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(DD-FTN) algorithm to overcome the drawbacks of
conventional equalizers [14]. We will discuss these algorithms
in more details in the next section.
CAP: An alternative intensity modulation format that can
provide high order modulation is CAP modulation that enables
the generation of QAM-type signals but with simpler
implementation. In this case, baseband QAM signal with a
frequency shift to a subcarrier is required. CAP uses FIR filter
to achieve this up-conversion and modulate QAM signal to a
real signal or demodulate QAM signal from a received real
signal. Although the shaping and matched filters in CAP
system can be implemented using analog techniques [15], we
focus on digital implementation since it is the preferred choice
given today’s DAC and ADC technologies [16].
The DSP structure of CAP is also shown in Fig. 4. At the
transmitter side, the in-phase (I) and quadrature (Q)
components of the QAM signal are sent into two shaping filters
with impulse responses
( ) ( ) cos(2 )
Ic
h t g t f t
and
( ) ( ) sin(2 )
Qc
h t g t f t
that form a Hilbert transform pair.
A square-root-raised-cosine shaping filter
with a roll-off
coefficient of
is used as the baseband impulse response. The
center frequency
is given by
where
is the
frequency offset in order to avoid spectrum aliasing. Fig. 5(a)
shows the time domain response of the shaping filter. Fig. 5(b)
depicts the baseband QAM signal. After the shaping filter, the
electrical spectrum of generated CAP signal is shown in Fig.
5(c). The signal is shaped to be a Nyquist-like signal and
up-converted to an intermediate frequency (IF) of f
c
. After the
shaping filter, pre-emphasis is employed to compensate for the
bandwidth limitation of DAC and transmitter laser nonlinearity
with a time domain FIR filter. The processed signal is then fed
into a DAC to generate the electrical drive signal. Fig. 5(d)
shows the optical spectrum of optical CAP signal. The optical
signal after transmission would be directly detected by PIN PD
or APD, sampled and sent into two matched filters. The two
matched filters are the time-reversed version of the shaping
filters at the transmitter i.e.
( ) ( ) cos(2 )
Ic
m t g t f t
and
( ) ( ) sin(2 )
Qc
m t g t f t
in order to separate the I and Q
components. The separated I and Q signals are then combined
to re-construct the complex QAM signal in digital domain
which is followed by a re-sampling function. As for complex
high-order QAM signals, common adaptive equalization
algorithms such as constant multi modulus algorithm (CMMA)
[17], multi constant multi modulus algorithm (MCMMA) [18]
or decision directed least-mean-square (DD-LMS) can be used
to compensate various channel impairments (DD-LMS will be
discussed in more detail in the next section).
Fig. 6. Bit- or-power-loading for DMT transmission system. The blue curve is
the estimated SNR as a function of frequency and different amount of signal
powers (represented by the height of the green rectangles) and modulation
format can be encoded in each sub-carrier.
DMT: Also known as direct detected orthogonal frequency
division multiplexing (OFDM), DMT is another attractive
modulation scheme for low cost short-reach systems
[19][20][21]. In contrast with OFDM, only half of the
subcarriers in DMT are coded with information while the other
half are the complex conjugate of the first half to ensure that the
DMT signal is real for intensity modulation in IM/DD systems.
Like all multi-carrier systems, DMT enables bit loading or
power loading [22] that allow a flexible set of modulation
formats for each subcarrier optimized with respect to the
channel transfer function to maximize overall bit rate or power
margin. DMT has advantages such as high spectral efficiency,
high tolerance to impairments and flexible coding. The most
popular bit loading method is Chow’s algorithm [23] and Fig. 6
shows the principle of bit loading. Before signal transmission, a
probe signal would be transmitted and received to estimate the
end-to-end SNR at each frequency sub-carrier as shown by the
blue curve. In this case, high order modulation formats such as
128-QAM, 64-QAM can be coded in the subcarriers at low
frequency which have high SNR. 32-QAM, 16-QAM and
8-QAM can be coded in the subcarriers at the mid-frequencies
and QPSK or BPSK is coded in the subcarriers at high
frequency part to achieve similar bit error ratio performance
across all subcarriers. In this case, the bandwidth usage is
maximized. The DSP configuration for DMT systems is also
shown in Fig. 4. After FEC encoding, the S/P function transfers
Fig. 5. (a) Response of shaping filter (b) Electrical spectrum of baseband signal
(c) electrical spectrum of electrical CAP signal (d) optical spectrum of CAP
signal.