05-05-2011, 03:38 PM
1 Introduction
Orthogonal frequency division multiplexing (OFDM) is widely used today due to it's robust-
ness to multipath e®ects and e±cient implementation using FFT. The most common one called
OFDM/QAM, which uses QAM as modulation and rectangular pulse as shaping ¯lter. For
OFDM/QAM, the robustness to multipath is attained by inserting guard interval. If the max-
imum delay of transmitting channel is less than guard interval, there exists neither intersymbol
interference (ISI) nor interchannel interference (ICI) [1]. For discrete implementation, the guard
interval is realized by inserting cyclic pre¯x (or su±x).
OFDM/QAM has a couple of drawbacks. First the inserting of guard interval reduces spectral
e±ciency since less time slots are available for transmitting of useful information. This also lead to
a lower power e±ciency since the receiver ¯lter is not matched to transmitter ¯lter. Furthermore,
the large sidelobe level of rectangular pulse makes system spectral incompact. To counteract these
drawbacks, OFDM with band-limited shaping pulses was ¯rst suggested by Chang [2]. To satisfy
orthogonality, o®set QAM (OQAM) is used as modulation in subchannels. Such kinds of OFDM
is now called OFDM/OQAM. The e±cient implementation based on FFT is also possible for
OFDM/OQAM [3][4][5].
Since the lack of guard interval, OFDM/OQAM can attain higher spectral e±ciency. But
equalizer is needed to eliminate the multipath e®ects. Tu [6] explored the MMSE equalization
problem for OQAM transmission. Hirosaki [7] found that a single branch T=2 fractionally spaced
equalizer is enough to eliminate ISI and ICI simultaneously. Such an equalizer is highly e±cient.
It can also be easily implemented since the signal out of FFT module [4] is just sampled with an
interval T=2. Similar approach is also addressed for echo cancellation problems [9].
First we will present a base-band model and formulate the output T=2 sampled sequence before
detector in Section 2. Then we derive the optimal MSE equalizer in section 3. Although similar
work has been done by Hirasaki [7], the equalizer coe±cients in his work are real-value based and
thus can't be directly used for our further discussion. By way of parenthesis, we also derive the
adaptive recursion. In section 4, by noting that Hirasaki doesn't fully explore the property of
non-weighting OFDM/OQAM system, we prove mathematically that the correlation functions is
stationary. This good property leads a complex-valued matrix-vector formed objective function,
which is same to ordinary single carrier QAM transmitting system. Then in section 5, based on
the simpli¯ed objective function, we derive the relationship of the minimum mean square error
(MMSE) with respect to equalizer taps.
Download full report
http://www.iet.ntnu.no/projects/beats/Do...ion_v2.pdf
Orthogonal frequency division multiplexing (OFDM) is widely used today due to it's robust-
ness to multipath e®ects and e±cient implementation using FFT. The most common one called
OFDM/QAM, which uses QAM as modulation and rectangular pulse as shaping ¯lter. For
OFDM/QAM, the robustness to multipath is attained by inserting guard interval. If the max-
imum delay of transmitting channel is less than guard interval, there exists neither intersymbol
interference (ISI) nor interchannel interference (ICI) [1]. For discrete implementation, the guard
interval is realized by inserting cyclic pre¯x (or su±x).
OFDM/QAM has a couple of drawbacks. First the inserting of guard interval reduces spectral
e±ciency since less time slots are available for transmitting of useful information. This also lead to
a lower power e±ciency since the receiver ¯lter is not matched to transmitter ¯lter. Furthermore,
the large sidelobe level of rectangular pulse makes system spectral incompact. To counteract these
drawbacks, OFDM with band-limited shaping pulses was ¯rst suggested by Chang [2]. To satisfy
orthogonality, o®set QAM (OQAM) is used as modulation in subchannels. Such kinds of OFDM
is now called OFDM/OQAM. The e±cient implementation based on FFT is also possible for
OFDM/OQAM [3][4][5].
Since the lack of guard interval, OFDM/OQAM can attain higher spectral e±ciency. But
equalizer is needed to eliminate the multipath e®ects. Tu [6] explored the MMSE equalization
problem for OQAM transmission. Hirosaki [7] found that a single branch T=2 fractionally spaced
equalizer is enough to eliminate ISI and ICI simultaneously. Such an equalizer is highly e±cient.
It can also be easily implemented since the signal out of FFT module [4] is just sampled with an
interval T=2. Similar approach is also addressed for echo cancellation problems [9].
First we will present a base-band model and formulate the output T=2 sampled sequence before
detector in Section 2. Then we derive the optimal MSE equalizer in section 3. Although similar
work has been done by Hirasaki [7], the equalizer coe±cients in his work are real-value based and
thus can't be directly used for our further discussion. By way of parenthesis, we also derive the
adaptive recursion. In section 4, by noting that Hirasaki doesn't fully explore the property of
non-weighting OFDM/OQAM system, we prove mathematically that the correlation functions is
stationary. This good property leads a complex-valued matrix-vector formed objective function,
which is same to ordinary single carrier QAM transmitting system. Then in section 5, based on
the simpli¯ed objective function, we derive the relationship of the minimum mean square error
(MMSE) with respect to equalizer taps.
Download full report
http://www.iet.ntnu.no/projects/beats/Do...ion_v2.pdf