Chapter 1 Introduction
2.6 Summary
In Chapter 2, the optimization and theoretical performance of relay-assisted cellular networks have been investigated in the multi-cell environment. A GA is proposed for joint multi-cell optimization of system parameters, including RS’s positions, path selection, frequency reuse pattern, and resource allocation, to maximize system SE. Four different system configurations are considered, including FBA-SE (fixed-bandwidth allocation with SE-based path selection), FBA-SINR (fixed-bandwidth allocation with SINR-based path selection), FTA-SE (fixed-throughput allocation with SE-based path selection) and FTA-SINR (fixed throughput allocation with SINR-based path selection). Numerical results show that (i) RSs provide significant improvement with respect to system SE and user throughput over the traditional cellular networks. (ii) The uniformity of user data rate comes at the expense of a large loss in system SE when FTA is employed. (iii) Somewhat surprising, the low-complexity SINR-based path selection performs nearly as well as the SE-based one for the no-reuse case, while it is slightly better in the frequency reuse case.
Chapter 3
Uplink Performance and Optimization of Relay-assisted Cellular Networks
In this chapter, we aim to investigate the uplink performance of a general relay-assisted cellular system with optimal system parameters. Two performance measures, average power consumption of MSs and uplink system spectral efficiency (SE), are optimized by jointly considering the system parameters of RSs’ locations, reuse patterns, path selections and resource allocation. The optimization is done based on a genetic algorithm (GA) and a method for multiple access interference (MAI) estimation. Numerical results show that the average MS’s transmit power is significantly reduced and the uplink system SE is largely enhanced as RSs are deployed and used in the optimal way. The background, the system setups, the objective functions, the proposed optimization algorithm, and the numerical results are presented in the following subsections.
3.1 Background
There have been few studies on the uplink performance of the relay-assisted cellular systems [25], [38], [68]. In [25], the issues of capacity, cell coverage, and MS transmit power were considered in a relay-assisted CDMA network with six RSs under different frequency allocation methods. In [38], the issues of RS positioning and spectrum partitioning were studied by searching optimal RSs locations along the lines connecting BS and the six vertices of a hexagonal cell to maximize the mean user data rate. In [68], the uplink capacity of an 802.16j system was discussed, where a simplified one-dimensional model is analyzed for the maximal capacity gains, and fixed number of RSs with uniform placement is also simulated.
These studies, however, have been done for very limited system scenarios: fixed number RSs and locations, fixed reuse pattern, or seeking optimal RSs’ positions with a simplified one-dimensional model.
In this dissertation, two important uplink performance measures, average MS’s power consumption and uplink system SE, have been optimized for a general relay-assisted cellular system.
3.2 System Setups
For the uplink performance evaluation, the system parameters and setups are mostly similar to those in Section 2.2. Slight differences are highlighted as follows. For the cell configuration, the system parameters are adopted as described in Section 2.2.1, except that the single cell structure in the uplink evaluation is taken into consideration. In the uplink, MS
RSs and MSs) are equipped with an omni-directional antenna and one RF transceiver. For the PSD setting of an RS, the same setting as (2.8) is applied and we assume that RSs use the same power level (PSD) to communicate with BS in the reverse link. For the relaying technology, the propagation models, and the frequency reuse adopted in this chapter, please refer to Section 2.2.2, 2.2.3, 2.2.5, 2.2.7, respectively. With regard to the uplink path selection, different criteria will be mentioned in Section 3.3 in terms of different objectives.
3.3 Problem Formulation
In the uplink, in addition to the system SE, MSs’ power consumption is also an important performance measure due to the limited battery life. In this section, given a fixed amount of bandwidth for each MS, two system performance measures are investigated: one is to minimize the average MS’s transmit power for a specified throughput; the other is to maximize the uplink SE by given a fixed MS’s transmit power, by jointly searching optimal RSs’ positions, reuse pattern, path selection and bandwidth allocation.
Let wu (Hz per unit area) be the uplink bandwidth allocated to an MS at locationm
1
a targeted throughput Tu.
Derived by (3.1) and (3.4), the MS’s transmit power for a direct path is given by
( ) (2 1) ( ) ( 0 ) .
. As a result, the bandwidth allocation for each hop is given by
( ) , transmit power to RS can be expressed as
( )
. Finally, the objective function is given
min PM avg, (3.11)
3.3.2 Measure 2—Maximization of Uplink System SE
In this subsection, given a fixed among of uplink bandwidth wu and a fixed transmit power PM of each MS, the system SE will be maximized.
For a direct-path, the throughput is
1
gives the highest SE. Therefore, when
( )
( ) ( ) equation for the optimal ( )
M Rj
The optimal path selection is then to select the direct path if ( ) ( )
M B M Rj B system bandwidth consumption, respectively. The objective function is then expressed by
max u (bps/Hz)
1
3.4 Genetic-Based Optimization
It is observed that (3.11) and (3.20) are highly nonlinear functions for RSs’ positions and the reuse pattern G so that the analytic solutions are not available in general. To solve these problems, a particular design of GA based optimization and an MAI estimation method for uplink are proposed. For the GA operation, the detailed concept is described in Section 2.4.1.
For the manipulation for uplink optimization, similar ideas from downlink optimization are adopted and please refer to Section 2.4.2. Besides, in the uplink, when applying intra-cell frequency reuse among the MS to RS links, MAI estimation is important since the exact locations of interferer are usually unknown to the MS. The design of MAI estimation algorithm is detailed in Section 3.4.1. The overall flowchart of GA operation and the MAI estimation is illustrated in Figure 17.
Figure 17. The operation of genetic algorithm.
3.4.1 MAI Estimation Algorithm
An MAI estimation algorithm, shown in Figure 17, is proposed to determine the MAI level when the frequency is reused over the MS-RS links.
First, MS chooses the nearest BS or RS as its serving station so that the ΩB and ΩRj are predetermined. Given an MS served by the k-th RS in the reuse group l, i.e.,
Rkl
m ∈Ω
,
the MAI for this MS is caused by the co-channel user in Gl. We calculate the MAI level for the MS by averaging over the potential interfering area, which is expressed by
1 ( ) ( )
Substituting (3.2) into (3.1), the average MAI level for the MS is obtained. Then, the transmit power of m
MS can decide its new serving station by choosing minimal transmit power among direct path and two-hop path. Then, ΩB and ΩR are re-determined.
In Measure 2, ( )
I i
M R I M
P → m =P
, and the throughput for two-hop path can be determined
by following the process (3.21) to (3.29). Again, MS can decide its new serving station by choosing maximization throughput among the direct path and the two-hop path so that ΩB and ΩR can be are re-decided.
The procedure is repeated until the service area is converged or the maximum iteration number is reached.
3.5 Simulation Results
In our numerical results, the cell radius is set as 1400 m, the cell region is divided into grids with each side equal to 20 m, and the locations of all stations (BS, RSs, and MS) are rounded off to the nearest grid vertices. Let Sedge be 0.5 bps/Hz for PSD setup of RSs. In
the GA operation, Npop= 200,
β
= 0.5 and Pmut = 0.05 are adopted. The Gaussian variable with variance equal to a grid length is used as the perturbation when performing crossover operations. Through the work, wu= 28.5 KHz per unit area is allocated to MS.Newton’s method is adopted to solve the nonlinear equation mentioned in (3.17) to (3.19).
Besides, the inter-cell interference is assumed to be constant and embedded into the thermal noise, while the effect of intra-cell interference caused by frequency reuse over MS-RS links is evaluated in our simulations. Note that the number of generations (iterations) in GA depends on the number of RSs involved; more generations are needed for a larger number of RSs.
3.5.1 Measure 1—Minimization of Average MS’s Transmit Power
frequency reuse among MS-RS links. Figure 18 shows the optimal RSs placement and the distribution of transmit power consumption (in dBm). Figure 18 (a) is the case for no RS (N =0). Clearly, more transmit power is needed for a more distant MS. The average transmit power is 14.54 dBm, which is summarized in Table 4. Figure 18 (b) is for the case of N =2. The optimal RSs positions are in ( 660, 0)± . The service area of BS and RSs is indicated by the black lines, where BS serves 31% of total area while two RSs serve the other 69%. The average transmit power is 10.75 dBm in this case, which is 3.79 dB lower than that of no RS case. Figure 18 (c) shows the case of four RSs, where the area served by RSs is 86% and the average transmit power is 3.18 dBm; gains of 11.36 dB and 7.57 dB as compared to N =0 and N =2, respectively. Figure 18 (d) is the case of 6 RSs. As can be seen, the optimal RSs positions are on the lines connecting the cell center and six vertices of the hexagonal cell with distance 900m from the BS, and the whole area is almost evenly partitioned by the BS and six RSs, where each station serves about 14% of total area. The average transmit power is -2.05 dBm, which is reduced 16.59 dB as compared to N =0. It is clear that if the RS-BS link was perfect in the two-hop path, the service area border of the BS and RSs would be in the perpendicular bisection of the line segment connecting the BS and RSs. Table 4 summarizes the service area ratio of the BS and RSs, bandwidth allocation ratio for MS-BS links, MS-RS links, and RS-BS links, and the average uplink transmit power for N =0 to N =10. Figure 19 depicts the complementary cumulative distribution functions (CDFs) of MS’s power consumptions. As can be seen, the percentage of large power consumption area is significantly reduced with the help from RSs.
Table 4. System parameters of Measure 1 for N = 0 to N = 10.
N Ω ΩB: R (%) wM→B:wM→R:wR→B (%) PM avg, (dBm)
0 100:0 100:0:0 14.54
2 31:69 31:65:4 10.75
4 14:86 14:80:6 3.18
6 14:86 14:80:6 -2.05
8 14:86 14:79:7 -3.75
10 11:89 11:82:7 -5.07
(a) N = 0 (b) N = 2
(c) N = 4 (d) N = 6
Figure 18. Optimal RSs’ positions and uplink transmit power distribution (in dBm).
Figure 19. Complement CDFs of uplink transmit power.
In this subsection, frequency reuse over the MS-RS links is explored to further utilize the radio resource. The case of N =6 is taken as an example. Figure 20 (a) to (d) depicts the optimal RSs’ locations and the distribution of power consumptions for the following reuse patterns, G={G , G , G , G , G , G } , 1 2 3 4 5 6 G={G , G , G } , 1 2 3 G={G , G } and 1 2
G={G } , respectively. Note that each reuse group has equal number of RSs. As can be seen, 1
RSs are placed on the line connecting the cell center to six vertices of the cell in each case with RSs in the same reuse group being pulled as far apart as possible. Table 5 provides more detailed parameters of all cases. The uplink system SE is getting better when the frequency is more aggressively reused (i.e., G={G } ); however, it costs more transmit 1 power to achieve the same targeted throughput due to larger MAI.
A simplified shadowing model is also given to verify the effectiveness of the deployment of RSs. Two obstacles of length 800 m are centered at (690, 0) and (-690, 0).
The shadow loss δ ====10 dB is adopted if the line of sight of MS and BS is blocked by any obstacle. In Figure 21 (a), MS in the shadowed area needs very high transmit power level to achieve the targeted throughput Tu =14.25 Kbps, as one might expect. The average MS’s transmit power is 20.47 dBm in this case. Figure 21 (b) shows the case with two RSs deployed into the cell. The optimization algorithm suggests that the RSs should be placed at (700, -420) and (-700, 420) to reduce the percentage of blocked line of sight between an MS and its serving station (BS or RS). Black lines circle the service area of each RS. As can be seen, the ratio of MSs in the shadowed area is significantly decreased, except the case that a few MSs which are close to RS still have smaller propagation loss to RS than that to BS even if they suffer from shadowing loss to connect to RS. The average MS’s transmit power is reduced to 10.89 dBm, which saves 9.58 dB in average as compared to Figure 21 (a).
From this example, the shadowing effects can be largely removed by deploying RSs.
(a) G={G1, G2, G3, G4, G5, G6} (b) G={G1, G2, G3}
(c) G={G1, G2} (d) G={G1}
Figure 20. Transmit power distributions (in dBm) of different frequency-reuse patterns.
Table 5. System parameters for different frequency-reuse patterns of Scenario 1, N = 6.
G Ω ΩB: R
(%)
: :
M B M R R B
w → w → w → (%)
Avg. P M (dBm)
SΩ
(bps/Hz)
1 2 3 4 5 6
{G , G , G , G , G , G } 14:86 14:80:6 -2.05 0.5
1 2 3
{G , G , G } 14:86 23:66:11 -2.03 0.83
1 2
{G , G } 14:86 29:57:14 -2.02 1.07
{G } 1 15:85 42:39:19 -1.57 1.46
(a)
(b)
3.5.2 Measure 2—Maximization of Uplink System SE
In this section, given a fixed MS uplink transmit power, the system SE improvement offered by RSs is studied. Recall that the allocated uplink bandwidth to MS wu is set as
28.5 kHz/m2. There is no frequency reuse among MS-RS links.
First, we look at the case of PM =15 dBm. Figure 22 describes the ideas of optimal RSs positions and the uplink throughput distribution of each location. Figure 22 (a) is for
0
N = , where the link SE decreases as the MS to BS distance increases. The system SE is 1.58 bps/Hz. Figure 22 (b) is the case of N =2. The optimal RS positions are at ( 700, 0)± . With the help of the RSs, the system SE is improved to be 2.54 bps/Hz, which is 60%
improvement as compared to the case of N =0. Figure 22 (c) shows the case of N =4. The RSs provide service for 86% of total area and the system SE is 3.37 bps/Hz. Figure 22 (d) is for N =6, where the optimal RSs positions are on the line connecting the cell center to the six vertices of the cell with distance 740m from BS. Notice that since the RS-BS link is not perfect, the maximum throughput for two-hop links is limited by the RS-BS link throughput no matter how close the MS and the RS is. Table 6 summarizes the service area ratio, bandwidth partition ratio and the system SE of each case. As the number of the RSs increases, the system SE is enhanced and the service area ratio of the RSs is also raised.
However, since the average service area of each RS is reduced as the increment of deployed RS number, the system efficiency improvement of each additional RS is also narrowed.
Figure 23 shows the CDF of link SE. The low SE area is significantly improved by the RSs.
All lines merge together to the maximum SE 21.41 bps/Hz when the SE is greater than 10.
(a) N = 0 (a) N = 2
(a) N = 4 (a) N = 6
Figure 22. Optimal RSs’ positions and uplink throughput distribution.
Figure 23. CDF of link SE for PM=15 dBm.
Table 6. System parameters of Measure 2 for N = 0 to N = 10.
N Ω ΩB: R (%) wM→B:wM→R:wR→B (%) SΩ (bps/Hz)
0 100:0 100:0:0 1.58
2 36:64 36:49:15 2.54
4 14:86 14:59:27 3.37
6 13:87 13:53:34 3.83
8 12:88 12:51:37 4.02
10 11:89 11:50:39 4.16
Figure 24 summarizes the results of different reuse patterns for N =6 with equal number of RSs in each reuse group. The system SE is getting better if the frequency is more aggressively reused (i.e., G={G } ). With respect to the service area ratio, 1 ΩR tends to be larger in G={G , G , G } and 1 2 3 G={G , G } cases. However, in the case of 1 2 G={G } , 1
ΩR is shrunk due to large MAI.
The simplified shadowing model mentioned in Section 3.5.1 is investigated in this subsection. The shadow loss δ = 10 dB is adopted. MS’s transmit power PM is set as 20 dBm. As can be seen in Figure 24 (a), the throughput (link SE) of the MSs in the shadowed area is relatively low when only served by the BS. On the other hand, with two RSs’ help, as shown in Figure 24 (b), the link SE is significantly improved. The optimal RSs’ positions are at (700, -420) and (-700, 420), where the MSs may have higher probability to avoid blocking by any obstacle to its serving station. Similarly, the link SE of any two-hop link is restricted by the minimal throughput of the MS-RS link and the RS-BS link. Note that the optimal RSs’ locations may highly depend on the topography and other constraints. The example we demonstrate here is to show the feasibility of the proposed method in the shadowed environment.
(a)
(b)
Figure 24. Optimal RSs’ positions and uplink SE distribution (bps/Hz) in shadowed
Table 7. System parameters for different frequency-reuse patterns of Measure 2, N = 6.
G Ω ΩB: R (%) wM→B :wM→R:wR→B (%) SΩ (bps/Hz)
1 2 3 4 5 6
{G , G , G , G , G , G } 13:87 13:53:34 3.83
1 2 3
{G , G , G } 10:90 14:44:42 5.31
1 2
{G , G } 9:91 16:39:45 6.08
{G } 1 13:87 31:27:42 6.23
3.6 Summary
In this work, the uplink performance of relay-assisted cellular networks is investigated with optimized system parameters. The optimal RSs’ positions, reuse pattern, path selection and bandwidth allocation are searched to achieve two goals: one is to minimize the MS’s average transmit power to achieve a specified throughput, and the other is to maximize the uplink system SE by given a fixed MS transmit power. The advance formulation of each objective function is contributed. The GA approach along with a multiple access interference estimation method designed for uplink performance evaluations are adopted to resolve the issues. The numerical results conclude that given a fixed allocated bandwidth to each MS, the average MS’s transmit power is significantly reduced for a targeted throughput, and the user throughput as well as the system SE are largely enhanced for a fixed uplink transmit power with the assistance of RSs as compared to the conventional cellular system.
Chapter 4
Resource Scheduling with Directional
Antennas for Multi-hop Relay Networks in a Manhattan-like Environment
Multi-hop relay (MR) networks have been proposed for user throughput improvement, coverage extension and/or system capacity enhancement to the traditional mobile cellular networks. In particular, an MR network has been adopted by the IEEE 802.16j Task Group as an amendment to the IEEE 802.16e standard. This chapter investigates the issue of resource scheduling for the IEEE 802.16j MR networks in the Manhattan-like environment.
New scheduling methods are proposed for the MR networks with directional antennas equipped at both BSs and RSs. Simulation results show that the system throughput can be dramatically increased by the proposed methods as compared to the system with omni-directional antennas.
4.1 Background
In recent years, more and more research has been devoted to the design of relay-assisted network. In [69], a relay-assisted network was adopted as an amendment to the IEEE 802.16e standard [14], [70] for cell coverage extension, user throughput improvement and/or system capacity enhancement. In [26], [71], [72], a scenario of relay-assisted networks, named Scenario 1, was proposed for the Manhattan-like environment, where four RSs are deployed outside of the BS’s coverage in a cell in order to extend the cell coverage, which is illustrated in Figure 25. In order to achieve frequency reuse factor of 1, the multi-cell setup and the transmission frame structure as illustrated in Figure 26 and Figure 27 are proposed in [72]. Through proper coordination between adjacent cells, when BSs in cell group A serve RSs and MSs in the phase 1, BSs in cell group B keep silence and RSs serve their MSs. Similarly, the BSs in cell group B and the RSs in cell group A become active in phase 2. In addition, by utilizing the spatial isolation which is inherent in the Manhattan-like environment, two relay stations (e.g., RS1 and RS2, or RS3 and RS4) within the same cell can be scheduled to be active simultaneously.
However, as shown in Figure 27, since there are always some inactive BSs in every transmission phase, the radio resource is not fully utilized in this design.
Another relay-assisted network, Scenario 2, was proposed in [27], where RSs are deployed within the service range of the BS for the purpose of user throughput enhancement, which is illustrated in Figure 28. In this design, both the BS and RSs employ omni-directional antennas to serve users and to communicate with each other. Consequently,
The previous research works have been mostly focused on the aspects of coverage extension and end-to-end user-throughput enhancement of a relay-assisted network [26], [27], [71], [72]. In this chapter, we consider the overall system capacity enhancement issue
The previous research works have been mostly focused on the aspects of coverage extension and end-to-end user-throughput enhancement of a relay-assisted network [26], [27], [71], [72]. In this chapter, we consider the overall system capacity enhancement issue