Apparatus and method for performing properrizing frequency shift(p-FRESH) vectorizing
To achieve these and other advantages and in accordance with the purpose of the present invention, as embodied and broadly described herein, there is provided a method for performing properizing frequency shift (p-FRESH) vectorizing, the method comprising: converting a scalar-valued input signal of length L into a 2L-by-1 vector-valued output signal including complex conjugate signal of the input signal; modulating the input signal and the complex conjugate signal each with L different carriers; and bandpass filtering the modulated signal to form the output signal, wherein the output signal is band-limited to a half-Nyquist zone (F + ).
1. A method for performing properizing frequency shift (p-FRESH) vectorizing, the method comprising:
converting a scalar-valued input signal into a 2L-by-1 vector-valued signal including L signals of the input signal and L complex conjugate signals of the input signal, wherein L is an integer;
modulating the 2L-by-1 vector-valued signal with L different carriers by modulating each of the L signals and the L complex conjugate signals with the L different carriers;
bandpass filtering the modulated 2L-by-1 vector-valued signal to form an output signal; and
transmitting the output signal,
wherein the output signal is defined by a following expression:
Y
l
(
t
)
=
{
(
X
(
t
)
ⅇ
-
2
j
π
f
l
t
)
*
g
(
t
)
,
for
l
≤
L
(
X
(
t
)
*
ⅇ
-
2
j
π
f
l
-
L
t
)
*
g
(
t
)
,
for
l
>
L
,
where t denotes time, f l denotes center frequency of an l-th Nyquist zone, X(t) is the input signal, X(t)* is the conjugation of the input signal, g(t) is the impulse response bandpass filtering a half-Nyquist zone(F+), Y l (t) is the output signal, and l=1, 2, . . . , 2L.
2. The method of claim 1 , wherein a fourier transform G(f) of the g(t) is defined by following expression:
G
(
f
)
=
{
1
,
∀
f
∈
ℱ
+
0
,
elsewhere
.
3. The method of claim 1 , wherein the input signal has zero-mean, and the output signal is proper-complex zero-mean vector-wide-sense stationary (WSS) process when the reference rate has integer values of the cycle period of the input signal.
4. The method of claim 1 , wherein the output signal is jointly wide-sense stationary (WSS), and an auto-correlation function of the output signal has second-order property of the input signal.
5. An apparatus for performing properizing frequency shift (p-FRESH) vectorizing in a wireless access system, the apparatus comprising:
a Radio Frequency (RF) module configured to transceive signals; and
a processor configured to control the RF module, wherein the processor is further configured to:
convert a scalar-valued input signal to a 2L-by-1 vector-valued signal including L signals of the input signal and L complex conjugate signals of the input signal, wherein L is an integer,
modulate the 2L-by-1 vector-valued signal with L different carriers by modulating each of the L signals and the L complex conjugate signals with the L different carriers
bandpass filter the modulated 2L-by-1 vector-valued signal to form an output signal, and
transmit the output signal,
wherein the output signal is defined by a following expression:
Y
l
(
t
)
=
{
(
X
(
t
)
ⅇ
-
2
j
π
f
l
t
)
*
g
(
t
)
,
for
l
≤
L
(
X
(
t
)
*
ⅇ
-
2
j
π
f
l
-
L
t
)
*
g
(
t
)
,
for
l
>
L
,
where t denotes time, f l denotes center frequency of an l-th Nyquist zone, X(t) is the input signal, X(t)* is the conjugation of the input signal, g(t) is the impulse response bandpass filtering a half-Nyquist zone(F+), and Y l (t) is the output signal, l=1, 2, . . . , 2L.
6. The apparatus of claim 5 , wherein a fourier transform G(f) of the g(t) is defined a following expression:
G
(
f
)
=
{
1
,
∀
f
∈
ℱ
+
0
,
elsewhere
.
7. The apparatus of claim 5 , wherein, the input signal has zero-mean, and the output signal is proper-complex zero-mean vector-wide-sense stationary (WSS) process when the reference rate has integer values of the cycle period of the input signal.
8. The apparatus of claim 5 , wherein the output signal is jointly wide-sense stationary (WSS), and an auto-correlation function of the output signal has second-order property of the input signal.