Optimizing radio resources for multicasting on high-altitude platforms

EURASIP Journal on Wireless Communications and Networking

Table 1 Notation definitions for E-Prob formulation

Notation	Definition
M	Is the number of multicast sessions in the HAP service area.
S	Is the number of HAP antennas onboard.
K	Number of users in the service area.
C	Is the number of available subchannels.
T	Total number of time slots available over OFDMA frame.
Δ B	Is the subchannel bandwidth.
Δ T	Is one time slot duration.
F	Is the OFDMA frame duration.
σ ²	Is the additive white Gaussian noise power per subchannel.
p _{m, i, c, t}	Is the value of the HAP power assigned for multicast session m on antenna i in the frequency-time slot (c,t).
g _{i, k, c, t}	Channel gain between antenna i and user k on frequency-time slot (c,t).
λ _{m, k}	Is a binary constant that indicates whether user k requests to join session m.
ϕ _{m, k}	Is a binary variable that indicates whether a user k gets assigned to receive multicast session m.
ρ _{m, k}	Is a positive integer constant that represents priority for user k on session m.
θ _m	Is a binary variable that indicates whether session m receives any resources, or equivalently, whether any user gets assigned to receive the session’s transmission.
y _{m, i, c, t}	Is a binary variable that indicates whether the trio combination (i,c,t) is assigned for session m.
\(\hat {M}\)	Is a very large arbitrary number.
\(\gamma ^{th}_{m,i}\)	Is the SINR value that satisfies a desired target BER for session m on antenna i. Different sessions transmitted on different antennas may be modulated and coded differently thus requiring different SINR thresholds.