Table 2 Important notation and acronyms

Notation

Description

G _c =(V _c,E _co,E _adj)

Conflict graph with vertices V _c and edges E _co,E _adj

F={1,..,M}

Set of M available frequencies

B _v

List of blocked frequencies at CRv due to PU

hard constraints

W _co={wvi vjco}∈[0,1]

Set of co-channel continuous interference

weight coefficients

W _adj={wvi vjadj}∈[0,1]

Set of adjacent channel continuous

interference weight coefficients

N _PU,N _SU

Number of primary and secondary users

hPUiPUi ^′ hPUiSUk ^′

Channel coefficients between PU Tx i ^′, SU Tx k ^′,

and PU Rx i

hSUlSUk ^′ hSUlPUj ^′

Channel coefficients between SU Tx k ^′, PU Tx j ^′,

and SU Rx l

P _{Rx_SUl_D},P _{Rx_SUl_I}

Desired received signal strength and interfering

received signal strength at the l t h SU

\(P_{\text {Tx}\_\text {PU}m^{\prime }}, P_{\text {Tx}\_\text {SU}l^{\prime }}\phantom {\dot {i}\!}\)

Transmitting power at m ^′th PU and l ^′th SU

S _vi

Saturation metrics label

Col_vi

Vertex coloring argument

Acronyms

Description

CR

Cognitive radio

FA

Frequency assignment

PU, SU

Primary user, secondary user

Tx, Rx

Transmitter, receiver

QoS

Quality of service

CminSumInt

Centralized minimum cumulative network

interference FA algorithm

CMaxSumCap

Centralized interference sensitive maximum

throughput FA algorithm

DminInt

Distributed minimum interference FA algorithm

DMaxCap

Distributed interference sensitive maximum

throughput FA algorithm