V. SIMULATION RESULTS We now present our simulation results obtained for an LTE HetNet deployment. We emulate a HetNet comprising of 57 macro cells with 10 pico cells being assigned to each macro and with a full buffer traffic model. Each macro base-station transmits with a power of 46 dBm whereas the transmit power at each pico node is 40 dBm and the system bandwidth is 10 MHz. A noise PSD of − 174 dB/Hz with a noise figure of 9 dB were assumed. Other major parameters such as the distributions used to drop users, macro and pico nodes are all as per 3GPP guidelines. TABLE II GELS Algorithm TABLE III Orthogonal Split Processing based Algorithm (OSPA) 1: Initialize with MaxIter ≥ 1 , ˜ Ω = Ω , Δ > 0 and ˆ G = φ . 2: Repeat %Optional Greedy Stage 3: Determine ( k $^{′}$, b$^{′}$) as the tuple in ˜ Ω \ ˆ G which satisfies ˆ G ∪ ( k $^{′}$, b$^{′}$) ∈ J and offers the best gain f $^{wsr}$( ˆ G ∪ ( k $^{′}$, b$^{′}$)) − f $^{wsr}$( ˆ G ) , among all such tuples. 4: If the best gain is positive update ˆ G = ˆ G ∪ ( k $^{′}$, b$^{′}$) . 5: Until the best gain is not positive. 6: Set ˘ G = ˆ G , Iter = 0 . 7: Repeat %Enhanced Local Search (LS) Stage 8: Increment Iter = Iter + 1 . 9: Swap: Find a pair of tuples: ( k $^{′}$, b$^{′}$) ∈ ˘ G and ( k, b ) ∈ ˜ Ω \ ˘ G such that the swapping ( k $^{′}$, b$^{′}$) ∈ ˘ G with ( k, b ) is in J and results in the best gain among such swaps. 10: Deletion: Find a tuple: ( k $^{′}$, b$^{′}$) ∈ ˘ G such that deleting this tuple results in the best gain among such deletions. 11: Addition: Find a tuple: ( k $^{′}$, b$^{′}$) ∈ ˜ Ω \ ˘ G such that ˘ G ∪ ( k $^{′}$, b$^{′}$) ∈ J and adding this tuple results in the best gain among such additions. 12: Determine the overall best among the three best gains and compute threshold Δ f $^{wsr}$( ˘ G ) 13: If the overall best gain is at-least as as large as the threshold, then update ˘ G according to the overall best choice. 14: Until the overall best gain is less than threshold or Iter = MaxIter . 15: Repeat Greedy and Enhanced LS stages intialized with ˜ Ω = Ω \ ˘ G and let ˜ G be the obtained output. 16: Output the choice yielding the larger of { f $^{wsr}$( ˘ G ) , f $^{wsr}$( ˜ G ) } . 1: Initialize with U , M , B$_{m}$ , ∀ m ∈ M . 2: Set S = M ∪ ( ∪$_{m}$$_{∈M}$B$_{m}$ ) and determine user associations { x$_{u,b}$ } ,u ∈ U ,b ∈ S by solving (28) 3: For each macro TP m ∈ M Do 4: Consider each user with x$_{u,m}$ = 1 and associate that user with the pico TP in B$_{m}$ yielding the strongest received power for that user. 5: Using the obtained association for TPs in B$_{m}$ obtain the optimal allocation fractions using Theorem 1. 6: End For 7: Output the user associations and allocation fractions.