rovides most favorable channel condi- tions, noting that the channel conditions in the frequency domain can be different to each user as a function of where in the frequency domain that user is allocated, as shown in Fig. 7 -10. Like in time-domain scheduling, a utility function is RUE,n is defined, in frequency- domain scheduling as the achievable throughput of a given user as a function of the allo- cated slice of spectrum in the frequency domain. The frequency-domain scheduling problem can now be formulated as: max(R) = UE dbase Read total # Update average Calculate queued Bytes achievable rate Calculate metric Force metric to 0 if UE non - active For all UEs Define TB Find N UEs with bound highest metric FIGURE 7-9 PF time-domain scheduling. PF, proportional fair. Chapter 7 Wireless scheduling and Quality of Service optimization techniques 253 RE(G) FIGURE 7-10 Frequency-domain scheduling challenge. where n = {0, , N) defines a slice of frequency-domain resource (i.e., RF spectrum). Note that there are allocation constraints involved-such as a requirement for users to be allo- cated contiguous pieces of spectrum. Typical implementations may slice the frequency- domain resources (subcarriers or resource blocks) into larger groups to simplify the algorithm. Several algorithms for this UE to subchannel allocation can be found in literature. Using greedy allocation (best fit first) to sort to the throughput metric (in this example RUE,n) is a common approach; but, this is known to be suboptimal in terms of finding the maximum summed rate. Linear programming can be employed to find the optimum solution to the problem, for example, by using the simplex method as described elsewhere. The best fit first method, or greedy allocation, is among the simplest heuristic algorithms for solving the problem. The algorithm sequentially finds the highest possible utility in the matrix defined by user and n until all frequency-domain resources (n) are exhausted and/or all users are scheduled. The best fit first method is as foll