Adaptive Resource Allocation

Algorithm for Multiuser

Mimo-Ofdm Systems

Presented By: Mohammed Akber Ali,

ID: G200806120.

Overview

Introduction-Basic DefinitionsSchedulingOptimization problemConventional method of solving

problemOptimal Algorithm proposedAnalyzing results for OFDMA

systemExtending the algorithm to

Multiuser MIMO-OFDMResults

INTRODUCTION:• OFDMA:

(i). OFDMA also employs multiple sub-carriers as OFDM, where sub-carriers are divided into groups of sub-carriers known as sub-channels. (ii). In a downlink scenario, a sub-channel may be intended for different receivers.

INTRODUCTION• MIMO:

-Spatial multiplexing: Several data are simultaneously transmitted over multiple antennas, increasing the capacity drastically.

-Space-time coding: Same data is transmitted over multiple antennas, to combat signal fading by increasing diversity.

• Multiuser MIMO-OFDM : - Further increases the systems capacity, by scheduling multiple users to share the same spatial channel simultaneously.

User 1

User 2

User K

SCHEDULING:

Periodically selecting the best user to serve in order to improve the system performance is Scheduling

Resource Allocation Problem:Task is to Distribute frequency subchannels and total power among

various users.

Such that they maximize the overall network throughput specified by:

Resource Allocation Problem:

Constraints to be satisfied by an resource allocation algorithm:• The total power constraint –that should assure,

Where pk,n is power allocation for (k,n) subchannel.

• The sub channel allocations Ωk’s for different users must be mutually exclusive, disjoint :

• The proportional rate constraints are to be satisfied for a promised QoS,

introducing a level fairness among users: R1/ γ1= R2/ γ2 ... = RK / γK .

are proportional rate constraint constants (for QOS).

Conventional Method for solving optimization problem:• In general to solve such problem, a cost function is constructed from a set of

Lagrange multipliers as done by shen et al.[3]:

• Total power assigned to the kth user is given by, The constants Vk and Wk are given by:

• Using the derived cost function the total power allocation (Pk,total) for a particular user can be found,

gives us the power allocations for the individual subchannels.• These power allocations are made in such a way that we can achieve

maximum capacity, satisfying all constraints.

,,

Conventional Method for solving optimization problem:

Therefore,• Use of equally weighted capacity sum as the optimizing function, • Introducing the scheme of proportional fairness among users,Gives us a benefit of explicitly controlling the capacity ratios among

various users, while ensuring each user his maximum data rate.

Considering the complexity of the cost function, many researchers (Rhee et al.[2] & Shen et al.[3]) , tried solving a simplified version of it,

- Assuming channel power gains to be large and similar, - Thus, the proportional rates constraint is not satisfied in strict sense.

Optimal Algorithm Proposed• In 2008, Dr. Ashraf et al.[1] proposed an algorithm that

- Solves the utility function without making any assumption about the channel power gains &

- Satisfies the proportional rates constraint in strict sense.

• The proposed algorithm in [1]: Modifys the set of subchannel allocations Ωk's for a given user k, by

dropping weak channels untill a valid solution for optimization problem is obtained.

• The obtained solution -Maximizes the system throughput,- Guarantees that the provided users rates Rk’s satisfy the proportional rates constraint in strict sense, such that R1: R2: ...: RK = γ1: γ2: ...: γK.

Analyzing Results in [1]:The results were reproduced under conditions similar to that in paper [1],

• Considering a frequency selctive multipath channel modeled as 6 independent Rayleigh multipaths,

• Total power available is assumed to be1 Watt,

• Noise PSD of 65 dBW ,

• The Overall Bandwidth of 1 MHz, divided among 64 sub-channels.

Analyzing Results in [1]:

The optimal scheduling algorithm proposed in [1] provides significantly higher capacity than that proposed in [3].

Analyzing Results in [1]:

If the proportionality rate constraints are satisfied in strict sense then all Гk’s =1 => fairness index nearly equals 1

Jain’s Fairness Index [1]:

Therefore, The algorithm proposed in [1] satisfies the proportional rates constraints in strict sense.

Extending- To Multiuser MIMO-OFDM system:• The problem of resource allocation in a multiuser MIMO-OFDM system is

formulated similar to that of OFDMA system,But is more challenging & complicated due to multiple antennas.

• Channel Model: For Mt transmit & Mr receive antennas.

Where, is power gain relative to noise power from Mtth transmit

antenna & Mrth receive antenna for kth user over nth subcarrier.

Extending- To Multiuser MIMO-OFDM system:

• In a MU-MIMO-OFDM system the power & subcarrier allocations should maximize the overall network throughput, given by:

• While meeting all the constraints specified for an OFDMA system, The algorithm proposed in [1], is now used to solve the optimization

problem of a multiuser MIMO-OFDM system.

• Results are obtained under similar conditions, Ptotal=1Watt,Total bandwidth=1MHz, divided among 64 sub channels, for a noise PSD of 65dBW.

• For Mr=2&4,Mt=2&4 i.e. a 2 x 2 & 4 x 4 MIMO cases are considered.

RESULTS:

As expected the capacity increases drastically for a MU-MIMO-OFDM system when compared to OFDMA system.

RESULTS:

As expected a MU-MIMO-OFDM system has higher capacity when compared to OFDMA system.

RESULTS:

Proportional rates constraints are also satisfied in strict sense, as in case of an OFDMA system.

Conclusion:

• The numerical analysis of the optimal algorithm proposed in [1] (for OFDMA) shows that it outer performs and satisfies fairness constraint in strict sense.

• The results in that, capacity increases drastically when the channel is replaced with that of a multiuser MIMO OFDM channel. The capacity can be improved further by increasing number of receiving and transmitting antennas (as demonstrated by a 4 x4 MIMO-OFDMA system).

References:1. Ashraf S. Mahmoud, Ali Y. Al-Rayyah, and Tarek R. Sheltami - “Adaptive Power Allocation

Algorithm to Support Absolute Proportional Rates Constraint for Scalable OFDM Systems”. IEEE 71st VTC-Spring May 2010.

2. W. Rhee and M. Cioffi, “Increase in capacity of multiuser OFDM system using dynamic subchannel allocation,” in Proc. IEEE Vehicular. Technology Conference (VTC 2000), May 2000, pp. 1085-1089.

3. Z. Shen, J. G. Andrews, and B. L. Evans, ”Adaptive resource allocation in multiuser OFDM systems with proportional rate constraints,” IEEE Trans. Wireless Commun., vol. 4, no. 6, Nov. 2005, pp. 2726-2737.

4. S. Sadr, A. Anpalagan, and K. Raahemifar, ”Suboptimal Rate Adaptive Resource Allocation for Downlink OFDMA Systems,” Int. J. of Veh. Technol., vol 2009, Art 891367, 10 pages doi:10.1155/2009/891367.

5. Yang Hu, Changchuan Yin and Guangxin Yue -“Multiuser MIMO-OFDM with Adaptive Antenna and Subcarrier Allocation”. VTC Spring 2006: 2873-2877.

Thank you !