1. 1 11 Subcarrier Allocation and Bit Loading Algorithms for OFDMA-Based Wireless Networks Gautam Kulkarni, Sachin Adlakha, Mani Srivastava UCLA IEEE Transactions on Mobile Computing 2005

2. 2 22 Outline Introduction System Model and Problem Formulation Centralized Rate Allocation Algorithms Distributed Algorithm Performance Evaluation Conclusions

3. 3 OFDM Frequency Division Multiplexing (FDM) Orthogonal Frequency Division Multiplexing (OFDM) higher spectral efficiency

4. 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. 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. 6 System Model There are a total of M links in the network, each with a certain data rate requirement R i Let the spectrum of interest be divided into N subcarriers P c i is the power transmitted by transmitter i on subcarrier c I c i is the interference power Let G c ij 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. 7 SINR Threshold Let b c i be the number of bits transmitted by link i on subcarrier c b c i takes only integer values ∈ (0, 1, 2,..., b max ), where b max 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. 8 Matrix Form The data rate R i can be expressed as When K links (i 1, i 2,..., i K ) are transmitting on subcarrier c, we require that In matrix form, these conditions can be written as Where

9. 9 Example

10. 10 P c i is a function of {b c i } It was shown in [14] that a positive solution for P c exists if the maximum eigenvalue of F c 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 b c i and P c i for every link i and subcarrier c (the Pareto optimal solution) [14] J. Zander, “Performance of Optimum Transmitter Power Control in Cellular Radio Systems,” IEEE Trans. Vehicular Technology, vol. 41, no. 1, pp. 57-62, Feb. 1992.

11. 11 Problem Formulation Finding the global minimum requires an exhaustive search over all possible assignments of subcarriers to links

12. 12 Let △ P(i, c, b c i ) be the total increase in transmitter power over all links when one more bit of link i is loaded on subcarrier c

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14. 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 H c = (V, E c ) for all c ∈ 1, 2,..., N Step 2. Start with c = 1 Step 3. Find a maximal independent set of H c 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. 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 P c i (k) is the power transmitted by link i on subcarrier c in time slot k γ c 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 Control in Cellular Radio Systems,” IEEE Trans. Vehicular Technology, vol. 41, no. 1, pp. 57-62, Feb. 1992.

16. 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 G c i /I c i factor the subcarrier with the highest G c i /I c i factor is selected G c i and I c 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

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18. 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. 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 q thresh = 0.95

20. 20 Average Power Per Bit versus Network Load

21. 21 Normalized Throughput versus Network Load

22. 22 Variance of Normalized Throughput

23. 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