Praise for Fundamentals of WiMAX

6.3 Resource-Allocation Techniques for OFDMA 211P klLet , denote user k‘s transmit power in subcarrier l. The signal-to-interference-plusnoiseratio for user k in subcarrier l, denoted as SINR kl , , can be expressed asP h= .BL2kl , kl ,SINR kl , K2 2∑ Pjl,hkl,+ σj=1,j≠k(6.4)Using the Shannon capacity formula as the throughput measure, 3 the MSR algorithm maximizesthe following quantity:K LP kl , k =1 l=1maxBlogL∑∑ +with the total power constraint P ≤ P .KL∑∑kl ,k=1 l=1tot( 1 SINRkl, ), (6.5)The sum capacity is maximized if the total throughput in each subcarrier is maximized.Hence, the maximum sum capacity optimization problem can be decoupled into L simpler problems,one for each subcarrier. Further, the sum capacity in subcarrier l, denoted as C l, can bewritten asCl⎛⎞K ⎜ P ⎟kl ,= ∑ log⎜1 +⎟ ,2k=1⎜σ B ⎟⎜ Ptot, l− Pk , l+2⎝h L ⎟⎠kl ,(6.6)where Ptot, l− Pk , l denotes other users’ interference to user k in subcarrier l. It is easy to showthat C lis maximized when all available power P tot,l is assigned to the single user with the largestchannel gain in subcarrier l. This result agrees with intuition: Give each channel to the userwith the best gain in that channel. This is sometimes referred to as a “greedy” optimization. Theoptimal power allocation proceeds by the waterfilling algorithm discussed previously, and thetotal sum capacity is readily determined by adding up the rate on each of the subcarriers.6.3.2 Maximum Fairness AlgorithmAlthough the total throughput is maximized by the MSR algorithm, in a cellular system such asWiMAX, in which the pathloss attenuation varies by several orders of magnitude between users,some users will be extremely underserved by an MSR-based scheduling procedure. At the alternative3. Throughout this section, we use the Shannon capacity formula as the throughput measure. In practice,there is a gap between the achieved data rate and the maximum (Shannon) rate, which can besimply characterized with a SINR gap of a few dB. Therefore, this approach to resource allocationis valid, but the exact numbers given here are optimistic.