With the continued evolution of wireless communication technology, relaying is one of the features proposed for the 4G LTE Advanced (LTEA) system. The aim of relaying is to enhance both coverage and capacity. The idea of relays is not new, but relaying is being considered to ensure that the optimum performance is achieved to enable the expectations or good quality of service (QoS) of the users to be met while still keeping capital expenditure (CAPEX) within the budgeted bounds of operators. In this paper, we try to stand for an operator to propose a solution that determines where and how many relays should be deployed in the planning stages to minimize the development cost. In the planning stages, we not only derive a multicast tree routing algorithm to both determine and fulfill the QoS requirements to enhance throughput, but we also utilize the Lagrangian relaxation (LR) method in conjunction with optimizationbased heuristics and conduct computational experiments to evaluate the performance. Our contribution is utilizing the LR method to propose an optimal solution to minimize the CAPEX of operators to build up a relay network with more efficiency and effectiveness and the QoS can be guaranteed by service level agreement.
Providing a guaranteed service and good performance with budgets constraint is always an optimization problem of operators and vendors. During the last decade, this problem has however become much more difficult, because the traffic has grown significantly and demand for broadband data services is expected to increase tremendously [
In the ongoing standardization technology development by thirdGeneration Partnership Project (3GPP), relaying is one of the features proposed for the LTE Advanced (LTEA) system [
In order for the cellular telecommunications technology to be able to keep pace with technologies that may compete, it is necessary to ensure that new cellular technologies are being formulated and developed. But there are many realistic conditions influencing operators including the tough economic environment, declining budgets, limited resources, time pressures, and high user expectations.
This paper proposes a solution approach for relay network planning of where to build relays, and how to configure each relay, how the routing algorithm of relays and mobile stations is worked properly. This research can be divided into two parts. First, we constructed the relay network architecture with multicast tree routing concepts. Secondly, we proposed a precise mathematical expression to model this network and developed algorithms based on Lagrangian Relaxation Method to solve this problem. These model approaches might nevertheless be regarded as useful engineering guidelines for operators to build up a good network to extend services and reduce CAPEX efficiently and effectively.
This paper is organized as follows. Section
Multihop Wireless Networking has been widely studied and implemented throughout ad hoc networks and mesh networks to exploit the user diversity concept and improve overall performance. The original concept of general relaying problems was defined in [
Relay stations (RSs) have some characteristics or cost efficiency for the following reasons.
The transmission range is much less than a BS, meaning that the transmit power is also less than that of a BS. Relays are generally cheaper than BS, meaning reduced costs without site survey and easy to construct relays in the place which is not suitable to build a base station tower.
Relays do not have a wired connection to the backhaul. Instead, they receive signals from the BS and retransmit to destination users wirelessly and vice versa. The leases of wired broadband backhauls can be saved.
Relaying techniques have the dual advantages of performance improvement and coverage extension at the cell edge. These could feasibly be a deployment solution for the highfrequency band in which propagation is significantly more vulnerable to nonlineofsight (NLOS) conditions to overcome shadowing [
Coordinated multipoint (CoMP) is a relatively new class of spatial diversity techniques that are enabled by relaying [
Coordinated multipoint.
CoMP is a complex set of techniques which are distributed radios that jointly transmit information in wireless environments. The main purpose may be improved for the reliability of communications in terms of coverage extension, reduced outage probability, symbolerror, or biterror probability for a given transmission rate [
It makes better utilization of network: by providing connections to several BSs or RSs at once, using CoMP, data can be passed through least loaded BS or RS for better resource utilization.
It provides enhanced reception performance: using several sources cooperative BSs or RSs for each connection means that overall reception will be improved and the number of dropped calls should be reduced.
Multiple site reception increases received power: the joint reception from multiple BSs or RSs using CoMP techniques enables the overall received power at the handset to be increased.
When building a relay wireless network in a metropolis, various factors influence the design such as QoS requirements, throughput requirements, and total cost. The objective of our research is “to minimize the total building costs subject to QoS and throughput requirements.” Nonetheless, this objective is obviously a tradeoff because total building costs will increase if the QoS and throughput requirements increase. Based on this conventional tradeoff, we take multipath routing algorithms into consideration to solve the critical problem [
The purpose of this research is different from that of conventional network design problems. The assumptions are that multiple source nodes jointly transmit one single source of information if the signal strength is not robust enough in the link between one source node to the destination. The routing policy is no longer a single path but a more complex and interesting multipath algorithms.
A sequence of the wireless relay network design may be described as fellows. First, the location of each BS could be determined by site survey and how many BSs can cover the service area. Second, the set of BSs roughly divide the entire network into several subnetworks, each of which is rooted by one BS connected to the core network which is shown in Figure
Network separations with several BSs.
Figure
One OD pair routing multicast tree in DL transmission.
One OD pair routing multicast tree in UL transmission.
The relaying protocol in this model is
Once a location is selected to build an RS, it must home to one BS.
Each MS must home to either a BS or RS(s).
The RSs selected by an MS must associate with the same BS.
The routing path of each OD pair in DL (UL) is a multicast tree.
The capacity of a link
The spatial diversity gains are represented by the aggregate SNR with CoMP techniques.
The bit error rate (BER) of a transmission is measured by the receiving SNR value
The aggregate BER of the destination is the summation of BER of each node on the routing multicast tree.
The numbers of links of each path adopted by each MS are assumed to be equal to ensure that the CoMP can be achieved within limited delay.
Error corrections and retransmissions are not considered in this problem.
The set of BSs, candidate locations and configurations of RSs, MSs,
required data rate of an MS in DL and UL,
fixed and configured cost of an RS,
the set of all spanning trees, paths,
distance of each link,
attenuation factor,
thermal noise function,
transmit power of BS, RS, and MS,
sNR function,
the minimum SNR requirement for an MS in DL and UL to home to a BS or an RS,
the maximum BER threshold of a OD pair transmission in DL and UL,
nodal and link capacity functions,
the maximum spatial diversity of an MS in DL and UL.
RS selection constraints,
nodal capacity constraints,
cooperative relaying constraints in DL and UL,
routing constraints in DL and UL,
link capacity constraints in DL and UL.
Whether or not a location should be selected to build an RS,
the cooperative RSs of each MS,
the routing paths of an OD pair (a BS to an MS or contrary), which form a multicast tree from the BS to the cooperative RSs selected by each MS.
Notations of given parameters.
Given parameters  

Notation  Description 
General  

The set of transmission direction, where 

The set of BSs, where 

The set of RS candidate locations, where 

The set of RS configurations, where 

The set of MCs, where 

The data rate required to be transmitted of MC 

The fix cost of building an RS on location 

The configured cost of building RS 

An arbitrarily large number 
 
Routing  

The set of paths from BS 

The indicator function which is 1 if link 
 
SNR and attenuation  

The distance of link 

Attenuation factor 

Transmit power of RS 

Thermal noise strength function in dBm/Hz, where 

Transmit power of BS 

Transmit power of MC 

Signal strength received by node 

The minimum SNR requirement for a MC to receive from a RS in DL 

The minimum SNR requirement for a RS to receive from a MC in UL 

The maximum SNR can be received by node 

The maximum SNR can be received by node 
 
BER  

The BER requirement for the transmission received by a destination in direction 

The BER value of each node 
 
Capacity  

The nodal capacity of BS 

The nodal capacity of RS 

The capacity of link 
 
Relaying  

The maximum spatial diversity of a MC in direction 
Notations of decision variables.
Notation  Description 

Decision variables  

1 if candidate location 

1 if RS 

1 if node 

1 if link 

1 if path 
 
Auxiliary variables  

The SNR received by node 

The SNR received by node 

The summation of SNR received by MC 

The summation of SNR received by node 
Constraint (
Constraint (
Constraint (
An MC must select either one BS or RS(s) in direction
Constraints (
The minimum SNR constraints for an MC to receive from a BS or an RS in DL, and for an MC to transmit to a BS or an RS in UL, are expressed in (
Constraint (
Constraint (
Once MC
The minimum SNR constraint for a link
Constraint (
Constraint (
Once MC
The aggregative BERs constraints for DL in MC and UL in BS are expressed in (
Constraint (
Constraint (
There are two constructions in (
For each MC, every receiving RS
Constraint (
By applying the Lagrangian Relaxation (LR) Method and the Subgradient Method to solve the complex problem, based on the problem formulation mentioned previously, the first step would be that the constraints of the primal problem are relaxed by using the LR Method [
To obtain the primal feasible solutions for
The main purpose of determining the primal feasible heuristic is, in both DL and UL directions, and for each MS sorted by the distance to BS, to fully utilize the RSs built already to meet the BER requirement, and if not, to at least minimize the number of RSs necessary to reach the previous goal. The detailed procedure that decomposites the Lagrangian Relaxation Problem into several subproblems is described in the appendix.
In this session, we conduct several computational experiments to justify the proposed algorithms. Due to limitation of available experiment scenarios and parameters, we focus on IEEE 802.16j instead of LTEA; it is easier to build the network based on realistic and operable environment parameters. In order to effectively analyze the physical operations of an 802.16j network, Table
System parameters [
Parameters  Value 

Operation frequency  2500 MHz 
Channel bandwidth  10 MHz 
BS antenna gain  15 dBi 
RS basic antenna gain  5 dBi 
MS antenna gain  −1 dBi 
BS noise figure  4 dB 
RS noise figure  5 dB 
MS noise figure  7 dB 
BS transmit power  43 dBm 
RS basic transmit power  33 dBm 
MS transmit power  23 dBm 
RS config, set  3 
Attenuation factor  3.2 
Thermal noise figure  −174 dB 
Min. RS to RS SNR  7.9515 dB 
Min. SNR received by MS  2.6505 dB 
BER threshold  0.0001 
Max. spatial diversity  3 
Traffic required by MS (DL)  1 Mbps 
Traffic required by MS (UL)  0.5 Mbps 
BS capacity  100 Mbps 
RS basic capacity  15 Mbps 
RS fix cost  1 M dollars 
RS config. cost  0.2 M dollars 
Modulation and code rate [
Modulation  Code rate  SNR  DL rate (Mbps)  UL rate (Mbps) 

QPSK  1/2 CTC  SNR

6.34  4.70 
QPSK  3/4 CTC  9.4 < SNR 
9.50  7.06 
16 QAM  1/2 CTC  11.2 < SNR 
12.67  9.41 
16 QAM  3/4 CTC  16.4 < SNR 
19.01  14.11 
64 QAM  2/3 CTC  18.2 < SNR 
25.34  18.82 
64 QAM  3/4 CTC  22.7 < SNR  28.51  21.17 
In the meantime, and for the purpose of evaluating our solution of quality, two simple algorithms, minimum BER algorithm (MBA) and densitybased algorithm (DBA), are implemented for comparison. The purpose of each MBA is, for each MS
In this research, the SNR function we apply is listed as follows:
The BER evaluation functions we apply have been moderated with various modulation schemes [
For the unique characteristics of this network deployment problem, the given circumstances are BS and MS locations, but RSs would be candidate locations. There is no RS built at the beginning. The word “topology” introduced in the following refers to the geographic distribution (the position) of locations where an RS could be built. Two types of topologies, grid and random, are proposed with different numbers of RS and MS in one BS environment to analyze the impact on deployment cost. We then apply different numbers of RS and MS with two BSs in a random topology to analyze the deployment in multiple BSs environment. Table
Experiment scenarios.
Topology  Network scale  No. of BS  No. of RS  No. of MS 

Grid  3.2 km  1  8, 24, 48  20, 30, 40, 50 
Grid  6.4 km  1  24, 48  20, 30, 40, 50 
Grid  9.6 km  1  80  20 
Random  3.2 km  1  8, 24, 48  20, 30, 40, 50 
Random  6.4 km  2  16, 48  40, 60, 80 
Grid topology example.
Random topology example.
In Lagrangian relaxation approach, an upper bound (UB) of the problem, is the best primal feasible solution, while the solution to the Lagrangian dual problem guarantees the lower bound (LB) of the problem. By solving the Lagrangian dual problem iteratively and getting a primal feasible solution, we derive the LB and the UB, respectively. Thus, the gap between the UB and LB, computed by (UB − LB)/LB × 100%, illustrates the quality (optimality) of the problem solution.
Figure
Algorithm comparison (1 BS, grid, 3.2 km).
No. of RS  No. of MC  LB  UB  GAP (%)  MBA  Imp. ratio of MBA (%)  DBA  Imp. ratio of DBA (%) 

8  20  901.7678  920  1.98176  960 

960 

8  30  1020.242  1060  3.750792  1280 

1120 

8  40  1258.947  1280  1.644797  1280 

1280 

8  50  1260.484  1280  1.524727  1280 

1280 

24  20  1156.286  1280  9.665148  1600 

1440 

24  30  1164.774  1280  9.002031  1920 

1600 

24  40  1208.743  1320  8.428545  2080 

1920 

24  50  1269.846  1440  11.81623  2400 

2080 

48  20  860.6118  880  2.203205  1760 

1120 

48  30  921.4716  960  4.013375  2240 

1220 

48  40  1082.548  1220  11.2666  2240 

1480 

48  50  1098.812  1260  12.79272  2560 

1640 

Deployment cost with different number of RS and MS (1 BS, grid, 3.2 km).
In RS grid topology, for a given network scale, the distance of RS is the farthest locations from BS to receive signals under BER threshold should be included mandatorily. This phenomenon can be observed in Figures
Deployment cost with different number of RS (1 BS, grid, 3.2 km).
Deployment cost with different number of MS (1 BS, grid, 3.2 km).
From Figures
Deployment cost with different number of RS and MS (1 BS, random, 3.2 km).
Deployment cost with different number of RS (1 BS, random, 3.2 km).
Figure
Algorithm comparison (1 BS, random, 3.2 km).
No. of RS  No. of MC  LB  UB  GAP (%)  MBA  Imp. ratio of MBA (%)  DBA  Imp. ratio of DBA (%) 

8  20  867.3459  900  3.628233  960 

960 

8  30  850.3321  900  5.518652  960 

960 

8  40  846.2536  900  5.971822  1120 

960 

8  50  909.7847  980  7.164823  1280 

1020 

24  20  811.1707  860  5.67783  1600 

960 

24  30  798.1251  860  7.19476  1920 

1020 

24  40  805.3412  900  10.51765  2080 

1020 

24  50  860.9539  980  12.14756  2400 

1340 

48  20  734.8455  820  10.3847  1760 

1020 

48  30  766.4685  860  10.87563  1820 

1080 

48  40  744.6947  880  15.3756  2260 

1140 

48  50  768.6480  920  16.4513  2420 

1260 

Figures
Deployment cost with different number of MS (1 BS, random, 3.2 km).
In random topology, it is difficult to generate a network capable of satisfying every MS’s transmission when a few RSs (ex. RS = 8) are deployed. In general, RSs are not distributed uniformly enough to fully cover all MSs. Figure
Algorithm comparison (2 BSs, random, 6.4 km).
No. of RS  No. of MC  LB  UB  GAP (%)  MBA  Imp. ratio of MBA (%)  DBA  Imp. ratio of DBA (%) 

16  40  1542.505  1620  4.78362  1760 

1680 

16  60  1726.22  1840  6.18371  2240 

1840 

16  80  1737.373  1920  9.5118  2400 

2020 

48  40  1409.38  1540  8.48179  3040 

1760 

48  60  1533.7687  1720  10.8274  3360 

1940 

48  80  1550.1775  1820  14.82541  3840 

2280 

Deployment cost with different number of BS in random topology.
If these scenarios experimented previously are double the size of those in which BS = 1, how the result is. With random topology in BS = 1, it is also difficult to get a feasible network when RS number is small (ex. RS = 16 here). Figure
Figure
Experiment results (1 BS, grid, 6.4 km).
No. of RS  No. of MC  LB  UB  GAP (%)  MBA  Imp. ratio of MBA (%)  DBA  Imp. ratio of DBA (%) 

8  20  N/A  N/A  N/A  N/A 

N/A 

8  30  N/A  N/A  N/A  N/A 

N/A 

8  40  N/A  N/A  N/A  N/A 

N/A 

8  50  N/A  N/A  N/A  N/A 

N/A 

24  20  2155.106  2340  7.901457  2720 

2420 

24  30  2212.838  2480  10.77267  3520 

2840 

24  40  2469.994  2820  12.41156  4800 

3360 

24  50  2699.765  3440  21.51847  5440 

4480 

48  20  1537.11  1700  9.581763  2880 

1960 

48  30  2059.57  2320  11.22543  4480 

2640 

48  40  2309.617  2720  15.08761  5600 

3480 

48  50  2445.661  3280  25.43715  6240 

4880 

Deployment cost with different number of RS and MS (1 BS, gird, 6.4 km).
Figure
Deployment cost and lower bound (LB) values in different network scales (1 BS, grid, 20 MSs).
With 3G technology established, it was obvious that the traffic is increased significantly, but the average revenue per user (ARPU) is decreased very fast. The business challenges of operators would be that increasing revenues by finding other solutions more efficiency and effectiveness. But the network development of a new 4G system started to be investigated and made huge investments of macro base station deployments. In one early investigation which took relays would be able to speed up extend services and expanded market share at this stage economically. So, the operators can make new revenues and cost reduction balance.
Although our experiments do not cover large network scales with large number of RSs and MSs for the restrictions of computational capabilities, these model approaches can nevertheless be regarded as useful engineering guidelines for future LTEA relay network development.
In this paper, we stand for an operator to propose a solution that determines where and how many relays should be deployed in the planning stages to minimize the development cost. In the planning stages, we not only derive a Multicast Tree routing algorithm to both determine and fulfill the QoS requirements and also enhance throughput on both downlink and uplink communications, but we also utilize the Lagrangian Relaxation Method in conjunction with optimizationbased heuristics and conduct computational experiments to evaluate the performance of the proposed algorithms.
Our contributions in this research can be divided into three parts. First, we have constructed the network architecture with multicast tree routing concepts. Secondly, we proposed a precise mathematical expression to model the network architecture problem. This is not an intuitive mathematical model for considering the solvability of this problem. We have designed the entire model not only to be solvable but also to not violate the physical meanings. Finally, we provide the lagrangian relaxation and optimizationBased algorithms to solve this problem; we prove it to have superior quality after verification with other simple algorithms and lower bound value. This optimal solution is a good strategic method to minimize the CAPEX of operators to build up a relay network with more efficiency and effectiveness and the QoS can be guaranteed.
Because the configuration of BS is constant,
For each
Equation
For each
Equation
The two directions of DL and UL are independent;
The algorithm to optimally solve
Use SNR function to calculate the SNR value
Find the BS
Examining all sets of configuration for each RS in the SNR function to determine the SNR value
If the coefficient of
Equation
Similar to
Equation
The algorithm to optimally solve
Examining all sets of configuration for each source node
For each MC
For
We can calculate the value of
In the same situation like Subproblem 7, we introduced constraint (
Similar to
Let the vector
It is hereby asserted that all the coauthors of this paper do not have any personal or financial interest with any model or system used in this paper.