Table 1 List of selected symbols (in order of appearance)

P _T

BS transmit power

N _T , N _R

Number of transmit and receive antennas

N _m

Number of active MSs

T _s

Time slot duration

T _o

OFDM symbol duration (without the cyclic prefix)

T _CP

OFDM cyclic prefix duration

N _o

Number of OFDM symbol per slot

B

System bandwidth

B _b

Subband bandwidth

N _b

Number of orthogonal subbands

Nsc

Number of subcarriers per subband

${\mathcal{N}}_m$

Set of active MSs

${\mathcal{N}}_b$

Set of frequency subbands

p _{m, b} (t)

Power allocated to MS m on subband b during the time slot t

δ _{m, b} (t)

Equivalent MRT/MRC channel gain for MS m on subband b during the time slot t

${\sigma }_{\nu }^2$

Noise variance

$Q_m\left(t\right),{\hat{Q}}_m\left(t\right),{\bar{Q}}_m\left(t\right)$

Measured, predicted and sample average queue length of MS m at the beginning of time slot t

A _m (t)

Number of arriving bits to the queue of MS m during time slot t

λ _m

Average arrival data rate for MS m

r _m (t), R _m (t)

Allocated and effective data rates of user m during time slot t

${Ŵ}_m\left(t\right),{\bar{W}}_m\left(t\right)$

Predicted and sample average delay (waiting time) for MS m at the beginning of time slot t

${\bar{T}}_m\left(t\right)$

Throughput sample average for MS m at the beginning of time slot t

${\tau }_m^{\left(A\right)}\left(t\right),{\check{\tau }}_m^{\left(A\right)}\left(t\right)$

Measured and predicted arrival time of the HOL packet in the queue of MS m

$W_{\text{HOL},m}\left(t\right),{Ŵ}_{\text{HOL},m}\left(t\right)$

Measured and predicted HOL delay for MS m at the end of time slot t

p(t)

Vector of power allocation values during time slot t

Set of allowed power allocation vectors

ρm, b(t)

PHY layer transmission rate of MS m over subband b during time slot t

${\mathcal{N}}_k$

Set of available MCSs when using discrete-rate AMC

N _k

Number of available MCSs when using discrete-rate AMC

${\rho }_m^{\left(k\right)}$

Data rate characterizing MCS k when MS m uses discrete-rate AMC

${\Gamma }_m^{\left(k\right)}$

Instantaneous SNR boundaries defining MCS selection intervals for MS m

Λ _m

Coding gap for MCSs used by MS m

θ _m (t)

Set of quantitative QoS measures used to characterize the satisfaction of user m

${\check{\mathit{\Omega }}}_m$

Set of QoS requirements for MS m

${\check{\epsilon }}_m,{Ď}_m,{\check{\xi }}_m$

Maximum tolerable BER, absolute delay and outage delay probability for MS m

${Ť}_m$

Minimum sustainable throughput for user m

${\tilde{W}}_m$

Delay threshold related to Ť _m in MDU scheduling rule

φ _m

Set of constants used by the MDU scheduler to differentiate between heterogeneous services

w _m (t)

Weighing (prioritization) coefficient for MS m during the time slot t

U(⋅)

Utility function used to express the satisfaction of user m

$\mathcal{L}\left(\cdot \right)$

Lagrangian of an optimization problem

μ

Lagrange multiplier

g(⋅)

Dual problem