1.6 Symbols and Common Definitions
We use the notation in Table 1.2 and assign specific definitions to the variables in Table 1.3 throughout this text.
Table 1.2 Generic notation used in this text.
≜ 
by definition 
⋆ 
convolution operator 
a 
bold lowercase is used to denote column vectors 
A 
bold uppercase is used to denote matrices 
α A 
nonbold letters are used to denote scalar values 
α 
magnitude of scalar α 
∥a∥ 
vector 2norm of a 
∥A∥_{F} 
Frobenius norm of A 
A 
calligraphic letters denote sets 
A 
cardinality of set A 
A^{T} 
matrix transpose 
A* 
conjugate transpose 
A^{c} 
conjugate 
A^{1/2} 
matrix square root 
A^{1} 
matrix inverse 
A† 
MoorePenrose pseudo inverse 
a_{k} 
k^{th} entry of vector a 
[A]_{k,l} 
scalar entry of A in k^{th} row l^{th} column 
[A]_{:,k} 
k^{th} column of matrix A 
[A]_{:,k:m} 
column consisting of rows k, k + 1,..., m of matrix A 
(·) 
used to index a continuous signal 
a(t) 
continuous scalar signal and value at t 
a(t) 
continuous vector signal and value at t 
A(t) 
continuous matrix signal and value at t 
[·] 
used to index a discretetime signal 
a[n] 
denotes discretetime scalar signal and value at n 
a[n] 
discretetime vector signal and value at n 
A[n] 
discretetime matrix signal and value at n 
a[n] 
denotes discretetime vector signal in frequency domain at subcarrier n 
A[n] 
discretetime matrix signal in frequency domain at subcarrier n 
log 
denotes log2 unless otherwise mentioned 
Table 1.3 Common definitions used in this text.
E_{s} 
signal energy 
N_{o} 
noise energy 
L 
channel order 
discretetime ISI channel impulse response with (L + 1) taps 

frequency domain channel transfer function 

y[n] 
symbol sampled received signal 
x[n] 
symbol sampled transmitted signal 
s[n] 
symbol sampled transmitted signal before precoding 
I_{N} 
N × N identity matrix 
0_{N,M} 
N × M all zeros matrix 
j 
imaginary number 
E 
expectation operator 
x ~ N(m, σ^{2}) 
means that x is a Gaussian random variable with mean m and variance σ^{2} 
x ~ N_{c}(m, σ^{2}) 
means that x is a circularly symmetric complex Gaussian random variable with complex mean m, total variance σ^{2}, the real and imaginary parts of x are independent, and the variance of the real and imaginary parts are each σ^{2}/2 
A_{eff} 
effective aperture of an antenna (square meters) 
A_{max} 
maximum effective aperture of an antenna (square meters) 
d 
transmitterreceiver separation distance (meters) 
EIRP 
effective isotropic radiated power 
λ 
wavelength (meters) 
c 
speed of light in free space = 3 × 10^{8} m/s 