[STDS-802-16] [PREAMBLE] Complexity of GCL sequences
Dear preamble group member,
I would like to talk about the complexity concern people has on
polyphase sequences (e.g., GCL) versus PN sequences. But before the
analysis, I want to point out that for any sequence length (say P), we
have a simple and systematic way to come up at least P-1 GCL sequences
with optimal cross correlation (i.e., as simple as just picking a
smallest prime number that is larger than P and generating the
sequences, then truncating the sequences to length P). The design is a
5 minute work since we need to only choose a subset of them with the
best PAPR (all the P-1 sequences have 0dB PAPR at the Nyquist sampling
rate, but due to the oversampling effect caused by null subcarriers,
some sequences will have better PAPR than the others).
It is understandable that it can be difficult for people to accept it,
because GCL looks different than the PN sequences used in the 2K mode.
But GCL sequence is obviously a better choice if we are based on a
technical ground. It is worthwhile to mention that polyphase has
already been used in 802.16 OFDM mode (I hope this helps the emotional
transition). But there, only one sequence is of concern as there is no
cell-specific preamble. Once we need many polyphase sequences with low
PAPR and good cross correlation, GCL sequence is clearly a superior
solution.
Now let's analyze the complexity of GCL and PN sequences for two cases:
1) Case #1: We are acquiring initial synchronization:
In this case, a time-domain correlator of length Nfft may be used. The
coefficients of the correlator are complex for both PN and polyphase
sequences. In fact, the polyphase sequence in frequency is also a
polyphase sequence in time, which can help the implementation.
2) Case #2: Assuming timing is obtained (or if a timing hypothesis is
being tested):
In this case, the best way to detect the cell ID is to correlate the
received signal with all sequences, which can be performed in time or
more efficiently, in frequency domain. If in frequency domain, we take
the FFT, divide the sequence at each subcarrier, and IFFT back to time.
For polyphase sequence, it is a multiplication process at each
subcarrier, versus a sign change for BPSK PN sequences. The mobile
certainly has the capability to do complex valued multiplication at each
subcarrier. Actually it is the first step of demodulation, where the
signal at each subcarrier will be divided by the estimated channel. By
doing this correlation, not only the cell ID will be detected
reliably, but also we have the channel estimate.
Some people suggested to correlate the frequency domain data with the
sequence directly for PN sequences (assuming timing is obtained), which
amounts to adding the results at each subcarrier after dividing the
sequence. They may think that the autocorrelation of PN sequences can
be good enough to detect the cell ID. The problem is that we have a
channel with a lot frequency selectivity, so some subcarriers can be in
fade relative to the other subcarriers. As a result, only a portion of
PN sequence is contributing to the sum. Even in the case of a
single-tap channel (i.e, a non frequency selective channel), if the
arrival time is not zero, we will have a phase ramp in the frequency
domain after dividing that sequence. The sum of the phases at all
subcarriers is then zero, or close to zero since we have null
subcarriers, not a peak that we think we will get. In summary,
frequency domain correlation with a PN sequence cannot be give reliable
cell ID detection.
From the contributions, I see that everybody feels the need to have at
least new sequences for the other FFT modes. We are on the same page
from this perspective. I hope we can move the discussion fast (we do
not have much time left) and let's talk about whatever concerns we can
think of. Otherwise, we have to live with the existing preambles (non 2K
modes) that nobody is happy with.
Regards,
Jeff Zhuang
Motorola