Protocol Efficiency with ODSTCi

In addition to the ARQ efficiency with ODSTCi, the protocols' efficiencies in regards of overhearing, relay reselection and ODSTCi are demonstrated in Fig. 14. Subplot (a) presents , , for and 2 when

and , and compares them with the optimal throughput corresponding to randomly choosing at most relays out of for ARQ with DSTC. The throughput of this type is denoted by with . The results show

that and . The

overhearing and reselection function of the Type-C protocol can provide

roughly a 0.4b/s/cu gain over . While, the relay reselection function alone does not offer a meaningful gain over or of the Type-A protocol when . The small advantage in makes the Type-B with ODSTC1 an attractive ARQ scheme for as there is no synchronization and coordination required among the participant relays to perform DSTC.

On the other hand, when increases from 2 to 8 as shown in subplot (b), both and get improved, with gaining some extra but small advantages from the relay reselection at ARQ2. On the contrary, only gets some minor improvement from the functions of overhearing and relay reselection.

The Type-A protocol with ODSTC2 turns out to be an effective yet efficient scheme as relay selection takes place only once when turns non-empty. This result together with those for in subplot (b) are reminiscences of the results in Fig. 8 for outage probabilities, which also show that ODSTC2 is necessary for the Type-A protocol, while ODSTC1 works well with the Type-B protocol at high SNR.

Fig. 14.The protocols' efficiencies in regards of overhearing, relay reselection and ODSTCi for ARQs.

Subplot (a) compares the throughput of various protocols when , and for and . Subplot (b) demonstrates the effects of on the throughput.

Despite the functions of overhearing and relay reselection that provide huge diversities to the Type-C protocol, the throughput does not show a proportional gain over that of the other types of protocols in the above cases.

This motivates us to study the interplay between the outage and the delay constraints, and their effects on the throughput. We investigate this problem by studying the system parameters that might affect the outage probabilities of ARQs, which include the S-D to S-R link ratio ( ), relay reselection and overhearing, and examining the efficiency in terms of and of ODSTCi.

B.1 Effects of the Outage Constraint and the S-D to S-R Link Ratio

Recall from (75) to (79) that the forms of are in fact the same when or 1. Based on the observations from Fig. 13, the differences among mainly result from the terms corresponding to

in (81) and the individual constraint of for each type of the protocol. Since the two-term approximations with are almost the same for the Type-A and B protocols, the fact that disproves the advantage of relay reselection of the Type-B protocol when . In contrast, that justifies the throughput advantage of overhearing of the Type-C protocol when the S-R to S-D link ratio is relatively low at . Nevertheless, the results in Fig. 13 (b) show that this overhearing advantage is marginal when .

The simulation studies presented thus far all show that , , appear to be greatly affected by and the constraint on . To study the effects of and on while to circumvent the complexity in the analysis for the optimal , we investigate this problem from the viewpoint of the maximum multiplexing gain, . We assign

and for the source and relay transmissions, respectively, and use a SNR scaling factor to control the outage probability.

Since this rate assignment method sets the highest possible multiplexing gain,

Fig. 15.The comparison of the delay and outage limited throughput between the optimal approach and a

suboptimal one with and when and for ARQ2.

The left plot compares the results for the Type-C protocol with ODSTC2, while the right plot for ODSTCM.

, for transmissions, it will cause the highest outage probability as well for all subject to the same outage constraint. Though not optimal, this approximated analysis is mathematically tractable and provides valuable insight into the interplay between and . Besides, simulation results in Fig. 15 also show that the resultant throughput with is very close to the optimal one in the practical operating range of SNR even if may lead to a lower throughput at high SNR due to its higher chances of

retransmissions.

Given and , we have and ,

respectively. The outage probabilities from (6) to (9) become invariant to the SNR under this setting as and . More specifically, ,

and become functions of s only, and

(82) whose value depends on the ratio of . Here we use to stand for the different values of for the different protocols to achieve with ODSTCi relaying. Following this rule for notationing, the probability, , in (37) for the Type-C protocol becomes

(83)

Denote the probabilities, , , , and ,

under this setting by , , , and ,

respectively. Substituting them back into (32), (34) and (39), the outage probabilities, , become solely determined by , given the values of the link ratios, , and . In particular, and are functions of and only. As a result, given a predetermined constraint, , on

, one can obtain the corresponding for each and

. With and, hence, , the throughput, ,

can be determined accordingly. More specifically, for the of each type, the associated in (75) to (79) are evaluated by setting in ,

, , or .

0.4998 0.7216 0.7981 0.5174 0.8993 1.1164 0.8879 1.1184 1.1985

TABLE II

The values of to achieve at ARQ2 for different whe and .

As pointed out earlier, for , the approximated in (81) are in fact the same . Therefore, the difference between and lies mainly in the distinct and for each type of the protocol to achieve the same outage constraint . Table II shows the values of to achieve at ARQ2 for different values of when , ,

and . As shown in the table, when , , thus, and

are almost indistinguishable. On the other hand, when , of different types are already close to each other. Besides, for the Type-C protocol, , which is large enough such that the overhearing function of the Type-C protocol does not make much difference in enlarging . Therefore, the differences among of different protocols are small as shown in Fig. 14 when .