Multiuser OFDM with Adaptive Subcarrier, Bit, and Power Allocation Wong, et al, JSAC, Oct. 1999

outline Introduction Problem Formulation Optimal Solution Pretty Pictures Conclusion

introduction High speed data invites frequency selective fading. OFDM approaches maximum capacity in a single user channel. Simple time or frequency division misses capacity gain from multiuser channel diversity (Lectures 3&4).

multiuser system and notation K users, N subbands R k bits per OFDM symbol for kth user c k,n bits assigned by kth user to nth subband c k,n  D = {0, 1, 2, …, M} if c k’n  0, c kn = 0 for all k  k’ f k (c) SNR required for c bits/symbol

so what’s the problem? Simple mathematical formulation: C1 : For all k  {1, …, K}, C2 : For all n  {1, …, N}, if there exists k’ with c k’,n  0, then c k,n = 0 for all k  k’.

review: single user case Optimal single user subcarrier, bit, and power allocation given a rate constraint has same problems as multiuser case. No analytic solution, optimality arrived at through successive (greedy) bit allocation: Initialization: For all n, let c n = 0, and  P n = [f(1)-f(0)]/  n 2 ; Bit Assignment Iterations: Repeat the following R times: ñ = argmin n  P n ; c ñ = c ñ + 1;  P ñ = [f(c ñ + 1)-f(c ñ )]/  ñ 2 ; End;

modified problem Reformulate problem in a convex sense (r k,n represents user k’s (continuous) rate in subcarrier n,  k,n represents her “time- sharing factor): subject to:and

lagrangian (ewww… math)

solution (math)

solution (intuition) Similar to Lecture 3 (Broadcast ISI), optimal allocation depends strongly on channel quality, required rate, and QOS requirement (though here, the QOS connection is masked). For any situation in which the total data rate is < MN, there is a guaranteed solution. (maximizing rate vs. minimizing power)

adaptive solution Increase Lagrangian multipliers iteratively until all users’ rate constraints are satisfied. But this is a modified problem. Generate final solution using single user bit allocation technique among assigned subcarriers. P T  P T *  P T, and the difference between final (suboptimal) and modified solutions gives upper bound on performance.

simulation results (1)

simulation results (2)

simulation results (3)

simulation results (4) “Increase in Capacity of Multiuser OFDM System Using Dynamic Subchannel Allocation”, W. Rhee and J. Cioffi, Proc. VTC 2000.

conclusions and further work Clearly, multiple access channel has larger freq.-selective fading capacity, and the method proposed more fully exploits this capacity than any of the optimizations alone or pair-wise. Perfect channel estimation is a large assumption, as is time-varying fading. Adaptive solution is guaranteed to converge, but no iteration limit is given.

comments… In comparison with spread spectrum, OFDM seems preferable in slowly changing multiple-user freq.-selective fading environments. The results of this paper could be extended to FDMA (e.g. MAC rather than broadcast) solutions, but the sensitivity to implementation becomes a dominant factor.