Chapter 3. Modulation Level Allocation for Unicast Service over Multi-hop
4.3. Proposed Algorithm
4.3.3. Resource Allocation
The resource allocation algorithm allocates each CH to one of the MCPs and determines the transmit power and the MCS for each CH so the total service quality is maximized. As a result, the requested bit rate for each regular
Chapter 4. Power and Bandwidth Allocation for Unicast and Multicast Service over OFDMA Channels
71
service and the minimum bit rate for each MBMS can be guaranteed and the average PSNR of the MBMS users can be maximized. As aforementioned, we propose to quantify the service quality in order to achieve the objectives, where the service quality can be written in function of bit rate as
(4.14)
and
(4.15) The total service which we want to maximize can be written as
(4.16)
The proposed algorithm is designed to find the resource allocation that maximizes the total service quality subject to total power constraint. Therefore, we can denote the objective as
(4.17) where the is total power allocated to CHs. As discussed in Section 4.2, each user is included in only one of the CGs. Therefore, for user that included in CG , the bit rate can be written as
(4.18) Accordingly, total service quality of CG can be written as
(4.19)
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where the is the number of users included in CG . Therefore, the total service quality (4.16) can be written as
(4.20)
The bit rate of each user of CG, , in (4.20) can be determined by
(4.21)
where the is index set of the MCPs and the indicator denotes that whether MCP transmit service to users ( ) or not ( ). For example, in case of Table 4.3, is 1 and is 0.
The in (4.21) is total bit rate of all the CHs allocated to MCP , which can be written as
(4.22)
The indicator denotes whether CH is allocated to MCP ( ) or not ( ), where each CH can be allocated up to one MCP, i.e.,
. Bit rate in (4.22) is the bit rate of CH provided that the CH is allocated to the MCP . According to [71], capacity of LTE system can be approximated by Shannon capacity by using bandwidth loss factor and SNR loss factor . That is, if we assume an LTE system, the maximum bit rate that can be robustly transmitted to users of MCP with transmit power over CH can be determined by
(4.23)
Chapter 4. Power and Bandwidth Allocation for Unicast and Multicast Service over OFDMA Channels
73
where the is the bandwidth of each CH. The is the worst channel quality of users , i.e., , where is the index set of users included in MCP .
In addition, total power over all the CHs can be written as
(4.24)
In this chapter, we consider the two resource allocation functions for maximizing the total service quality. That is, we introduce power allocation function (PAF) designed to find the power allocation that maximizes the total service quality for a given CH allocation
. Also, we present the CH allocation function (CAF) designed to find the CH allocation for a given power allocation . That is, by cooperatively operating the two functions, we can determine the optimal power allocation and CH allocation . More specifically, if the CH allocation determined by the CAF with the is identical to , and the power allocation determined by the PAF with the is also identical to (as shown in Figure 3.6), then the and the can be considered as the optimal resource allocation that maximizes the total service quality. Therefore, we consider cooperatively (and iteratively) operating the two functions as shown in Figure 4.6(b), where the power or CH allocation determined by one of the functions is fed back to the other function. If the and the (or the and the ) become stable over the iterative operations in Figure 4.6(b), the resource allocation can be considered as the optimal resource allocation in as described in Figure 4.6(a).
In the rest of this section, we present the two functions, respectively. Then, we explain the iterative operation of the two functions in detail.
74
(a) (b)
Figure 4.6 Descriptions of (a) power and CH allocation function with optimal resource allocation and (b) cooperative operation of the two functions for finding the
optimal resource allocation.
- Power Allocation Function: As shown in Figure 4.6(b), the PAF is designed to find the that maximizes the total service quality, given the
(determined by the CAF). According to (4.17), the Lagrange function can be written as
(4.25) where the denotes the Lagrange multiplier. As the optimal value of power
that maximizes the makes the derivative of the zero, it can be written that
(4.26)
According to (4.20) and (4.24), equation (4.26) can be written as
(4.27)
According to (4.15) and (4.20), it can be written that Subchannel
allocation function
p* a*
Power allocation
function
a*
p*
Subchannel allocation
function pin aout Power
allocation function
ain
pout
Chapter 4. Power and Bandwidth Allocation for Unicast and Multicast Service over OFDMA Channels
75
(4.28)
Therefore, (4.27) can be written as
(4.29) according to (4.21-23), where the is
(4.30)
According to (4.15), we can see that the is sum of the bit values of the users , multiplied by . Therefore, the is referred to as total bit value (TBV) of MCP in the rest of this chapter. If the is 0, the equality of (4.29) is satisfied regardless of the . If not, the that satisfies the equality can be obtained as
(4.31)
As the power according to (4.31) can be negative, the CH allocation is determined by
(4.32)
According to (4.24) and (4.31), the total power allocated to the all CHs can be written as
(4.33)
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In order to fully utilize the given total power , we need to find which is defined as
(4.34)
According to the , the power can be obtained as
(4.35)
Finally, is obtained as
(4.36) Because the given CH allocation may not be the optimal allocation, the PAF also finds the power for the MCPs that are not allocated to each CH (according to the ) so the CAF can modify the CH allocation by using the power allocation as described in Figure 4.6(b).
- Subchannel Allocation Function: As shown in Figure 4.6(b), given the
(determined by the PAF), the CAF is designed to find the thatmaximizes the total utility of the CHs, where the utility of CH by allocating it to MCP can be determined by
(4.37)
where the (the increase in the total service quality by using CH for MCP ) and the (the cost of using CH for MCP ) can be obtained as
(4.38)
Chapter 4. Power and Bandwidth Allocation for Unicast and Multicast Service over OFDMA Channels
77 and
(4.39)
respectively. The in (4.38) is the bit rate of each user in CG , which is allocated by the CHs excluding CH and the is the bit rate determined by the according to (4.23). The in (4.39) is determined by PAF according to (4.34). In order to maximize the total utility, each CH is allocated to the MCP that results in the largest utility. By defining the index of the MCP allocated to CH , we can denote that
(4.40)
That is, for all the CHs, if the is identical to , which is defined as
(4.41)
then the CH allocation maximizes the total utility. However, the is dependent on the which is dependent on the MCPs allocated to the other CHs. Therefore, we propose to implement the CAF as described in Algorithm 4.1, where the in Algorithm 4.1 is the number of CHs that is identical to . First, the CAF allocates the MCP with the largest utility to each CH. Then, initiate the to 0. After that from CH 1, the CAF 1 checks if the allocated MCP is the MCP with the largest utility. If the allocated MCP is identical to the MCP with the largest utility, the is increased by 1. If not, the is set to 0, and then the CH is allocated to the MCP with the largest utility. This operation is iterated over the CHs until all the CHs are allocated to the MCP with the largest utility, i.e., is increased to . After the algorithm is terminated, the CH allocation is obtained as
(4.42)
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The determined CH allocation is fed back to the PAF as shown in Figure 4.6(b) in order to find the optimal resource allocation.
Algorithm 4.1. CH allocation algorithm (CAF).
for to
Determine , and then to . end for
Initiate to 0.
Initiate to 1.
while is identical to , iterate:
Determine .
if is identical to , increase by 1.
else set to 0 and set to . increase by 1 (if , set to 1).
end while
- Cooperative Operation of Power and Subchannel Allocation Functions:
The cooperative operation of the two function described in Figure 4.6(b) is implemented as described in Algorithm 4.2, where TBVs in (4.30) also have to be given in addition to in order to operate the PAF. In Algorithm 4.2, the terms , and are the th , and determined by the algorithm, respectively. Also, the in Algorithm 4.2 is th TBV of MCP determined by the algorithm. First, the algorithm equality distribute the over the CHs. Then, determine the CH allocation according to the CAF. After that, the TBVs are determined, and then the PAF is operated to determine the power allocation. Then, CAF is operated to determine the CH allocation, and therefore the TBVs can be determined.
However, from the second iteration of the PAF, each TBV is averaged with the previously determined TBVs, because the current resource allocations for determining the TBVs are not deterministic unless the resource allocations are stable over the iterative operations. This cooperative operation of the two functions is iterated until the resource allocation becomes stable and finds the optimal resource allocation scheme.
Chapter 4. Power and Bandwidth Allocation for Unicast and Multicast Service over OFDMA Channels
79
Algorithm 4.2. Cooperative operation of the CAF and the PAF in Figure 4.6(b).
Initiate the to 1.
Initiate each element of to .
while every element in , and converges, iterate:
Determine by using the CAF with . According to and , determine . if is larger than 1, then
Modify to for all . end if
Determine by using the PAF, and . Increase the by 1.
end while