111

Subcarrier Allocation and Bit Loading Algorithms for OFDMA-Based Wireless

Networks

Gautam Kulkarni, Sachin Adlakha, Mani Srivastava

UCLAIEEE Transactions on

Mobile Computing 2005

222

Outline

Introduction System Model and Problem Formulation Centralized Rate Allocation Algorithms Distributed Algorithm Performance Evaluation Conclusions

3

OFDM

Frequency Division Multiplexing (FDM)

Orthogonal Frequency Division Multiplexing (OFDM) higher spectral efficiency

4

OFDMA

Orthogonal Frequency Division Multiple Access (OFDMA) the sub-carriers are divided into groups of sub-carriers

Each group is named a sub-channel sub-channels can be allocated to users depending on

their channel conditions and data requirements different transmit power and modulation

5

Goal

We address the problem of subcarrier, bit, and power assignment for networks that employ OFDMA

Our objective is to minimize the total transmitted power over all links while maintaining the data rates on each link

6

System Model

There are a total of M links in the network, each with a certain data rate requirement Ri

Let the spectrum of interest be divided into N subcarriers Pc

i is the power transmitted by transmitter i on subcarrier c

Ici is the interference power

Let Gcij be the gain from the transmitter of link j to the

receiver of link i for subcarrier c The SINR of link i for subcarrier c is given by

7

SINR Threshold Let bc

i be the number of bits transmitted by link i on subcarrier c bc

i takes only integer values ∈(0, 1, 2, ..., bmax), where bmax is the maximum modulation level used

When M-ary quadrature amplitude modulation (M-QAM) [13] is used, the corresponding SINR threshold is ex: 16-QAM, 64-QAM

where BER is the target bit error rate and Q(.) is the Gaussian tail function given by

[13] J.G. Proakis, Digital Communications. McGraw Hill, 2001

8

Matrix Form

The data rate Ri can be expressed as

When K links (i1, i2, ..., iK) are transmitting on subcarrier c, we require that

In matrix form, these conditions can be written as

Where

9

Example

(D)

(C))(

(B)

(A)

1

1

1

13

2,11

1,1

3,132,121111,1

1,1

113

1,1

3,112

1,1

2,111

3,3

33

2,2

22

1,1

11

3

2

1

3,3

2,33

3,3

1,33

2,2

3,22

2,2

1,22

1,1

3,11

1,1

2,11

rGPN

PG

GPGPNrPG

G

NrP

G

GrP

G

GrP

G

Nr

G

Nr

G

Nr

P

P

P

G

Gr

G

Gr

G

Gr

G

Gr

G

Gr

G

Gr

iii

10

Pci is a function of {bc

i}

It was shown in [14] that a positive solution for Pc exists if the maximum eigenvalue of Fc is less than 1 Otherwise, the set of SINR thresholds (modulation levels) used by all

the links on subcarrier c, is not feasible The goal is to find bc

i and Pci for every link i and subcarrier c

(the Pareto optimal solution)

ccc UFIP 1)(

[14] J. Zander, “Performance of Optimum Transmitter Power Controlin Cellular Radio Systems,” IEEE Trans. Vehicular Technology,vol. 41, no. 1, pp. 57-62, Feb. 1992.

11

Problem Formulation

Finding the global minimum requires an exhaustive search over all possible assignments of subcarriers to links

12

Let P(i, c, b△ ci) be the total

increase in transmitter power over all links when one more bit of link i is

loaded on subcarrier c

13

14

Graph-Based Approach We adopt the strategy of using small modulation levels and spreading

the data rate over a large number of channels This would imply smaller power levels per channel and higher spatial

reuse

Procedure Step 1. Construct the interference graphs Hc = (V , Ec) for all c ∈ 1,

2, ..., N Step 2. Start with c = 1 Step 3. Find a maximal independent set of Hc using the Minimum

Degree Greedy Algorithm [25] Step 4. From the maximal set, find a feasible set of transmissions (S) Step 5. Trim the interference graphs for all channels by removing S Step 6. Proceed to next channel—stop if all channels scheduled or all

sublinks are scheduled

15

Distributed Algorithm (1)

In this case, node have no knowledge of channel gains for the entire network

Time is divided into slots and every link updates its power at the end of each slot as follows

Pci(k) is the power transmitted by link i on subcarrier c in time

slot k γc

i is the measured SINR at the receiver of link i It was shown in [14] that the power update (11)

converges to the Pareto optimal[14] J. Zander, “Performance of Optimum Transmitter Power Controlin Cellular Radio Systems,” IEEE Trans. Vehicular Technology,vol. 41, no. 1, pp. 57-62, Feb. 1992.

r

r

kP

kP

)(

)1(

16

Distributed Algorithm (2)

A link selects a particular subcarrier and loads one bit and then performs power control to try to achieve the corresponding SINR threshold The criterion for selecting the subcarrier is the Gc

i/Ici factor

the subcarrier with the highest Gci/Ic

i factor is selected

Gci and Ic

i are the channel gain and interference, respectively

After a few power control updates (W slots), the power transmitted by the link on the selected subcarrier may not stabilize and is still increasing Each link i drops out with a probability q(i) The probability q(i) is increased with each unsuccessful attempt to

gain access to the channel

17

18

Comparison with the Optimal Solution

The performance of our algorithms vs. the optimal solution for small instances of the problem the two link, two channel case

19

Simulation Environment

10 links in an area of 200 m by 200 m Receivers are randomly placed within a 20 m

radius of the corresponding transmitter 48 subcarriers in the OFDM system The path loss exponent is taken to be 4 bit rate requirements of the links are normal

random variables For the distributed algorithm, we choose W = 10

slots and qthresh = 0.95

20

Average Power Per Bit versus Network Load

21

Normalized Throughput versus Network Load

22

Variance of Normalized Throughput

23

Conclusions

Consider the problem of subcarrier and bit allocation for point-to-point links of fixed wireless networks without base stations The objective was to minimize the total transmitted

power over all links while trying to satisfy the data rate requirement of each link

Present centralized and distributed heuristic algorithms for allocating rates to the links