and R = I. Therefore, the BER of DSTC, denoted by P DST C b,hop2 (r, L, h (2) ), can also be determined from Eq. (3) by replacing h ij with h (2) .

B. End-to-End PER Performance for R-DSTC
We derive the average PER by simulations, using the BER formulation in Section IV-A along with the channel code. Each relay adopts a convolutional code C r for error correction, for a given rate r. In our simulation, for each hop we first produce the coded bits and then generate random errors according to the computed instantaneous BER. This bit stream is then fed into the convolutional decoder to produce the decoded bit sequence. The instantaneous PER for both hops is then obtained by comparing the output bit stream at the destination with the original bit stream.
Let us denote by RS the instantaneous set of relays that correctly decode the source signal in the first hop and jointly forward the signal over the second hop. In the first hop, the instantaneous channel gain vector is defined as h (1) including all h ij , j ∈ RS. Consequently, for a given r 1 , r 2 , L, the end-to-end instantaneous PER between station i and the destination for the R-DSTC scheme is given by where In Eq. (6) Following Eq. (6) for instantaneous end-to-end PER, the average end-to-end PER can be obtained by averaging over all first and second hop channel gains and the random weight vector R, and is given by

C. End-to-End PER Performance for Other Schemes
Below we formulate the end-to-end PER performance for the other schemes in order to provide comparison with the proposed R-DSTC scheme. For the direct transmission scheme, the average end-toend PER between the source station i and the destination can be found using the direct-link instantaneous PER, and is given by where the direct rate is r and P id p (r, h id ) denotes the instantaneous PER between source station i and the destination for a given h id and r.
For CoopMAC scheme, the average end-to-end PER performance of source station i also depends on the chosen single relay j, j ∈ S i and is given by where h ij and h jd denote the instantaneous channel gain for the first and second hops, respectively. P ij p (r 1 , h ij ) and P jd p (r 2 , h jd ) denote the instantaneous PER for the two hops, for a given h ij and h jd .
For DSTC, the instantaneous end-to-end PER between source i and destination d depends on a fixed and predefined relay set, denoted as RS i , and is formulated as In Eq. (11), P DST C p (r 1 , r 2 , L, RS i , h (1) , h (2) ) denotes the instantaneous end-to-end PER and is given by where RS ′ is an instantaneous subset of relays from RS i that participate in relaying and P DST C p,hop2 (r 2 , L, h (2) ) denotes the instantaneous PER between relays and the destination for fixed rate r 2 , STC dimension L and channel gains h (2) based on relays in RS ′ .

D. Optimizing end-to-end rate and the choice of transmission parameters
We now describe how to choose the optimal transmission parameters in order to maximize the endto-end transmission rate for each station, while ensuring the end-to-end average PER is bounded by γ.
Even though our emphasis is on R-DSTC, we also discuss direct transmission, CoopMAC and DSTC schemes. In our rate adaptation, every scheme relies on knowledge of the average channel statistics rather than the instantaneous channel gains, thus making it suitable for a WLAN where the average channel statistics change slowly. Assuming the WLAN channel is reciprocal, the source station can estimate the average channel statistics for direct transmission and relayed transmission by listening beacons from AP and overhearing transmissions of other stations. For WLAN systems are typically a stationary or low-mobility environment, the average channel statistics are measured and reported every few seconds, producing only negligible performance loss in throughput. We also discuss rate adaptation based only on number of users in the network.
The set of transmission parameters is different for each scheme and is discussed below. In this paper, all transmission parameters are computed at the source station, as opposed to the protocol in [12] that conducts the computation at the destination station. The maximum end-to-end rate of station i is achieved by minimizing the end-to-end transmission time for each scheme. In addition, we will also discuss the channel information assumed by each scheme for rate adaptation.

1) Direct transmission scheme:
When the source station i transmits to the destination directly, assuming the source station knows the channel statistics to the destination, the optimal transmission parameter is the transmission rate r and the optimum rate r * is given by where P direct p (r) is given by Eq. (9). Note that the optimal transmission rate r is modified whenever the source or destination move to a new location, since the average channel gain for the direct link changes.

2) Two-hop single-relay (CoopMAC) scheme:
We assume there is no signal combining at the destination. A practical MAC protocol for this scheme is CoopMAC [6]. Assuming the source knows the channel statistics between itself and all other stations and between other stations and the destination, the transmission parameters include r 1 , r 2 and the selected relay j. In CoopMAC [6], the optimum relay information is stored in a CoopTable at each source station. The optimum rates r * 1 , r * 2 and the best relay j * are selected by minimizing the end-to-end transmission time over two hops, and is formulated by where P coop p (r 1 , r 2 , j) is given by Eq. (10). When the network topology changes, e.g., the source, destination or any other station move to new locations, the optimal parameters are reselected using Eq. (15).
Hence, CoopMAC is more suitable for a stationary environment with low mobility. When the stations move rapidly, the demand for collecting the global channel knowledge leads to a large overhead for the system. An inaccurate estimation of the channel results in a non-optimal rate adaptation scheme and thus degrades the system performance, as further illustrated in Section V.
3) DSTC scheme: Assuming the available space-time codewords have dimensions denoted by T = {L 1 , L 2 , . . . , L max }, DSTC needs to select its relay set RS i consisting of L relays, where L ∈ T and L = |RS i |. Thus, the transmission parameters are rates r 1 , r 2 , L and RS i . Similar to CoopMAC, the source station is assumed to know the average channel statistics between itself and each stations and between other stations and the destination. The optimum transmission parameters can be obtained by, where P DST C p (r 1 , r 2 , L, RS i ) is given by Eq. (11), and R c is the rate of the orthogonal STC with dimension L. It is known that it is only possible to have full rate (R c = 1) orthogonal STC for L = 2, otherwise R c < 1 [17]. In order to reduce the complexity of relay selection, we propose a greedy algorithm and use it to evaluate DSTC performance in Section V. The basic idea is to sequentially add L relays to the optimal relay set. For each step, we find a single relay that, when combined with the relays selected in the previous steps, will maximize the end-to-end throughput if DSTC is used to assist transmissions from the source.
For the first relay, we choose the best relay from the N-1 stations that maximizes the end-to-end rate in a two-hop manner (single relay based CoopMAC [6]) and add it into the relay set. Then, the second relay is chosen from the remaining N-2 stations in such a way that it can achieve the maximal end-to-end rate along with the first selected relay, using DSTC. Such a selection is iterated until all L relays are picked and added to the relay set. Our simulation shows only 5% throughput difference between this greedy algorithm and exhaustive search when L=2 and N=10.
Like CoopMAC, DSTC need to reselect the transmission parameters whenever the network topology changes and incurs a large amount of channel estimation overhead especially in a mobile environment. • The STiCMAC-CS scheme is assumed to have the same channel knowledge of channel statistics as in DSTC and CoopMAC. That is, the source station i is assumed to know the channel statistics between itself and other stations and between other stations and the destination. The optimal transmission parameters r * 1 , r * 2 , L * are given by (r * 1 , r * 2 , L * ) = arg min where the end-to-end PEP for R-DSTC is given by Eq. For all rate adaptation schemes with full channel statistics, namely direct, CoopMAC, DSTC and STiCMAC-CS, we assume optimal parameters are recomputed whenever the channel statistics change.
For STiCMAC-UC, a two-dimensional look-up table can be pre-computed for the optimal transmission parameters and saved at each source, corresponding to the total number of stations, N, and the distance from the source to the AP in each cell. Once a station enters or leaves the WLAN cell, the BS will broadcast such user count information in its beacon frame to all stations and each station can update its optimal transmission parameters. Thus, STiCMAC-UC does not need real-time computation during network operation. Obviously, in all the relay-assisted schemes, if the end-to-end rate derived by the used rate adaptation scheme is lower than the direct transmission rate, the source station chooses the direct transmission mode instead of cooperation.

V. PERFORMANCE EVALUATION
In order to evaluate the performance of the proposed STiCMAC scheme, we developed a detailed simulation model using OPNET modeler. We compare STiCMAC with direct transmission, CoopMAC and DSTC MAC for both stationary and mobile environments. Additionally, all schemes use the rate adaptation algorithm described in Section IV. The comparison and evaluation was done on a typical single-cell WLAN.

A. Network Topology and Configuration
We assume that the considered wireless LAN complies with the IEEE 802.11g standard and the cell radius is 100 meters. Independent Rayleigh slow fading among each pair of stations and additive white Gaussian noise is adopted as the channel model. The simulated system consists of one AP at the center of a cell and N mobile stations. According to [17], both for DSTC and R-DSTC, a full-rate orthogonal STC is employed for L = 2 with R c = 1, while a R c = 3/4 rate orthogonal STC is employed for L = 3, 4. Each AP or mobile station is equipped with a single omnidirectional antenna. Our simulations are conducted on the uplink from the mobile stations to the AP, with the parameters shown in Table. II. The simulation results display 90% confidence intervals.

B. Mobility Model
Our simulations are performed for both stationary and mobile scenarios. In the stationary scenario, all stations are uniformly distributed within the cell coverage. In the mobile scenario, the stations are assumed to move across the cell using the random walk with reflection (RWkRlc) model [18]. The RWkRlc model is widely adopted to characterize the movement of mobile stations. The RWkRlc model initially deploys stations randomly according to a uniform distribution over the cell. Then, it assigns a random speed to each station that is uniformly distributed in the range [V min , V max ]. Each station picks a random travel duration uniformly distributed in the range [T min , T max ] and a uniformly distributed random direction.
Once a station has walked for the selected duration of time, it may dwell for a random amount of time T d based upon a uniform distribution before it reselects a new travel duration, speed and direction. In contrast to the classic Random Walk model [19], the RWkRlc-governed model includes reflection as an additional feature. Namely, whenever a station reaches the cell boundary during its walk, it will be reflected by the boundary in a similar way that a ray of light reflects off a mirror. This reflection functionality will ensure that the random walk is bounded within a given cell coverage. Accordingly, the RWkRlc model produces a uniform spatial distribution of all stations across the cell and thus enables us to make a fair comparison with the static scenario. The typical parameters of the RWkRlc model we used are shown in Table II. As the distance to the AP grows, all the two-hop schemes outperform the direct transmission, since two high-speed hops provide a higher end-to-end throughput than a low-speed direct transmission, especially as the stations get closer to the cell edge. For large distances, STiCMAC-CS and STiCMAC-UC schemes show the highest per-station throughput gains, followed by the DSTC and CoopMAC. for each relay) from all these relays before every packet transmission is initiated, as is described in [8].

C. Simulation Results
The more relays are recruited by DSTC, the higher the overhead. As the number of stations increases, STiCMAC shows a significant throughput gain over the other schemes (up to 50% gain over direct) due to the following reasons: a) A large number of stations lead to a larger probability of finding more relays, which results in higher diversity and power gain over the second hop. b) Compared to the DSTC MAC [8], STiCMAC needs substantially reduced signaling overhead and handshaking. Also, the overhead of STiCMAC is constant and independent of the number of relays, while the DSTC overhead increases as the number of relays increases. It is also noted that the aggregate throughput of STiCMAC-UC is only slightly lower than STiCMAC-CS. This is because a sufficiently large number of stations supplies enough potential relays and thus eliminates the need for a global knowledge of node locations. This validates our argument that STiCMAC operates efficiently without a global knowledge of channel statistics. in medium access delay for all schemes due to the increased delay before successful access to the channel. However, STiCMAC achieves the lowest delay compared to direct transmission, CoopMAC and the DSTC, since R-DSTC supports a higher end-to-end rate for each connection, and therefore decreases the end-to-end transmission time.
In addition to throughput and delay performance, STiCMAC also reduces the interference generated to neighboring cells when loaded with traffic at the same level. This is because STiCMAC supports a higher average data rate per packet transmission and thus needs reduced air time to deliver the same amount of data on an end-to-end basis, as compared to the other schemes. Consequently, the average transmission power emanating from the reference cell is reduced, even though more relays have been recruited. Fig.   8 shows the interference in a mobile scenario where the average interference power generated by a cell is calculated assuming N=24 users in each cell. The average interference power is illustrated in Fig. 8 and measured in units of dBm at a distance of (100 -300 m) away from the AP of the reference cell.  Instantaneous channel gain between stations i and j h (1) Instantaneous channel gain vector between source and relays h (2) Instantaneous channel gain vector between relays and destination RS i Deterministic relay set of source station i for DSTC RS Instantaneous relay set of source station i for R-DSTC P ij b (r, h ij ) BER for a direct connection between stations i and j for given r and h ij . P ij p (r, h ij ) PER for a direct connection between stations i and j for given r and h ij .
BER for R-DSTC between relays and destination for given r, L, h (2) and R.
PER for R-DSTC between relays and destination for given r, L, h (2) and R. P DST C b,hop2 (r, L, h (2) ) BER for DSTC between relays and destination for given r, L and h (2) . P DST C p,hop2 (r, L, h (2) ) PER for DSTC between relays and destination for given r, L and h (2) . P id p (r, h id ) End-to-end PER for a direct transmission for given r and h id .
End-to-end PER for DSTC for given r 1 , r 2 , L, RS i , h (1) and h (2) . P R−DST C p (r 1 , r 2 , L, h (1) , h (2) , R) End-to-end PER for R-DSTC for given r 1 , r 2 , L, h (1) , h (2) and R. P direct p (r) Average end-to-end PER for a direct transmission for given r. P coop p (r 1 , r 2 , j) Average end-to-end PER for CoopMAC for given r 2 , r 2 and relay j.
Average end-to-end PER for R-DSTC for given r 1 , r 2 and L. P DST C p (r 1 , r 2 , L, RS i ) Average end-to-end PER for DSTC for given r 1 , r 2 , L and RS i . The available rate set for both the first hop (r 1 ) and the second hop (r 2 ) is {R 1 , R 2 , ..., R P }, and the set of available orthogonal STC dimensions for R-DSTC is L, where L ∈ {L 1 , L 2 , ..., L max }. Initialize R * = 0. 2: for Each possible set of transmission parameters {r 1 , r 2 , L} do 3: Find P R−DST C p (r 1 , r 2 , L) for R-DSTC using Eq.(8). 4: if P R−DST C p (r 1 , r 2 , L) < γ and for All possible locations of other stations do 4: Find P R−DST C p (r 1 , r 2 , L) for R-DSTC transmission using Eq. (8) and average over all these locations using χ.