where the choice of ∆c depends on the speed of convergence sought and the desired strength of variations around the value at convergence. By increasing the value of ∆c, faster convergence to the steady state of Ri can be reached but with more oscillations around this value. In order to avoid large variations around the average effective data rate values at convergence, in this simulation, ∆c is fixed at 0.01. As for the average smoothing parameter α, it is considered a value of 0.0001.
5.2. Operation under QoS Constraints
In this case, it is supposed that performs in the presence of users with specific requirements on the QoS, represented by a target data rate for each user. Under such constraints, the PF policy fails to ensure the desired QoS due to the fact that there is no consideration of the required QoS in its selection criterion. Moreover, even in its modified version, the DRC Exponent rule [27], fails to provide the desired QoS and fairness between users. When these exhibited differences in their propagating conditions, namely, differences in the variance associated with the channel of each user as described in previous Chapter. The proposed APF algorithm, on the other hand, is designed to satisfy the required QoS thanks to the features introduced in the selection and updating modules (Fig.5. 2). In this case, the user selection criterion is given by
(6)
where RTi denotes the target rate corresponding to user i. Compared to the previously studied case, the proportional data rate is defined here as the fraction of the data rate of
each user over his target data rate, i.e, i
i
RT R
. Thus, the updating of the control parameters ci, i = 1, 2,…, N, is performed according to the following rule:
The modified versions of APF are described below, APF with Delay Constrain (APFDC) and APF with Proportional Delay Constrain (APFPDC) consequently:
(8)
where DTi denotes the target delay corresponding to user i.
(9)
where Di denotes the delay corresponding to user i.
Fig.5.3. Illustration of the operation of the Adaptive Proportional Fairness modified algorithm under QoS constraints
Chapter 6
Simulations and Numerical Results
Foremost, in this Chapter, the simulation results is presented and comparisons of the Proportional Fairness method and the Adaptive Proportional Fairness algorithm. In this simulation, N active users are considered and only one user is selected in each TTI is supposed. In HSDPA, more than one user can be selected. This can be performed by this algorithm through ordering of the active users, selection of the first user, and verification of the availability of resources, namely, codes remaining out of the 16 available codes, that could be allocated to more users while satisfying the power budget constraint. In this way, time multiplexing is privileged over code multiplexing. Indeed, it is shown in [31]
that time multiplexing, where it is preferable to transmit for few users but at their full available rates, yields higher performance compared to code multiplexing.
It is assumed that all users are allocated the same transmission power, the only difference being the type of variations exhibited by the channel of a user (Rayleigh, Shadowing, Pathloss) [36]. As for the mapping of a channel state, given by the signal-to-noise and interference ratio (SNIR), into a CQI, the following rule is used:
(10)
)
6]),30 [SNIR
min(max(0,
CQI ≈ +
where SNIR is expressed in dB and [.] denotes the integer floor operator. Each CQI value indicates the suitable Transport Block (TB) size, and the modulation/coding that should
be used. The list of the thirty available TB sizes is shown in Table III [32].
Table III Channel Indicator table mapping
In this simulation, it is built using Matlab programming language and its run time was 100s for a single cell environment with 5 km radius with a specific channel model for all users. It provides the corresponding parameters used mentioned in the previous chapters. The target rate RTi(Kb/s) values are 230,68.5,631,117,68.5,230,188,631. The target DTi(ms)rate values are 30,50,10,20,50,30,25,10.
The System Simulation Model is shown in figure 6.1. In Figure 6.2, it compares the proportional allocated data rate for the PF method and the APF algorithm. For example, it is obvious that the PF policy allocates to user5 76% of his air data rate whereas user7 gets allocated only 20% of the data rate his channel can support. On the other hand, using the APF algorithm, the allocation is between 29% and 32% for all users.
However, and as expected, this improvement in fairness comes at the cost of a reduction in the throughput total data allocated as can be seen in Figure 6.3.
Fig.6.1. System Simulation Model
1 2 3 4 5 6 7 8 9 10 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
User Index
Allocated Data Rate (Ri) / Mean Channel Rate
APF PF
Fig.6.2. Comparison of the Proportional allocated data rate
i i
r
R for the PF and
APF Algorithm
Consequently, compared to the PF policy, the APF algorithm achieves the required fairness between users with heterogeneous channels with no significant loss in total data rate. Moreover, Usage Percentage in APF and PF comparison is shown in Figure 6.4 where APF gives more fairness in channel using percentage among users than PF.
As observed, even if the users have the same transmit power, the PF method does not allocate the data rates fairly among them. To the difference in the variations exhibited by the channels of the different users, namely, the difference in the variance associated to each channel distribution. The more the channel variations are, the higher is the average data rate Ri allocated to the corresponding user. Comparing these results with the ones
obtained using the APF algorithm shows how this algorithm outperforms the PF method by fairly allocating the data rates despite the differences in the channel distributions of the different users or the underlying variances.
Fig.6.3. Throughput of the total allocated bit: comparison among PF, APF and CIR Algorithms.
Fig.6.4. Usage Percentage in APF and PF
In the case that users Operate under constraints on the target rates, in Figure 6.5, it compares the allocated data rate to the Target Rate for PF and APF under constraints on the target rates. On one hand, the user6 the PF policy allocates twice more than the required data rate (RTi) while it allocates to user1, user3 and user8 no more than 50 % of their target values. On the other hand, using the APF algorithm yields approximately the same allocated Ratio rate, which is at least 100% of the target data rate of any user. By using the APF algorithm, it is ensured that the requested rates are allocated to all users in a fair manner despite the differences they experience in their channel conditions and the limitation of the discrete rate values in use. This way, the available resources are used more efficiently and the inter-cell interference gets significantly reduced, which yields more resources to be available in the adjacent cells making it possible to satisfy the QoS requirements of their corresponding users.
Fig.6.5. Comparison of allocated data rate to Target Rate for PF and APF under constraints of the Target Rates
Another QoS requirement is delay, the proposed methods described in the previous Chapter are implemented, where the percentage that i user do not get served (NS) while the delay (D)≥ Target delay (TD) is calculated, it is obvious that the probability for i user Pi(NS| D≥ TD) is smaller when the two modified APF methods are applied as depicted in Figure 6.6, but this come in the price of total throughput, where there is no significant loss in the total throughput as shown in Figure 6.7.
Fig.6.6. Comparison of Pi (NS| D≥ TD) for different modified APF algorithms under constraints on the Target Rates
Fig.6.7. Throughput of the total allocated bit: comparison among APF, APFDC and APFPDC algorithms.
Chapter 7
Conclusion
Scheduling is a way to improve spectrum efficiency by exploiting time-varying channel conditions. In this chapter, it summarizes the present framework for APF scheduling to maximize the average system performance value by exploiting variations of the channel conditions while satisfying certain fairness/QoS constraints. The framework provides the flexibility to study a variety of QoS Constrain problems (many of the previous works by us and other researcher’s goes well into this unified framework).
Using this framework, two QoS scheduling schemes have been studied: to achieve required target rate and required delay target for each user. This provides optimal solutions to each scheduling problem while discussing their properties. Different scheduling schemes may be suitable for different application scenarios. Also a deep study for behavior of Adaptive scheduling schemes is presented. Further, this work extends under more general QoS conditions. Lastly, this simulation shows that the proposed scheduling schemes result in substantial system gains while maintaining users' QoS requirements.
To improve spectrum efficiency, intuitively, it is needed to assign resources for users experiencing "good" channel conditions. At the same time, it is also desirable to provide some form of fairness or QoS guarantees. Otherwise, the system performance can be trivially optimized by, for example, letting a user with the highest performance value
to transmit. This may prevent "poor" users (in terms of either channel conditions or money) from accessing the network resource, and thus compromises the desirable feature of wireless networks: to provide anytime, anywhere accessibility. In this thesis, a new fast packet-scheduling algorithm is proposed, the Adaptive Proportional Fairness (APF) scheduling, which represents an enhancement of the DRC Exponent rule that fails to achieve fairness between users in heterogeneous channels. By adding a user control parameter in the criterion used to select the user will be served, and introducing an updating module to track the fast variations of the channels, the APF algorithm is shown to provide the required fairness between users. The heterogeneous propagating conditions experienced by the communicating users is considered and the APF performance for two scenarios is investigated, namely, the Best-effort service where no QoS constraints are specified, and the case where users have specific demands in terms of the rates and minimum delay they require. Taking into consideration HSDPA rate constraints, the simulation results, provided for the Best-effort case, show the high efficiency of the APF method in terms of fairness in that it yields between users, compared to the PF method and at no significant loss in total data rate. As for the second scenario, it also shows that the APF algorithm ensures servicing users at the required data rates while the PF policy fails to satisfy the users QoS requirements. The third scenario showed that the APFDC and APFPDC algorithm ensures servicing users with minimum delay while the APF policy fails to satisfy the performance of minimum delay. Future work can be working in multiuser scenario including more of QoS Constrain.
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