filling algorithm (explained in section 3.1). In [34], Yin and Liu simulate their algorithm and show that it outperforms OFDM-TDMA in terms of achievable rate and outage probability. Their results clearly show the advantages of OFDMA over OFDM-TDMA. By co
allocation of subcarriers has been made, each user is allocated power Pm to satisfy his or her minimum rate requirement given by Rm as shown in Box (2). Since the function F was previously defined as the achievable data rate per subcarrier for a given SNR
The following optimization problem, constrained by E15 and E31, illustrates the basic idea of the RA approach for the multi-user system being considered [26]:
ck ,n , pn
max ck , n F (SNRk , n , Pe ) (E32)
k n
where SNRk , n = pn
hk , n
2
2
(E33)
In the
4.1.3 Rate Adaptive Approach As mentioned before, the Rate Adaptive (RA) approach focuses on maximizing the sum of user data rates while using a fixed amount of power [26]. In this sub-section, I first define the RA approach using the simple case of a sin
4.1.2.2 Simulation Of Select Margin Adaptive Resource Allocation Algorithms I chose the following two MA algorithms to simulate in MATLAB: BABS+ACG and BABS+RCG [32]. The purpose of doing the simulations is to gather some experience in writing a MA resour
For each user k, set: 1 ! Rk # Ck = " $ " Rmax $ which is the number of blocks assigned to user k.
For each user k, nd: 2 Rk ! Tsym bk = nCk which is the number of bits carried by each subcarrier for user k.
SNRk = (2 bk ! 1)" which is the SNR required to
Another algorithm that uses the MA approach is presented in [33]. In this paper, the authors propose a block-wise subcarrier allocation algorithm that is shown in Figure 16. N subcarriers are divided into M blocks and each block has n adjacent subcarriers
For each user k:
Initialize Ck = cfw_! which is the set of subcarriers allocated to user k.
1
Set n = 0 If n < N
2
If n ! N
Choose
k * = arg max k H k (n )
2
3
If # Ck * ! mk *
If # Ck * = mk * Set H k * (n ) = 0
2
4
If # Ck * = mk * Choose k * = arg max
For each user k:
!1 Find rk (n ) = f ' ("k H k (n ) ) which is the transmission rate of user k on subcarrier n. Initialize C k = cfw_! 2
1
which is the set of subcarriers allocated to user k.
For each subcarrier n: Choose k * = arg max k rk (n ) Set C k
So the first stage of [32]s algorithm determines the number of subcarriers for each user. The BABS algorithm is unfair to the lowest rate user because the step in Box (3) may cause the allocation scheme to completely ignore the lowest rate user in an atte
The BABS algorithm first calculates how many subcarriers are needed for each user. This step is described in Box (1) of Figure 12. is the minimum require rate for user k and Rmax is the
average maximum rate available on each subcarrier. Next, the BABS alg
If
!m
k=0
K
k
< N For each user k, nd: 1 min !R # mk = " k $ " Rmax $ where mk is the number of subcarriers allocated for user k.
If
!m
k=0
K
k
=N
If
!m
k=0
K
k
>N
Choose k* = arg min k mk
2
If
!m
k=0
K
k
>N
Set mk * = 0 3
If
!m
k=0
K
k
=N
End of Step 1 6
In the above equations, k is the user index and Rk is the minimum rate requirement for user k. ck,n is the channel assignment matrix (as was defined before) with a restriction that each subcarrier is assigned to only one user. To formulate the problem as
The following optimization problem, constrained by E15 and E19, illustrates the basic idea of the MA approach for the multi-user system being considered:
ck ,n , pn
min ck , n pn (E20)
k n
where
c
n
k,n
F (SNRk , n , Pe ) Rk , k (E21)
hk , n
2
and SNRk ,
4.1.2 Margin Adaptive Approach As mentioned before, MA usually focuses on minimizing the total transmission power while requiring a minimum user data rate [28]. In general terms, MA minimizes the total transmit power while maintaining a minimum quality of
the multi-user system shown in Figure 11. The wireless system shown in Figure 11 is a cellular system that uses OFDMA for the downlink and consists of one base-station and K users. This system employs either an MA or an RA resource allocation algorithm th
4.0 RESOURCE ALLOCATION IN OFDMA SYSTEMS Adaptive resource allocation is done in order to optimize the performance of OFDMA systems. High performance can be achieved by assigning the best set of subcarriers for each user for the duration of one or more OF
water-filling algorithm that depends on the largest power difference. Figure 8 shows an example of a two-user system. In this example, water-filling is done at the noise level that corresponds to the largest power difference. For the example shown in Figu
sensitive applications. An interesting part of this capacity region is the zero-outage capacity region. In the zero-outage region, the allocation policy maintains a constant rate for each user regardless of the channel state. In other words, it ensures no
where + = 1, 0, 0 (E12)
Moreover, the Least Squares method and Linear Programming are special cases of convex optimization. The Least Squares method tries to minimize |Ax b|2 while the problem of Linear Programming is defined as follows: Minimize cTx with
of the loop iteration, the algorithm increases the water level by a bit and rechecks the if condition. Also N is the total number of channels that are available. A graphical illustration with one user and three channels is shown in Figure 6 below.
Figure
In the above equation, Pi is the power allocated to the ith channel and is a scaling factor. When we differentiate the information capacity with respect to Pi, we get Pi = Ni where Ni is the noise level on ith channel. Also, is the water level that satisf
PAPR requirements of OFDMA forced the standard to use Single Carrier Frequency Division Multiple Access (SC-FDMA) for the uplink in order to conserve battery life on the mobile devices. OFDMA was also proposed for digital video broadcasting return channel
Figure 4. Definitions of OFDM-TDMA, OFDMA and OFDM-CDMA In OFDMA, the entire bandwidth is divided into a number of subcarriers for parallel transmission of symbols from different users. Assignment of subcarriers to users is a very important issue and grea
Even though the PAPR for OFDM that was derived above is an upper bound, it is important to note that the PAPR varies linearly with the number of subcarriers N. To combat impairments in channels that are highly frequency-selective, a large will be preferab
The PAPR of a discrete-time signal is given by [15]:
max n x[ n ] PAPR = 2 En x[ n ]
2
(E9_1)
Now consider the OFDM TX from Figure 2; in particular, consider the discrete-time symbols xn generated when the frequency-domain symbols are passed through the