Table 2 Summary of the notation and mathematical operators used throughout this paper

∗

Linear convolution

(·)^∗

Complex conjugate

(·)^T

Transpose operator

⌈·⌉

Ceil operator (i.e., rounds to the nearest integer towards

infinity)

⌊·⌋

Floor operator (i.e., rounds to the nearest integer towards

minus infinity)

α

Reconstruction delay affecting the received source symbols

β

Reconstruction delay affecting the transmitted signal

B

Order of the polyphase network

B _r

Order of the polyphase network at the FBMC receiver

B _t

Order of the polyphase network at the FBMC transmitter

δ

Fraction of the symbol time devoted to cyclic prefix

${\mathcal{D}}_B\left\{·\right\}$

Downsampling operation by a factor B

DFT_i,P

i th output of a P-points discrete Fourier transform (DFT)

g[n]

Impulse response of the prototype filter

g _i [n]

i th polyphase subfilter

G _t,r

Complexity gain with respect a conventional

transmultiplexer implementation

${\mathcal{I}}_B\left\{·\right\}$

Upsampling operation by a factor B

IDFT_i,P

i th output of a P-points inverse discrete Fourier transform

(IDFT)

lcm

Least common multiple

mod(a,b)

a Modulo b (i.e. $a-\lfloor \frac{a}{b}\rfloor b)$

$N_{\text{CM}}^{\text{r}}$

Number of complex multiplications per multi-carrier

symbol at the FBMC receiver

$N_{\text{CM}}^{\text{t}}$

Number of complex multiplications per multi-carrier

symbol at the FBMC transmitter

N _sso

Integer number such that lcm (P_t,N_ss)=N_ssoP_t

P _r

Fundamental subcarrier period (samples) at the FBMC

receiver

P _t

Fundamental subcarrier period (samples) at the FBMC

transmitter

P _ro

Integer number such that lcm (P_r,N_ss)=P_roN_ss

P _to

Integer number such that lcm (P_t,N_ss)=P_toN_ss

ρ

Roll-off factor

s _n [l]

Source symbols to be transmitted on the n-th subcarrier at

the l th FBMC symbol

${\tilde{s}}_n\left[l\right]$

Phase-rotated version of the source symbols

${\breve{s}}_n\left[l\right]$

Source symbols recovered at the FBMC receiver

$S_{\text{mod}(i,P)}^P\left[l\right]$

IDFT transformed source symbols (i.e.,

$S_{\text{mod}(i,P)}^P\left[l\right]\doteq {\text{IDFT}}_{i,P}\left(\right[s_0\left[l\right],s_1\left[l\right],\dots ,s_{P-1}{\left[l\right]}^{\text{T}}\left]\right)$)

x[m]

FBMC transmitted signal

x _i [k]

Input signal to the i th polyphase filter

y _i [k]

Output signal from the i th polyphase filter