Suboptimal Resource Allocation for
Multi-User MIMO-OFDMA Systems
Tarcisio F. Maciel
Darmstadt, 22nd September 2008
22nd September 2008 | Tariciso F. Maciel
Outline
1. Resource Allocation Problem Overview
2. Suboptimal Resource Allocation Strategies: Single Resource
3. Suboptimal Resource Allocation Strategies: Multiple Resources
4. Conclusions and Outlook
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Outline
1. Resource Allocation Problem Overview
2. Suboptimal Resource Allocation Strategies: Single Resource
3. Suboptimal Resource Allocation Strategies: Multiple Resources
4. Conclusions and Outlook
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Scenario and Optimization Objective
 Frequency Division Multiple Access (FDMA)
Frequency
…
Time
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Scenario and Optimization Objective
Frequency
 Time Division Multiple Access (TDMA)
…
Time
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Scenario and Optimization Objective
Frequency
 Current systems  FDMA/TDMA (e.g., GSM)
…
Time
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Scenario and Optimization Objective
Frequency
 Future mobile radio systems
 High flexibility and high capacity
 Orthogonal Frequency Division Multiple
Access (OFDMA)
 Multiple Input Multiple Output (MIMO) 
Space Division Multiple Access (SDMA)
Objective  Maximize the capacity
of the system
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
Time
7
Resource Allocation Problem Overview
Scenario and Optimization Objective
Frequency
 Future systems
 High flexibility and high capacity
 Orthogonal Frequency Division Multiple
Access (OFDMA)
 Multiple Input Multiple Output (MIMO) 
Space Division Multiple Access (SDMA)
Objective  Maximize the capacity
of the system
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
Time
8
Resource Allocation Problem Overview
Description of Subproblems
SDMA grouping
problem
 Users must be separable in space
 Many possible groups of users
 Finding the group with highest
capacity requires an Exhaustive
Search
Objective  Maximize the capacity
of the system
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Description of Subproblems
SDMA grouping
problem
 Users must be separable in space
 Many possible groups of users
 Finding the group with highest
capacity requires an Exhaustive
Search
Objective  Maximize the capacity
of the system
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Description of Subproblems
SDMA grouping
problem
Precoding problem
 Beamforming done at the base station
 Linear precoding used to compute
precoding vectors and form beams
Objective  Maximize the capacity
of the system
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Description of Subproblems
SDMA grouping
problem
Precoding problem
Power allocation problem
 How should power be allocated to the
different users served by the system
Objective  Maximize the capacity
of the system
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Description of Subproblems
SDMA grouping
problem
Precoding problem
Power allocation problem
 How should power be allocated to the
different users served by the system
Objective  Maximize the capacity
of the system
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Description of Subproblems
SDMA grouping
problem
Resource assignment
problem
Precoding problem
Frequency
Power allocation problem
Objective  Maximize the capacity
of the system
22nd
Resource 2
Resource 1
Time
September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Description of Subproblems
SDMA grouping problem
Resource assignment problem
Precoding problem
Power allocation problem
Joint solution
of the subproblems
Separated solutions
to the subproblems
RA strategy
Optimal 
Suboptimal 
Complexity
Too high 
Low 
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Problem Overview
Description of Subproblems
SDMA grouping problem

SDMA algorithm
Resource assignment problem

Resource assignment algorithm
Precoding problem  Precoding algorithm
Power allocation problem  Power allocation algorithm
Joint solution
of the subproblems
Separated solutions
to the subproblems
RA strategy
Optimal 
Suboptimal 
Complexity
Too high 
Low 
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Strategies

Single-resource case
Multiple-resource case
SDMA algorithm
Resource assignment algorithm
Precoding algorithm
Power allocation algorithm
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Outline
1. Resource Allocation Problem Overview
2. Suboptimal Resource Allocation Strategies: Single Resource
3. Suboptimal Resource Allocation Strategies: Multiple Resources
4. Conclusions and Outlook
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Strategies: Single Resource
Single-resource case
Multiple-resource case
SDMA algorithm
Resource assignment algorithm
• Grouping metric
• Grouping algorithm
Precoding algorithm
Power allocation algorithm
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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SDMA algorithm
Grouping metric
 Group capacity
 Suitable to maximize sum rate, but quite complex
 Convex combination of spatial correlation and channel gains
 Less complex than group capacity
h2 

h1
h2
Spatially uncorrelated
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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SDMA algorithm
Grouping metric
 Group capacity
 Suitable to maximize sum rate, but quite complex
 Convex combination of spatial correlation and channel gains
 Less complex than group capacity
h2 

h1
h2
h1
Spatially uncorrelated
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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SDMA algorithm
Grouping metric
 Group capacity
 Suitable to maximize sum rate, but quite complex
 Convex combination of spatial correlation and channel gains
 Less complex than group capacity
h2 
h1
h2 

h1
h2
h2
h1
Spatially uncorrelated
Spatially correlated
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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SDMA algorithm
Grouping metric
 Group capacity
 Suitable to maximize sum rate, but quite complex
 Convex combination of spatial correlation and channel gains
 Less complex than group capacity
h2 
h1
h2 

h1
h2
h2
h1
Spatially uncorrelated
h1
Spatially correlated
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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SDMA algorithm
Grouping algorithm
1. Exhaustive Search + Group capacity metric  Upper bound
2. Random Grouping
 Lower bound
3. Best Fit
+ Group capacity metric  Benchmark
4. Convex Grouping + Convex comb. spatial correlation & channel gains

Channel gains
Spatial correlation
5. Best Fit
22nd
+ Convex comb. spatial correlation & channel gains
September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems

24
Resource Allocation Strategies: Single Resource
Single-resource case
Multiple-resource case
SDMA algorithm
Resource assignment algorithm
• Grouping metric
• Grouping algorithm
Precoding algorithm
Power allocation algorithm
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Precoding and power allocation algorithms
 Precoding algorithm

Linear Zero-Forcing
 Power allocation algorithm

Water-filling

 Other proposed/investigated algorithms can be found in the written work
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Simulation Parameters
Parameter
Value
System frequency
5 GHz
# of used subcarriers
48 subcarriers organized in 8 resources
Subcarrier spacing
9.77 kHz
Channel model
WINNER channel model, macro-cell urban scenario C2,
Non-Line of Sight
# of antennas at the BS
4 omnidirectional antennas in a uniform linear array
# of users
16 single-antenna users
Average user’s speed
10 km/h
Target SDMA group size
Initially set to 4 users
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Performance of the RA Strategies: Single Resource
3. Benchmark:
Cap.-based Best Fit
1. Upper bound: Cap.-based
Exhaustive Search
4. Proposed Convex
Comb.-based
Convex Grouping
5. Proposed Convex
Comb.-based Best Fit
2. Lower bound: Random Grouping
Single User
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Sequential Removal Algorithm

 Removes users from the SDMA group
 increase the group capacity
 User are removed, e.g., according to
their effective channel gain
 Users with the lowest channel gain
removed first
 Computes group capacity of the
resulting groups
 Keeps the group with the highest
capacity
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Performance of the RA Strategies: Single Resource
Improvement due to the Sequential Removal Algorithm
3. Benchmark:
Cap.-based Best Fit
1. Upper bound: Cap.-based
Exhaustive Search
5. Proposed Convex
Comb.-based Best Fit
2. Lower bound: Random Grouping
4. Proposed Convex
Comb.-based
Convex Grouping
Single User
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Performance of the RA Strategies: Single Resource
Computational complexity

 Benchmark and proposed strategies
 Sum rates close to those achieved through the Exhaustive Search
 But considerably different complexity
1. Upper bound:
Cap.-based
Exhaustive Search
3. Benchmark:
Cap.-based Best Fit
4. Proposed Convex
Comb.-based
Convex Grouping
5. Proposed Convex
Comb.-based Best Fit
2. Lower bound:
Random Grouping
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Outline
1. Resource Allocation Problem Overview
2. Suboptimal Resource Allocation Strategies: Single Resource
3. Suboptimal Resource Allocation Strategies: Multiple Resources
4. Conclusions and Outlook
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Strategies: Single Resource
Single-resource case
SDMA algorithm
Multiple-resource case
Resource assignment algorithm
• Grouping metric
• Priority
• Grouping algorithm
• Assignment algorithm
Precoding algorithm
Power allocation algorithm
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Strategies: Multiple Resources
Assignment Algorithms

1. Assign resources
one-by-one
2. Assign resources
to initial users
3. Assign resources
to SDMA groups
Assign a resource
to an initial user based
on user priorities
Assign resources
to initial users based
on user priorities
Build several
candidate SDMA groups
Build an SDMA group
Build an SDMA group
on each resource
Apply precoding
and power allocation
Apply precoding
and power allocation
Apply precoding
and power allocation
Assign resources to
SDMA groups based
on the user priorities
For capacity maximization  almost same sum rate of the Exhaustive Search
For proportional fairness  better degree of throughput fairness
 small reduction of the sum rate
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Strategies: Multiple Resources
Proportional Fair Priorities
Capacity Maximization
Benchmark: Cap.-based Best Fit
Proportional Fair
3. Assign resources
to SDMA groups
Proposed Convex Comb.-based Best Fit
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Resource Allocation Strategies: Multiple Resources
Throughput Fairness
SNR = 10 dB
1. Assign resources
one-by-one
Capacity
Maximization
Proportional
Fair
3. Assign resources
to SDMA groups
Proposed Strategy 2:
Convex Comb.-based Best Fit
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Outline
1. Resource Allocation Problem Overview
2. Suboptimal Resource Allocation Strategies: Single Resource
3. Suboptimal Resource Allocation Strategies: Multiple Resources
4. Conclusions and Outlook
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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Conclusions and Outlook
 Performance and complexity
 Proposed some new RA strategies
 Sum rate close to that achieved by the Exhaustive Search
 Lower complexity compared to the benchmark strategy and Exhaustive Search
 Provide a good trade-off between performance and complexity
 Throughput fairness
 Higher throughput fairness at the expense of small reduction of the sum rates
 Provide a good trade-off between performance and fairness
 Outlook
 Extension to multi-antenna users
 Extension to ensure minimum QoS levels
 Extension to multiple cells, including relay networks and cooperation among
base stations
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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…
Thank you !
22nd September 2008 | Tariciso F. Maciel | Suboptimal Resource Allocation for Multi-User MIMO-OFDMA Systems
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