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21.4.2 Resource allocation to maximize capacity Suppose there is no xed requirements per symbol and the aim is to maximize capacity. It has been shown in Viswanath et al. [60] that, for point-to-point links, a fair allocation strategy maximizes total capacity and the throughput of each user in the long run, when
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the user s channel statistics are the same. This idea underlying the proposed fair scheduling algorithm is exploiting the multiuser diversity gain. With a slight modi cation, the fair scheduling algorithm for point-to-point communication was extended to an algorithm for point-to-multipoint communication [53]. Suppose the user time varying data rate requirement Rk (t) is sent by the user to the base station as feedback of the channel condition. We treat symbol time as the time slot, so t is discrete, representing the number of symbols. We keep track of average throughput tk,n of each user for a subcarrier in a past window of length tc . The scheduling algorithm will schedule a subcarrier n to a user k according to the criterion {k, n} = arg max(rk,n /tk,n )
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where tk,n can be updated using an exponentially weighted low-pass lter described in Viswanath et al. [60]. Here, we are confronted with determining the rk,n values. We can set rk,n to Rk /N , where N is the number of carriers. With this setting, the peaks of the channel for a given subcarrier can be tracked. The algorithm schedules a user to a subcarrier when the channel quality in that subcarrier is high relative to its average condition in that subcarrier over the time scale tc . When we consider all subcarriers the fairness criterion matches with the point-to-point case as k = max Rk /Tk , where Tk =
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The theoretical analysis of fairness property of the above relation for point-to-point communication is derived in Viswanath et al. [60]. Those derivations can be apply for point-tomultipoint communication. 21.4.2.1 Performance example The required transmission power for c bits/subcarrier at a given BER with unity channel gain is [57]: f (c, BER) = N0 Q 1 3 BER 4
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Figure 21.9 shows the average data rates per subcarrier vs total power constraint when there are four users. Each user has a rate requirement of 192 b/symbo1 (maximum rate) and BER requirement of 10 4 . The performance of the iterative approach is close to that of the optimal and difference between suboptimal and iterative approaches decreases as the total transmit power increases.
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21.5 PREDICTIVE FLOW CONTROL AND QoS Even if the dimensioning of network resources has been done correctly and the admission control mechanism is good, the network may go into periods of congestion due to the transient oscillations in the network traf c. For this reason it is necessary to develop a mechanism to quickly reduce the congestion or pre-empt it, so as to cause the least possible
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2.8 Spectral efficiency (b/subcarrier) 2.6 2.4 2.2 2.0 1.8 1.6 36
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Figure 21.10 Individual link-level model. degradation of QoS to the underlying applications [61 81]. 4G networks will carry a mixture of real-time (RT) traf c, like video or voice traf c, and nonreal-time (NRT) traf c, like data. One approach to controlling the NRT traf c is to be able to predict the RT traf c (at the link of interest) at some time in the future, then, based on this prediction, control the NRT traf c. In Figure 21.10, Vl (n) and l (n) correspond to the aggregate RT traf c and NRT traf c, respectively, arriving at a link of interest (link l having capacity l ), at time n. One can then estimate Cl (n), the available link capacity for NRT traf c, at some time in the future. This information would then be used at the network-level to distribute the available link capacities to the NRT ows. On the network level the available link capacities for the NRT ows is then distributed to maximize throughput (or more generally some utility function), based on appropriate fairness requirements. An example network is shown in Figure 21.11, where ows traverse links with available capacities for the NRT ows calculated at the individual link level. In 7, the network-level problem has been investigated in the case when the available link capacity for NRT ows at each node is a constant. The problem remains open in the case when the available capacity is time-varying.