Digital Communications 2

Notations

B: bandwidth

B_c: coherence bandwidth

b(t): baseband additive white Gaussian noise

c_k = a_k + _jb_k: baseband complex symbol, with a_k its real part and b_k its imaginary part

d_min: minimum distance

E[x]: expected value of a random variable x

E_b: average energy per bit

E_s: average energy per symbol

f_c: carrier frequency of narrowband passband signal

g_c(t): impulse response of the transmit baseband channel

g(t): transmit filter

g_r(t): matched filter at the receiver

γ_xx(f): power spectrum density of a random process x

h(t): impulse response of the narrowband passband channel

H(z): linear digital equalization filter

N: noise power,or number of samples in an OFDM or FBMC symbol

N_CP: number of samples in OFDM cyclic prefix

n(t): noise filtered by the receive filter

N₀: one-sided noise power spectrum density

M: alphabet size of the modulation’s constellation

P: signal power

P_e: error probability per symbol

p: probability of a random variable

p(t) = g(t) * g_c(t) * g_r(t): complete equivalent channel

Ψ: phase of the passband signal

R_ss(t): autocorrelation function of random process s

r(t): output signal of narrowband passband channel

s(t): input signal of narrowband passband channel

T: symbol period

T_b: transmission duration of a bit

T_m: maximum delay of the channel

T_N: transmission duration of an OFDM or FBMC symbol

u(t): step function

x(t): transmitted signal on the baseband channel

y: received signal at channel’s output after matched filter and sampling

y(t): received baseband ...