The simulation results shown in this section assume a single-cell network with multiple DNs that are randomly distributed within a 120-degree section of the 600-meter radius
−3000 −200 −100 0 100 200 300 400 500 600 100
200 300 400 500 600
Figure 3.3: The user location distribution; r0 = 150 m.
circle centered at the BS. The RNs are placed on a circle with a 150-meter radius with a equal angular spacing. As shown in Fig. 3.2 and 3.3, the probability density function (pdf) of the DN locations is given by [20]
P = r40 r5 exp
·
−5 4
³r0 r
´4¸
. (3.11)
where r > 0 is the radius and r0 = 150 m. We also assume each subcarrier suffers from independent Rayleigh fading in any direct or relay link with a path loss exponent 3.5. For the convenience of comparison, we normalize each link gain with respect to the worst-case gain corresponding to the longest link distance.
We compare the performance of our subcarrier assignment (SA) algorithm (P2-solver) with two subcarrier assignment schemes which we refer to as greedy SA and weighted SA algorithms, respectively. These two algorithms were modified from those presented in [8] and [9], respectively. As the originally schemes were designed with perfect CSI assumption and have different RN selection criterion, we use our P1 and P3 solutions but keep that for P2 intact for the sake of fair comparison.
In Figs. 3.4–3.5, we assume there are 8 DNs, 3 RNs in a 32-subcarrier OFDMA cell
with a total system power of PT = 3.2 W (i.e. the average transmitted power for each subcarrier is 0.1 W) and varying minimum rate requirements. The first figure shows that the sum rate of our algorithm is closer to the greedy SA than the weighted SA does.
For a given subcarrier assignment scheme, we compare two power allocation methods–
equal power allocation and the proposed modified water-filling power allocation for the direct link. As expected, our scheme of [4.34] performs better than the equal power allocation approach. The second figure depicts the rate failure probability behavior, i.e., the probability that the algorithm fails to meet a user’s rate requirement. Obviously, our solution has a much lower rate failure probability than those achievable by either greedy SA or weighted SA scheme. In Fig. 3.6 and Fig. 3.7 we compare the sum rate
10 15 20 25 30 35 40 45 50
430 440 450 460 470 480 490
user rate constrain(bits/2 OFDM symbols)
sum capacity(bits/2 OFDM symbols)
greedy SA [8]+equal PA greedy SA [8]+mwf PA weighted SA [9]+equal PA weighted SA [9]+mwf PA proposed SA+equal PA proposed SA+mwf PA
Figure 3.4: Sum rate v.s. user rate constraint; 8 DNs, 3 RNs and 32 subcarriers with PT = 3.2.
and required rate failure probability (i.e., the probability that an algorithm fails to meet the rate requirement) performance as a function of the user number in a 32-subcarrier OFDMA network having 3 RNs, PT = 3.2 and a minimum user rate requirement of
10 15 20 25 30 35 40 45 50 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
user rate constrain(bits/2 OFDM symbols)
required rate failure probability
greedy SA [8]+mwf PA weighted SA [9]+mwf PA proposed SA+mwf PA
Figure 3.5: Rate failure probability v.s. user rate constraint;8 DNs, 3 RNs and 32 subcarriers with PT = 3.2.
48 bits/2 OFDM symbols. It is clear that our algorithm outperforms the weighted SA scheme. In Fig. 3.8, we examine the conditional average achievable rate ratio γ defined as γ = E [Rk/Rk,min|Rk < Rk,min], if P(Rk < Rk,min) 6= 0; otherwise γ = 1. We observe that our algorithm is far better than the greedy algorithm and when the user number is large, outperform the weighted SA algorithm of [9]. For fair comparison, all three algorithms employ the proposed mwf power loading scheme. In Fig. 3.9, we show the average probability of doing the load balancing step. While the user number increases, users are more likely not to satisfy their rate constraints, and thus the probability of doing the load balancing step increases.
In Figs. 3.10–3.11, we consider another scenario in which there are 8 DNs, 3 RNs in a 128-subcarrier OFDMA cell with a total system power of PT = 12.8 W. They also shows that the sum rate of our algorithm not only has the lower probability that users fail to meet their rate requirements but is closer to the greedy SA than the weighted SA does.
4 5 6 7 8 9 10 420
430 440 450 460 470 480 490 500
user number
sum capacity(bits/2 OFDM symbols)
greedy SA [8]+equal PA greedy SA [8]+mwf PA weighted SA [9]+equal PA weighted SA [9]+mwf PA proposed SA+equal PA proposed SA+mwf PA
Figure 3.6: Sum rate v.s. user number; 3 relay nodes and 32 subcarriers with PT = 3.2 and the minimum user rate requirement is 48 bits/2 OFDM symbols.
Moreover, the performance enhancement by the proposed modified water-filling power allocation for the direct link. Then in Fig. 3.12 and Fig. 3.13 we compare the sum rate and required rate failure probability performance as a function of the user number in a 128-subcarrier OFDMA network having 3 RNs, PT = 12.8 and a minimum user rate requirement of 48 bits/2 OFDM symbols. Our algorithm also outperforms the weighted SA scheme.
4 5 6 7 8 9 10 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
user number
required rate failure probability
greedy SA [8]+mwf PA weighted SA [9]+mwf PA proposed SA+mwf PA
Figure 3.7: Rate failure probability v.s. user number; 3 relay nodes and 32 subcarriers with PT = 3.2 and the minimum user rate requirement is 48 bits/2 OFDM symbols.
4 5 6 7 8 9 10
40 50 60 70 80 90 100
user number
γ ( the conditional average achievable rate ratio )(%)
greedy SA [8]+mwf PA weighted SA [9]+mwf PA proposed SA+mwf PA
Figure 3.8: Average achievable rate ratio for the rate failure event v.s. user number; 3 relay nodes and 32 subcarriers with PT = 3.2 and the minimum user rate requirement is 48 bits/2 OFDM symbols.
4 5 6 7 8 9 10 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
user number
probability of load balancing
Figure 3.9: Load balance probability v.s. user number; 3 relay nodes and 32 subcarriers with PT = 3.2 and the minimum user rate requirement is 48 bits/2 OFDM symbols.
10 15 20 25 30 35 40 45 50
1870 1880 1890 1900 1910 1920 1930 1940
user rate constrain(bits/2 OFDM symbols)
sum capacity(bits/2 OFDM symbols) greedy SA[8]+equal PA
greedy SA[8]+mwf PA weighted SA[9]+equal PA.
weighted SA[9]+mwf PA proposed SA+equal PA proposed SA+mwf PA
Figure 3.10: Sum rate v.s. user rate constraint; 8 DNs, 3 RNs and 128 subcarriers with PT = 12.8.
10 15 20 25 30 35 40 45 50 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
user rate constrain(bits/2 OFDM symbols)
required rate failure probability
greedy SA[8]+mwf PA weighted SA[9]+mwf PA proposed SA+mwf PA
Figure 3.11: Rate failure probability v.s. user rate constraint;8 DNs, 3 RNs and 128 subcarriers with PT = 12.8.
4 5 6 7 8 9 10
1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980
user number
sum capacity(bits/2 OFDM symbols)
greedy SA[8]+equal PA greedy SA[8]+mwf PA weighted SA[9]+equal PA.
weighted SA[9]+mwf PA proposed SA+equal PA proposed SA+mwf PA
Figure 3.12: Sum rate v.s. user number; 3 relay nodes and 128 subcarriers with PT = 12.8 and the minimum user rate requirement is 48 bits/2 OFDM symbols.
4 5 6 7 8 9 10 0
0.02 0.04 0.06 0.08 0.1 0.12
user number
required rate failure probability
greedy SA[8]+mwf PA weighted SA[9]+mwf PA proposed SA+mwf PA
Figure 3.13: Rate failure probability v.s. user number; 3 relay nodes and 128 subcarriers with PT = 12.8 and the minimum user rate requirement is 48 bits/2 OFDM symbols.
Chapter 4
Downlink Resource/Relay
Allocation for MIMO OFDMA Networks
In this chapter, we consider the scenario for a downlink input multiple-output OFDMA system. We also use the capacity lower bound and propose resource allocation schemes that assigns power, subcarriers and cooperative relays to each mobile station. However, we propose not only suboptimal power allocation but the optimal one.
Figure 4.1: MIMO system model
Figure 4.2: One cooperative path in Fig.4.1
4.1 System Model and Basic Assumptions
As shown in Fig. 4.1 and Fig. 4.2, we consider the downlink of an N-subcarrier OFDMA cooperative network which contains a BS, M fixed relay nodes, and K MS’s equipped with Ns, Nr and Nd antennas, respectively. We also consider the decode-and-forward (DF) cooperative relay scheme and assume a two-phase (time-slot) transmission scheme with perfect timing synchronization among all network users. Perfect decoding at the relays is assumed. Each subcarrier suffers from slow flat Rayleigh fading and there is no change of the channel state during a two-phase period. A data stream from a source user must be carried by the same subcarrier no matter it is transmitted by a source node or a relay node. However, we do not employ the maximum-ratio-combining detector for this MIMO system for simplification.
We also assume the mobile user estimate the channel information by MMSE estima-tor and the feedback of the estimate is instantaneous and perfect to the BS, then the same channel information about the channel gain with an estimation error is available simultaneously to both the transmitter and the receiver. In this chapter, the BS also acts as a central control device to allocate resources based on the imperfect CSI from all users and the minimum rate requirement of each MS.