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Table 3 Table of notations

From: Interference management for moving networks in ultra-dense urban scenarios

Symbol

Meaning

b(l, m, u)

The scheduling decision for the uth user in mth PRB in the lth subframe

b p(n)

Total number of PRBs scheduled for device n over \(\mathcal {R}_{\mathrm {p}}\)

b np(n)

Total number of PRBs scheduled for device n over \(\mathcal {R}_{\text {np}}\)

d(n)

A function that measures channel quality difference for the nth device over the protected and non-protected PRBs

i v

The number of active VUEs on the vth MN

j

The index of an interferer

k

The time index of received signal

l

The index of a subframe

m

The index of a PRB in a given subframe

n

The index of an arbitrary device, i.e., either a UE or an MN, connecting to a macro cell

n ∗(l, m)

The device is selected to be scheduled at the mth PRB in the lth subframe in the macro cell

p

The number of antennas equipped at the backhaul link of an MN

\(q_{n_{1}}\)

An arbitrary device served by macro BS sector 1

r(l, m, u)

The throughput of the uth macro UE at the mth PRB in the lth subframe

r 0,i (v)

The throughput of the access link of the vth MN when the ith subframe in the micro cells is configured as ABS

r 1,i (v)

Throughput of the access link of the vth MN when the ith subframe in the micro cells is not configured as ABS

r p(n)

The average rate of device n over \(\mathcal {R}_{\mathrm {p}}\)

r np(n)

The average rate of device n over \(\mathcal {R}_{\text {np}}\)

s(n)

The average throughput of device n, which can be either a macro UE or the backhaul link of an MN

s(u)

The average throughput of the uth macro UE

s(v)

The average throughput of the backhaul link of the vth MN

u

The index of a macro UE

u ∗(l, m)

The macro UE that is selected to be scheduled at the mth PRB in the lth subframe

x k

The desired signal transmitted at time k

x j, k

The interfering signal from the jth interferer at time k

n 1

The index of a device served by macro BS sector 1

v

The index of an MN

B p

The size of \(\mathcal {R}_{\mathrm {p}}\)

B np

The size of \(\mathcal {R}_{\text {np}}\)

G(ν)

\(G(\nu)=N\,\frac {\nu }{\left (1+\nu \right)}\) for ν≥0, a function defined to facilitate the solution of problem (7)

K

A parameter used in the solution of (11), where K∈{0, 1, …, N−1} and G(d(K+1))≤K≤G(d(K))

L

The number of total subframes in which the average throughput of a device in the macro cell is calculated

M

The total number of PRBs in each subframe

N

The total number of devices, i.e., N=N u+N m, connect to a macro cell

N 1

The number of devices served by macro BS sector 1

N c

The number of subcarriers in an OFDMA system

N L

The number of interferers experienced at the backhaul link of an MN

N m

The number of MNs in a macro cell

N u

The number of macro UEs in a macro cell

N sf

The number of total subframes that average throughput target of the backhaul link of the MNs are calculated in the micro cells

\(\bar {R}(v)\)

The average throughput target of the backhaul link of the vth MN during N sf subframes

α

A parameter used in the solution of (11), where α=λ p−K

γ k

The instantaneous output SINR at the MN backhaul receiver at time k

ε

An averaging constant that is required in updating the average throughput of a given device

λ p

A parameter used in the solution of (11), where λ p= max(G(d(K+1)), K)

λ np

A parameter used in the solution of (11), where λ np=N−λ p

\(\sigma _{\mathrm {n}}^{2}\)

The noise power at each antenna

μ(l, u)

The average throughput of user u

\(\mathcal {I}_{i}\)

\(\mathcal {I}_{i}\in \left \{ 0,\ 1\right \},\ i=1,\ 2,\ 3\ldots \,N_{\text {sf}}\) indicate the status of the ABSs at the micro cells

The sets denotes all the macro UEs in a cell

\(\mathcal {R}_{\mathrm {p}}\)

The set of protected PRBs in a macro cell

\(\mathcal {R}_{\text {np}}\)

The set of non-protected PRBs in a macro cell

\(\mathcal {S}_{1}\)

The set of users only scheduled in R p

\(\mathcal {S}_{2}\)

The set of users only scheduled in R np

\(\mathcal {S}_{3}\)

The set of users can be scheduled both in \(\mathcal {R}_{\mathrm {p}}\)and \(\mathcal {R}_{\text {np}}\)

To denote uniform distribution

The sets denotes all the MNs in a cell

h k

The channel vector of the desired signals at each reviver antenna of an MN at time k

h j, k

The channel vector of the jth interfering signal observed at each reviver antenna of an MN at time k

n k

The vector denotes the thermal noise at each receiver antenna of an MN at time k

w k

The vector that contains the weight applied at each receiver antenna of an MN at time k

y k

The vector that contains the received signal at each receiver antenna of an MN at time k

z k

The combined signal at the output of an MN backhaul receiver at time k

R

The noise covariance matrix of the reviver antennas of an MN

I p×p

The identity matrix of size p

(·)H

To denote the complex conjugate transpose of a matrix

EIGmax(·)

To denote the dominant eigenvector of a matrix