4.2 Downlink MU-MIMO LTE-LAA for Coexistence with Asymmetric Hidden
4.2.4 Proposed MU-MIMO LTE-LAA System
4.2.4.6 Power Allocation
of AHAPs inBt in descending order.
To find a feasible Bt, the eNB increases the table index t from 1 and checks PFeasibility of B1
until the problem can be solved. That is, we propose to change AHAPs, generating high average sum-interference to the UEs, into EAPs so that those APs defer their transmissions, which results in improved SINRs of the UEs. If the generating sum-interference from the AHAPs is the same for multiple AHAPs sets, we propose to choose the set including more AHAPs. Such a choice will protect eNB’s transmission to the UEs more reliably, given that the APs’ behaviors are in fact random.
If PFeasibility of B1 can be solved for given Bt, the eNB sets cα = 1, ∀α ∈ Bt and cα0 = 0,
∀α0 ∈ AAH\ Bt, and then solves PB2 to find we∗. If there is no feasible case for all possible AHAPs sets, the eNB finds the beamforming vectors from
PDefault of BF: max min
wl,u,∀l,uγ˜l,u (97a)
s.t kwl,uk2 = 1, ∀l∈[1, NsubL ],∀u∈ U. (97b) The PDefault of BF does not have the constraint (83c), where only the performance of LTE-LAA is considered. The solution of PDefault of BF can be readily obtained in the same way for PB1.
rewritten as
maxpL
θ (99a)
s.t (pL)T·(Ql·gl,u)≥θ zl,u,∀l, u (99b)
pL0, (99c)
(pL)T·1NUENL
sub ≤PL, (99d)
(pL)T·vLWeNB,α≥ΓED, ∀α∈ AE∪ B0, (99e) where1N is anN-dimensional all-ones vector, and
gl,u= h
−θ|(we∗l,1)Hh(l)eNB,u|2, . . . ,−θ|(we∗l,u−1)Hh(l)eNB,u|2,
|(we∗l,u)Hh(l)eNB,u|2, −θ|(we∗l,u+1)Hh(l)eNB,u|2, . . . ,
−θ|(we∗l,N
UE)Hh(l)eNB,u|2iT
, (100)
zl,u= X
α∈AAH NsubW
X
w=1
(1−cα)E[eα]pWα,w|h(w,l)α,u |2+N0, (101)
vLWeNB,α=h
NsubW
X
w=1
|(we∗1,1)Hh(1,w)eNB,α|2, . . . ,
NsubW
X
w=1
|(we∗1,NUE)Hh(1,w)eNB,α|2,
. . . ,
NsubW
X
w=1
|(weN∗L
sub,1)Hh(NeNB,αsubL ,w)|2, . . . ,
NsubW
X
w=1
|(weN∗L
sub,NUE)Hh(NeNB,αsubL ,w)|2iT
. (102)
In addition, Ql,u ∈ RNUEN
L
sub×NUE consists of all zeros except for the ((l−1)NUE + 1)-th to the ((l·NUE)-th rows, which are equal to theNUE×NUE identity matrix. Note that vLWeNB,α∈ RNUENsubL ×1 andgl,u∈RNUE×1.
By fixing θto a given value, we finally have
PP2:Find pL (103a)
s.t (pL)T·(Ql·gl,u)≥θ zl,u,∀l, u (103b)
pL0, (103c)
(pL)T·1NUENL
sub ≤PL, (103d)
(pL)T·vLWeNB,α≥ΓED, ∀α∈ AE∪ B0. (103e) The problem PP2 is a convex problem with respect to the variable pL since all the constraints construct a Polyhedron, a convex set. Therefore, this problem can be solved by the SDP to obtain the solutionp∗L.
4.2.4.6.2 Feasibility Check Even though we∗ is designed by the proposed rank-1 ap- proximation such that the condition (86c) is met, there is still a chance that the condition (86d)
is broken after the rank-1 approximation. Furthermore, the AHAP set B obtained in Section 4.2.4.5.4 may become infeasible after the rank-1 approximation.
To resolve these issues, we propose to find B0 once again in the power allocation process, which can be different from B. Fortunately, the power allocation problem PP1 for given we∗ is a convex problem, requiring no approximation or relaxation. Thus, the solution pL and the recalculated feasible B0 ensure that all the constraints inPP1 are met.
To find B0 which makes the problem PP1 feasible, we define the feasibility problem by
PFeasibility of P1:Find pL (104a)
s.t pL0, (104b)
(pL)T1N
UENsubL ≤PL, (104c)
(pL)TveNB,αLW ≥ΓED,∀α ∈ AE∪ B0. (104d) As in Section 4.2.4.5.4, to find a feasible B’, the eNB constructs the AHAPs combination list and evaluatesPFeasibility of P1 for each case of the list. The list of possible AHAPs combinations is constructed in the analogous method in Section 4.2.4.5.4. If there is no feasible case out of all possible AHAP combinations, the eNB uses the power coefficients obtained by the following default power allocation problem:
PDefault of PA: max min
pL
˜
γl,u (105a)
s.t pLl,u ≥0, ∀l∈[1, NsubL ],∀u∈ U, (105b) X
u∈U NsubL
X
l=1
pLl,u≤PL. (105c)
The problem PDefault of PA does not have the constraint (98d), i.e., only the performance of LTE-LAA is considered, and can be solved following the same steps as in solvingPP1.
Algorithm 2: Proposed MU-MIMO LTE-LAA System Initialization
1) Set OFDM parameters, the thresholdΓED, the maximum transmit powers,PL andPW, and the transmit power vectorpWα,j=PW/NsubW,∀α.
Chooseas a small positive value.
2) Go to Default Design Module.
procedureDefault Design Module
1) ViaPDefault of BF,we∗Default is determined as follows.
• Initializeθmax= 0 andθmin to be a large positive value.
• Perform the bisection line search with PDefault of BF as follows.
whileθmax−θmin> do Defineθ= θmax−θ2 min.
Forθ, solve PDefault of BF to obtainW.
Ifθ is feasible,θmin←θ, else θmax←θ.
end
• ForW, find the approximated solution we∗Default according to (95).
2) With we∗Default,p∗L, Default is determined as follows.
• Initializeθmax= 0 andθmin to be a large positive value.
• Perform the bisection line search with PDefault of PA as follows.
whileθmax−θmin> do Defineθ= θmax−θ2 min.
Forθ, solve PDefault of PA to obtain p∗L, Default.
Ifθ is feasible,θmin←θ, else θmax←θ.
end
3) Go to Interference Control Module with the results.
procedureInterference Control Module 1) Make the AHAPs combination list based onAAH
as discussed in Section 4.2.4.5.4.
2) Search over the AHAPs sets, Bt, fromt= 1.
IfPFeasibility of B1 can be solved for someBt, stop searching and setB=Bt. If there is no feasible case at all,B=∅.
3) IfB=∅, terminate the algorithm and usewe∗Default and p∗L, Default, else Go to the next step.
4) For given B, obtain E[eα]from Lemma 1 and 2,
∀α∈ B.
5) From PB2,we∗Proposalis determined as follows.
•Initialize θmax= 0 and θmin to be a large positive value.
•Perform the bisection line search with PB2.
•ForW, find the approximated solution we∗Proposal according to (95).
6) Withwe∗Proposal, find B0 again as in 2).
7) IfB0=∅, terminate the algorithm and usewe∗Proposal and p∗L, Default, else obtainE[eα],∀α∈ B0 and
Go to 8).
8) For given weProposal∗ ,p∗L, Proposal is determined as follows.
•Initialize θmax= 0 and θmin to be a large positive value.
•Perform the bisection line search with PP2. 9) Terminate the algorithm withwe∗Proposal
and p∗L, Proposal.
Table 10: Simulation Parameters
Parameters LAA-LTE’s Wi-Fi’s values values Unlicensed bandwidth 20 MHz 20 MHz
Subcarrier spacing 15 kHz 312.5 kHz
Number of subcarriers 2048 64
Slot time size 9µs 9µs
Initial CW size 16 16
Maximum CW size 64 1024
Transmission duration 8 ms 1 ms Energy detection
threshold −72dBm −62dBm
Transmission power limit 23 dBm AWGN noise power -174 dBm/Hz
Finally, Algorithm 2 presents how our MU-MIMO LTE-LAA system operates in the LAA- WLAN coexistence with AHAPs. In Algorithm 2, weDefault∗ and p∗L, Default is the solution of PDefault of BF and PDefault of PA, respectively. In addition, weProposed∗ and p∗L, Proposed is the solu- tion ofPB2 and PP2, respectively.