The purpose of this section is to obtain the relationship between the SNR values and the resulting network throughput based on the results obtained from the previous sec-tion. For the derivation of throughput performance, a contention-based MAC protocol with cooperative communications is adopted. It is designed based on the IEEE 802.11 CSMA/CA scheme associated with the usage of the RTS/CTS exchanges. For the
purpose of informing the nodes in the network regarding the activation of cooperative communication, the new control frames named cooperative ready-to-send (cRTS) and cooperative clear-to-send (cCTS) are created. It is noted that the cRTS and cCTS fames have the same structures as the RTS and CTS frames respectively except the subtype field of MAC header. In other words, several reserved values of the subtype field in IEEE 802.11 standard can be utilized to create these new control frames for representing different control messages. Moreover, the channel will be secured to be collision-free after the exchanges of the RTS/CTS or the cRTS/cCTS frames as defined in IEEE 802.11 specification. Specifically, nodes in the cooperative group first initiate the delivery of the data frame by sending the cRTS frame in order to notify the other nodes for the request of cooperative communication. The cooperative communication will therefore be activated if the cCTS frame is issued by the corresponding destination.
Subsequently, the source will transmit the data frame in the first phase to both the relay and the destination. The relay will forward the received data frame to the destination after a short inter-frame space (SIFS) duration, which completes the second phase of the cooperative scheme. On the other hand, nodes in the non-cooperative group will transmit their data frame based on the conventional RTS/CTS exchange for channel reservation. Due to the much smaller size compared to the data frames, the frame error of the non-data frames is considered neglected. It is noticed that the scheme mentioned above will be utilized as a preliminary evaluation of the saturated network throughput in the next section. Other contention-based MAC protocol with cooperative diversity can also be designed and analyzed in the similar manner.
Similar to the work presented in [19], the saturation throughput is defined as the fraction of time utilized to successfully transmit the payloads. In order to facilitate the computation of the network throughput, two associated probabilities ptr and pwc are introduced as follows. The parameter ptr denotes the probability that at least one
transmission occurs in the considered time slot, i.e.
ptr =1 − (1 − τcoop)Ncoop(1 − τdir)Ndir (3.7)
Moreover, pwc indicate the probability of a non-collided transmission on the condition that at least one node is transmitting. It is composed by two probabilities pwc(cg) and pwc(ncg), i.e. pwc = pwc(cg)+ pwc(ncg). The parameter pwc(cg) represents one node in the cooperative group reserves the channel while the other nodes remain silent during the time slot, i.e. no collision occurs. On the other hand, pwc(ncg) represents that one node in the non-cooperative group successfully reserves the channel and transmits its data frames. These two probabilities can be obtained as
pwc(cg) =N ptr
[Rcgτcoop(1 − τcoop)Ncoop−1(1 − τdir)Ndir] (3.8) pwc(ncg) =N
ptr[(1 − Rcg)τdir(1 − τdir)Ndir−1(1 − τcoop)Ncoop] (3.9)
Furthermore, the saturation throughput S, which is defined as a function of Rcg, Pf (dir), and Pf (coop), can be expressed as
S(Rcg, Pf (dir), Pf (coop)) = E[LP]
E[TB] + E[TS] + E[TC] + E[TE] (3.10)
The expected values within (3.10) are obtained as follows. E[TB] = (1 − ptr)δ indicates the average duration of the non-frozen backoff time in a virtual time slot. It is noted that the virtual time slot represents the time duration between two consecutive backoff timers. The parameter δ is defined as the size of one slot time specified in the physical layer of the IEEE 802.11 standard. The average duration of the successful transmission
in a virtual time slot is acquired as
E[TS] = ptr[pwc(cg)(1 − Pf (coop))Ts(coop)+ pwc(ncg)(1 − Pf (dir))Ts(dir)] (3.11)
where Ts(dir) and Ts(coop) are the required time intervals for a successful transmission via the direct and the cooperative communications respectively. These two parameters are obtained as
Ts(dir)=TRT S+ TCT S+ THeader+ TP ayload+ TACK+ 3TSIF S + 4ρ + TDIF S (3.12) Ts(coop)=TcRT S + TcCT S+ 2THeader+ 2TP ayload+ TACK + 4TSIF S+ 5ρ + TDIF S (3.13)
where ρ is denoted as the propagation delay. It is noted that the meanings of the other parameters are revealed by their corresponding subscripts, e.g. THeader indicates the time interval for transmitting the header in a frame, and TDIF S corresponds to the time duration of a distributed inter-frame space (DIFS). Moreover, E[TC] represents the average time duration for the transmission with collisions in a virtual time slot.
The mean duration of a failure transmission caused by the channel fading and noises is denoted as E[TE]. Both E[TC] and E[TE] are obtained as
E[TC] =ptr(1 − pwc)Tc (3.14)
E[TE] =ptr[pwc(cg)Pf (coop)Te(coop)+ pwc(ncg)Pf (dir)Te(dir)] (3.15)
where Tc denotes the time interval for the transmission which occurs collision, i.e.
Tc = TRT S + ρ + TDIF S. On the other hand, the parameters Te(dir) and Te(coop) are the required time durations to receive and detect the error frame caused from the channel fading and noises. Both values are considered the same as that for successful transmissions, i.e. Te(dir) = Ts(dir) and Te(coop) = Ts(coop). Finally, the parameter E[LP]
represents the average payload bits that is successfully transmitted in a virtual time slot, which can be acquired as
E[LP] = ptr{pwc(cg)(1 − Pf (coop))E[LP ayload] + pwc(ncg)(1 − Pf (dir))E[LP ayload]} (3.16)
where E[LP ayload] indicates the average length of payload bits in a data frame. Two special cases for the saturation throughput S are considered as follows. Sdir represents the saturation throughput if all of the nodes are in the non-cooperative group; while Scoop indicates the case that the cooperative protocol is adopted for the entire system, i.e. all the nodes are in the cooperative group. These two special cases can be defined as
Sdir ,S(Rcg = 0, Pf (dir), Pf (coop) = 0) (3.17) Scoop ,S(Rcg = 1, Pf (dir) = 0, Pf (coop)) (3.18)
Whether it is suitable to adopt the cooperative schemes can be intuitively observed from the two extreme cases as described in (3.17) and (3.18). In general, the cooperative protocols can improve the FER with the cooperation of the relay, i.e. Pf (coop) < Pf (dir). However, the successful transmission time via the cooperative link is inherently longer than that from the original direct communication, i.e. Ts(coop) > Ts(dir). Due to the tradeoff between the FER and the required transmission time, there is no guarantee that the saturation throughput from the cooperative communication (Scoop) will be higher than that from the direct link (Sdir). The analytical models derived in this section will be utilized to determine the suitable occasions to exploit the cooperative communication, as will be presented in the next section.