Heuristic TMCR Algorithm

Finally, the U_TMCR scheme contains a heuristic TMCR algorithm to solve the radio resource scheduling problem given in (4.14)-(4.16). Because the optimal method by exhaustive search [41] to find an optimal solution takes too much time, which is infeasible to realize, the heuristic TMCR algorithm is proposed to maximize throughput and to reduce complexity. It can also conform to the allocation map structure defined in the standard [61]. Figure 4.2 shows the flow chart of the heuristic TMCR algorithm. The heuristic TMCR algorithm mainly contains two functions: maximum utility allocation (MUA) and consistent allocation (CSA). It finds an allocation map of a frame, allocates the radio resource from the first symbol of each subchannel, and schedules the allocation until there is no unallocated OFDMA symbol in the frame. At the initialization, the heuristic TMCR algorithm calculates the individual utility value ( , , )U k n r given in (4.10) by using the MAS scheme [56], [57], where 1≤ ≤k K, 1≤ ≤n N, and 1≤ ≤r Q_k. Then, it uses the MUA function to schedule the allocation according to the individual utility value. It also uses the CSA function to perform continuous allocation to the user, determined by the MUA function, by an appropriate number of symbols for QoS fulfillment. In the heuristic TMCR algorithm, a possible allocation of a subchannel and a receiving antenna to a user is named as an allocation trial; the process to find the right channel and the right receiving antenna to the right user is called an allocation iteration. Notice that the heuristic TMCR algorithm is a greedy method, and the result of the greedy method is close to the optimal solution when the number of user is large [41].

Furthermore, its computational complexity is much smaller than that of the exhaustive search.

1 l l= +

l L≤ 1 l=

Figure 4.2. Flow chart of the heuristic TMCR algorithm

[MUA Function]

The maximum utility allocation (MUA) function is to find an optimal allocation indictor ( , , ),δ_l k n r which can have the largest individual utility value for the lth OFDMA symbol. The MUA function finds the highest individual utility value, denoted by ( , , )U k n r^{∗ ∗ ∗} , and then assigns to the user k^∗ with the receiving antenna r^∗ on the subchannel n^∗ and checks whether the number of allocated users equal to Q (comply with the constraint of (4.15)). When the subchannel is assigned, the next allocated user cannot interfere the previously assigned user. The MUA adopts the MAS scheme to guarantee the orthogonality among mobile users and to recalculate the radio resource function ^{R k n r}

(

^{, ,∗}

)

of the subchannel. Afterwards, the MUA function will call the CSA function to accomplish the resource allocation for the user k^∗. Repeat the next highest individual utility value user allocation and QoS requirement fulfillment until there is no unallocated user or no free subchannel in the lth OFDMA symbol. The

pseudocode of the MUA function is given below. Step 3: Call the CSA function

Step 4: Find ( , , ) arg max ( ( , , )), and go to step 2

Note that, in the above pseudocode, S^l_free is the set of available subchannels which can be allocated at the lth OFDMA symbol, Ω is the set of unallocated users, Ψ is the ^l_{n k,} unallocated antenna of user k on subchannel n at the lth OFDMA symbol, and S is the _k set of subchannels that are allocated to user k.

[CSA Function]

The consistent allocation (CSA) function is to perform continuous allocation to fulfill the QoS requirement and to reduce the computational complexity, besides the allocation map structure defined by the specification [61] conformed. In order to satisfy the user’s QoS requirement, the CSA function first determines an appropriate number of transmission symbols required for the allocated user selected by the MUA function and then performs the consistent allocation for the user. Assume that the selected user is user k. The required number of transmission symbols for user k, denoted by τ_k, is according to its degree of urgency ( )ζ k , which was given in (4.6) ((4.7)) if the user k is with RT

make service fulfill its QoS requirement as much as possible. The τ_k is designed as

If the unallocated OFDMA symbols of the allocated subchannel is smaller than the τk, the CSA function will go to Step 4 of the MUA function. The MUA function will assign another new subchannel to the user according to the utility value, add the subchannel to the S , and recalculate _k τ_k based on (4.17) and (4.18). Repeat above steps until τ_k is smaller than unallocated OFDMA symbols of the allocated subchannel or there is no any free subchannel. Then, the CSA function generalizes the allocation to the same user in the following consecutive τ_k (remaining) unallocated OFDMA symbols, and removes the user k from the unallocated users. Thus the constraint of (4.16) can be observed and the computation complexity of the U_TMCR can be reduced. The pseudocode of the CSA function is given below.

Function: [CSA]

Go to Step 4 of the MUA function else

Go to Step 5 of the MUA function else

Note that the CSA function extends the allocation result spreading over following consecutive OFDMA symbols, and this can reduce the system overhead for the U_TMCR scheme. The reason is that the CSA function makes the user using the same subchannel with the same modulation order on several continuous OFDMA symbols in a frame. Therefore, the allocation map just needs to record information which includes subchannel number and transmission period. For conventional allocation schemes, a user may be allocated on different subchannels in adjacency OFDMA symbols and this needs a large number of overhead bits to record it. Note that the TMCR algorithm immediately uses the CSA function to generalize the allocation result after the MUA function finds an allocation indictor. Therefore, the urgent user has high probability to have long length for generalization and easily fulfill the QoS requirement.

4.4 Simulation Results

system are set to be compatible with the IEEE 802.16 standard [42], and the scalable parameters are configured according to the suggested values in [62] and listed in Table 4.1. The path loss model is modeled as 128.1+37.6 log(R) dB, where R is the distance between the base station and the user in kilometers [63]. The log-normal shadowing is assumed with zero mean and standard deviation of 8 dB. The QoS requirements of each service are listed in Table 4.2.

Table 4.1 System-Level Parameters

Parameters Value

Cell size 1.6 km

Frame duration 5 ms

System bandwidth 5 MHz

FFT size 512

Subcarrier frequency spacing 10.9375 KHz

Number of data subcarriers 384

Number of subchannels 8

Number of receiving antennas 2

Number of transmitting antennas 2

Number of data subchannel 8

Number of data subcarriers per subchannel 48 Number of slots for downlink transmission per frame 24

Maximum transmission power BS 43 dBm Thermal noise density -174 dBm/Hz

Table 4.2 QoS requirements of each service

Service

In the simulations, it is assumed that each user is assumed to have one service type and the traffic intensity is defined as the ratio of the total average arrival data rate of all service types of all users over the maximum system transmission rate. Besides, the average arrival data rates of voice, video, HTTP, and FTP are 4.8 Kbps, 64 Kbps, 14.5 Kbps, and 88.9 Kbps, respectively. Thus, the traffic intensity varies from 0.15 to 0.90 as the number of users varies from 80 to 480.

The voice service is modeled as the ON-OFF model, in which lengths of ON (OFF) period follow an exponential distribution with means 1.0 (1.5) seconds [63]. The video data is assumed to arrive at a regular interval of 100ms, each frame is decomposed into eight slices (packets), and the size of a packet is distributed in a truncated Pareto distribution [64]. In which, there are delay intervals between two consecutive packets of a frame which denote the encoding delay at the video encoder. These intervals are modeled by a truncated Pareto distribution. The HTTP of NRT service is modeled as the behavior of web browsing. Thus, the HTTP traffic is modeled as a sequence of page downloads, and each page download is modeled as a sequence of packet arrivals. The interval between two consecutive page downloads, representing the reading time in web browsing, is distributed in an exponential distribution. For detailed parameters of video and HTTP traffic models please refer to [64]. The FTP traffic of BE user is modeled as a sequence of file downloads. The size of a file is distributed in a truncated lognormal distribution with mean 2M bytes, standard deviation 0.722M bytes, and a maximum value 5M bytes. In addition, the interval between files is distributed in an exponential distribution with mean 180 seconds.

In the following, the proposed U_TMCR scheme is compared to the exhaustive search method [41], the CDPS [30] scheme and the ARRA [32] scheme for performance

solution of the optimization equations given in (4.14)-(4.16). The CDPS scheme and the ARRA scheme are modified to fulfill the MIMO OFDMA system.

Figure 4.3 shows the system throughput versus the traffic intensity for the proposed U_TMCR scheme, the exhaustive search method, the CDPS scheme in [30], and the ARRA scheme in [32]. It can be seen that the system throughput of the proposed U_TMCR scheme is very close to that of the exhaustive search method; the former is less than the latter by only an amount of 2.12% at traffic intensity 0.75. The reason is that the heuristic U_TMCR is a kind of greedy method [41]. Also, at high traffic intensity, the proposed U_TMCR scheme can achieve system throughput higher than the ARRA scheme and the CDPS scheme by an amount of 8% and 21% at traffic intensity 0.75, respectively. It is because the U_TMCR scheme allocates the resource according to the utility function given in (4.10), where a user with a high individual utility value is the one who is urgent and with the good channel quality; whereas, the services order of users in the ARRA scheme is only based on the urgency which denotes the residual time to expiration. This would make the U_TMCR scheme attain higher system throughput than the ARRA scheme. Also, the U_TMCR scheme designs the maximum urgency values of RT and NRT packets to be the same but set the priority constants in the QoS monitoring function to further differentiate the services so that the urgent RT packet will have higher probability to be served than the urgent NRT packet. The ARRA scheme adaptively adjusts the priority of users according to just the time to expiration. There are possibilities that the priority value of NRT packet may be larger than that of the RT packet. Thus, some packets of RT traffic will be squeezed and not be served in time at high traffic intensity. These RT packets will be dropped, resulting in the system throughput decrement for the ARRA scheme. On the other hand, the CDPS scheme serves users by the fixed priority, and thus the multiuser gain cannot be obviously

appeared. Additionally, when the traffic intensity increases, the probability of serving video packets would become small and the video packet dropping rate intuitively increases. This makes the system throughput of the CDPS scheme be the smallest.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Traffic Intensity 2

4 6 8 10 12 14 16 18

U_TMCR ARRA CDPS

Exhaustive Search

Figure 4.3 System Throughput

Figures 4.4(a) and 4.4(b) show voice and video packet dropping rates, respectively, where the dropping rate requirements (1%) are also given. It can be seen that the U_TMCR performs quite close to the exhaustive search solution in the performance measures of the two RT packet dropping rates. The U_TMCR (ARRA) scheme keeps the voice packet dropping rate lower than the voice packet dropping probability requirement of 1% until the traffic intensity is above 0.9 (0.8), while the CDPS scheme always attains the voice packet dropping rates close to zero. Also, the U_TMCR scheme keeps the video packet dropping rate lower than the video packet dropping probability requirement of 1% until the traffic intensity is near 1.0, while that of the CDPS (ARRA) scheme violates the requirement at traffic intensity 0.56 (0.76). The reasons are quite similar to

and CDPS schemes in Fig. 4.3.

Figure 4.4 (a) Voice packet dropping rate; (b) Video packet dropping rate

Figs. 4.5(a) and 5(b) show the mean voice and video packet delays, respectively, where the maximum packet delay requirements (D ) are also included. It can be seen ^* that the mean RT packet delays by the U_TMCR scheme are larger than that by the exhaustive search method. The CDPS scheme employs the fixed priority, thus it has the smallest voice packet delay but the largest video packet delay. Both of the U_TMCR scheme (exhaustive search method) and the ARRA scheme exploit the dynamic priority and make full use of the voice packet delay tolerance. The three schemes delay the voice packets to serve more video packets in time. Thus, the delays of video packet of these three schemes are smaller than that of the CDPS scheme. It can also be found that the voice and video packet delay by the U_TMCR scheme are smaller than by the ARRA scheme at traffic intensity over 0.5. The reason is that the urgent packet of RT user in the U_TMCR scheme has the highest priority while the priority of urgent packet of RT user in the ARRA scheme may be smaller than that of NRT packet; the urgent RT users in the

U_TMCR scheme have higher probability to be served in time.

Traffic Intensity (a)

Mean Delay of Voice Packet (ms)

Maximum Delay Requirement

Mean Delay of Video Packet (ms)

Maximum Delay Requirement

Figure 4.5 (a) Mean delay of voice packet; (b) Mean delay of video packet

Figure 4.6 illustrates the guaranteed ratio for HTTP packets. Unlike the RT traffic, packets of the HTTP traffic will not be dropped but still wait for service when the requirement of minimum transmission rate R cannot be kept. It can be observed that _min^* the guaranteed ratio of the U_TMCR scheme is close to that of the exhaustive search method, and it is much higher than that of the CDPS scheme but lower than that of the ARRA scheme. As the same reason given above, by the CDPS scheme, the priority of HTTP packets is the third one which means that HTTP packets have to wait until all real time packets are served. By the U_TMCR scheme (exhaustive search method) and the ARRA scheme, since the priority of users are dynamically adjusted frame by frame, it can avoid more resource being always occupied by RT traffic. Thus more HTTP packets can be guaranteed to be served with the minimum transmission rate. Additionally, the ARRA scheme further gives the NRT service to override the RT service to be first served

transmission rate R is going to be violated. Thus, the ARRA scheme has the largest _min^* guaranteed ratio for HTTP packets.

Figure 4.6 Guaranteed ratio of HTTP packets

Figure 4.7 shows the BE throughput versus the traffic intensity. It can be found that the U_TMCR scheme has BE throughput lower than the exhaustive search method, as the system throughput shown in Fig.3.3; the U_TMCR scheme (exhaustive search method) and the ARRA scheme outperform the CDPS scheme in the BE throughput. The BE service in the U_TMCR scheme (exhaustive search method) still has more chances to transmit. The reason is that the design of utility function in (4.10) can achieve higher multiuser gain and make the resource allocation more efficiently. Furthermore, it could make the RT users be delayed near the delay bound and the NRT users with good channel quality be served with high probability. It can also be found that the BE throughput of the U_TMCR scheme (exhaustive search method) increases until traffic intensity is 0.6 and then decreases. It is because the U_TMCR scheme (exhaustive

search method) will give the RT services more resource in order to satisfy their QoS requirements when traffic intensity is higher, which can be seen in Fig. 4.4. For the CDPS scheme, the FTP traffic will be transmitted only when voice, video, and HTTP traffic have already been served. Thus its average throughput of BE is the lowest.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 2 3 4 5 6 7

Traffic Intensity

BE Throughput (Mbps)

U_TMCR ARRA CDPS

Exhaustive Search

Figure 4.7 BE throughput

Finally, the computational complexities among the exhaustive search method, the U_ TMCR, ARRA, and CDPS schemes are compared. The computation complexity of a scheme depends on the number of allocation trials in an allocation iteration and the total number of allocation iterations needed for the scheme. Theoretically, the worst-case computational complexity for the four schemes would be O LKN Q( ² _M), where Q is _M maximal number of receiving antenna Q . However, either the consistent allocation _k (CSA) function in the U_TMCR scheme or the generalization function in the ARRA scheme continue the allocation to the same user in several following OFDMA symbols.

least L times over the exhaustive search method and the CDPS scheme.

However, the U_TMCR scheme has lower computational complexity than the ARRA scheme in realistic operations. The U_TMCR scheme uses the CSA function to generalize the allocation result immediately after the MUA function has allocated a subchannel to a user. Thus, if a user needs more than one subchannels to transmit, the U_TMCR scheme performs the allocation for the user in just one iteration and removes the user from the unallocated user set. On the other hand, the ARRA scheme extends the results after all subchannels of an OFDMA symbol are allocated so that the ARRA scheme needs the number of allocation iteration equal to the number of required subchannels of the user and it removes the user until the QoS requirements of the user are satisfied. Therefore, the U_TMCR scheme needs a smaller number of allocation iteration to allocate the resource and a smaller number of allocation trials in the following allocation iteration than the ARRA scheme. Take one example. Assume that users are with packet length uniformly distributed between 72 bytes and 576 bytes. The number of allocation trials in a frame by the U_TMCR scheme is reduced by 6.25% ~ 29.2%, compared with the ARRA scheme. The larger the packet length is, the reduction of computation complexity by the U_TMCR scheme would be.

4.5 Concluding Remarks

In this chapter, a utility-based throughput maximization and complexity reduction (U_TMCR) scheduling scheme is proposed for downlink multiuser MIMO-OFDMA systems, where the radio resource allocation to multimedia users includes subchannel allocation, modulation order assignment and receiving antenna. The goals of the U_TMCR scheme are to maximize system throughput, fulfill QoS requirements, and lessen the computational complexity, while considering multiple service classes, such as

RT, NRT, and BE services. The proposed U_TMCR scheme designs a utility function, formulates the utility-based scheduling problem, and solves the problem by a heuristic TMCR algorithm. For RT (NRT) service, the value of the utility function is dynamically adjusted to maximize the spectrum efficiency and to fulfill the delay requirement (minimum transmission rate) and the BER requirement. The heuristic TMCR algorithm includes a maximum utility allocation (MUA) function to maximize the overall utility value and a consistent allocation (CSA) function to fulfill QoS requirements of users and reduce the computational complexity.

Simulation results show that the performance of the proposed U_TMCR scheme is very close to that of the exhaustive search method, and the proposed U_TMCR scheme outperforms the conventional ARRA scheme [32] and the CDPS scheme [30] in system throughput by an amount of 8% and 21.5%, respectively. The U_TMCR scheme can sustain users’ QoS requirement up to the traffic intensity 0.9, while the ARRA (CDPS) scheme can not guarantee QoS requirements after a traffic intensity of 0.8 (0.55). The overall QoS satisfaction by the U_TMCR scheme is higher than that by the ARRA and

Simulation results show that the performance of the proposed U_TMCR scheme is very close to that of the exhaustive search method, and the proposed U_TMCR scheme outperforms the conventional ARRA scheme [32] and the CDPS scheme [30] in system throughput by an amount of 8% and 21.5%, respectively. The U_TMCR scheme can sustain users’ QoS requirement up to the traffic intensity 0.9, while the ARRA (CDPS) scheme can not guarantee QoS requirements after a traffic intensity of 0.8 (0.55). The overall QoS satisfaction by the U_TMCR scheme is higher than that by the ARRA and

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