Continuous phase modulation processing for wireless networks
Various example embodiments are disclosed herein. According to an example embodiment, a method may include receiving a plurality of data symbols, generating a continuous phase modulated waveform based on the data symbols, generating a plurality of coefficients which represent the continuous phase modulated waveform, and wirelessly transmitting the plurality of coefficients via a plurality of subcarriers.
1. A method comprising:
receiving a plurality of data symbols;
generating a continuous phase modulated waveform based on the data symbols;
generating a plurality of coefficients which represent the continuous phase modulated waveform; and
wirelessly transmitting the plurality of coefficients via a plurality of subcarriers.
2. The method of claim 1 , wherein a complex baseband equivalent of the continuous phase modulated waveform is given by:
s ( t )=exp{ j φ( t;x )}
tε[nT,(n+1)T)
where φ(t;x) represents an information-carrying phase of the complex based band equivalent and T represents a symbol duration of the complex baseband equivalent.
3. The method of claim 2 , wherein the information-carrying phase φ(t;x) is defined as:
ϕ
(
t
;
x
)
=
2
π
h
∑
i
=
0
n
x
n
q
(
t
-
n
T
)
where h is a modulation index of the information-carrying phase, x denotes an information sequence included in a set {±1,±3, . . . , ±(M−1)}, and M denotes an M-ary alphabet size.
4. The method of claim 3 , wherein q(t) is defined as an integral of a frequency shaping function:
q
(
t
)
=
∫
0
t
f
(
τ
)
ⅆ
τ
where ƒ(τ) is defined as a frequency shaping function of duration LT defined such that q(LT)=½.
5. The method of claim 2 , wherein generating the plurality of coefficients includes performing a Gram-Schmidt orthonormalization procedure on a set of all possible continuous phase modulation waveforms over one symbol period in order to generate components of a filter bank.
6. The method of claim 1 , wherein generating the coefficients comprises passing a T-second interval of the continuous time modulated waveform through a bank of filters to obtain a vector of discrete-time coefficients └c 0,k , . . . , c N−1,k ┘, where
c
m
,
k
=
∫
k
T
(
k
+
1
)
T
s
*
(
t
)
f
m
(
t
-
k
T
)
ⅆ
t
.
7. The method of claim 6 , wherein s*(t) represents the continuous phase modulated waveform and ƒ m (t−kT) represents the bank of filters.
8. The method of claim 1 , wherein generating the coefficients comprises generating the coefficients which represent the continuous phase modulated waveform within a tolerable error, the tolerable error being based at least in part on a modulation level of the continuous phase modulated waveform.
9. The method of claim 1 , wherein wirelessly transmitting the plurality of coefficients includes performing a discrete Fourier transform on the coefficients to yield frequency domain coefficients.
10. The method of claim 9 , wherein wirelessly transmitting the plurality of coefficients further includes frequency division multiplexing the frequency domain coefficients.
11. The method of claim 10 , wherein wirelessly transmitting the plurality of coefficients further includes filtering the frequency division multiplexed frequency domain components.
12. The method of claim 11 , wherein wirelessly transmitting the plurality of coefficients further includes performing an inverse fast Fourier transform on the filtered frequency division multiplexed frequency domain components.
13. A method comprising:
receiving, by a wireless receiver, a plurality of symbols via a plurality of subcarriers;
performing a fast Fourier transform on the plurality of symbols;
demodulating the transformed symbols;
performing an inverse discrete Fourier transform on the demodulated transformed symbols to generate a plurality of coefficients;
generating a continuous phase modulated waveform based on the coefficients; and
sending data symbols to a hardware component based on the continuous phase modulated waveform.
14. An apparatus comprising:
a continuous phase modulator configured to receive a plurality of data symbols and generate a continuous phase modulated waveform based on the data symbols;
a filter bank configured to receive the continuous phase modulated waveform and generate a plurality of filter coefficients which represent the continuous phase modulated waveform;
a processor configured to map the filter coefficients onto a plurality of subcarriers; and
a wireless transmitter configured to wirelessly transmit the filter coefficients via the plurality of subcarriers.
15. The apparatus of claim 14 , wherein the filter bank is configured to generate the plurality of filter coefficients by Gram-Schmidt orthonormalizing the continuous phase modulated waveform.
16. The apparatus of claim 14 , wherein the filter bank includes a matched filter bank.
17. The apparatus of claim 14 , wherein the processor is configured to map the filter coefficients onto the plurality of subcarriers, the plurality of subcarriers including orthogonal subcarriers.
18. The apparatus of claim 14 , wherein the processor includes:
a discrete Fourier transformer configured to perform a discrete Fourier transform on the filter coefficients;
a frequency division multiple access modulator configured to map the transformed filter coefficients onto a plurality of subcarriers; and
an inverse fast Fourier transformer configured to perform an inverse fast Fourier transform on the mapped coefficients.
19. An apparatus comprising:
a wireless receiver configured to receive a wireless signal;
a fast Fourier transformer configured to perform a fast Fourier transform on the received signal;
a frequency division demodulator configured to demodulate the transformed signal;
an inverse discrete Fourier transformer configured to perform an inverse discrete Fourier transform on the demodulated signal to generate a plurality of coefficients;
a continuous phase modulated signal reconstructor configured to reconstruct a continuous phase modulated signal based on the coefficients; and
a symbol detector configured to detect signals based on the continuous phase modulated signal and send the detected signals to a hardware component.