[STDS-802-16] [PREAMBLE] sequence discusssion
(Resend because I got a message from LISTSERV saying I cannot post to
this address? I also fixed a couple of typos)
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Dear preamble members,
I would like to share my thoughts and talk a little about our
contribution on sequence design for preamble, for tomorrow's discussions
on the conference call. Comments/discussions are welcome.
1) Basically, I think both the PAPR and cross correlation are important
characteristics.
In some environment or deployment scenarios such as suburban/rural or
reuse factor of more than one, the performance can be noise limited, in
which case a power boost allowed by a low PAPR is important (2dB in SNR
can mean whether FCH and MAP can be decoded or not). The power boost of
preamble can also help the differentiation between preamble and data
portions in a frame, if an energy based detection is used for rough
timing offset detection. In some other environment or deployment
scenarios such as urban/micro-cell or reuse one, the performance can be
interference limited, in which case a good cross correlation among
preambles is important for channel estimation and for reducing false
alarms in cell ID detection.
So, what does a cross correlation between two sequences mean under
multipath environment? And how is it defined? Just like
auto-correlation, the cross correlation is a vector with each element
corresponding to each possible relative lag (or shift) between the two
sequences. This means that each multipath of the undesired channel
interferes with the desired channel at each tap. A good cross
correlation means that, after correlating with the desired sequence, the
interference will be spread more evenly over a window of the sequence
length. Therefore, at least the significant taps of the desired
channel will be preserved better.
In an OFDM system, because of the CP, a time domain linear correlation
will turn into a cyclic one for the Nfft samples excluding the CP (i.e.,
the results of cyclic correlation are equivalent to those of linearly
correlating with a sequence that extends itself cyclically. So, we can
use the efficient FFT tool to do correlation, which is to perform
element wise division in frequency domain and then IFFT back to the time
domain.
2) Polyphase sequences
Polyphase sequence has amplitude one and a set of discrete phases.
Chirp sequences (such as the Generalized Chirp Like or GCL sequences) is
a polyphase sequence with special subsets including Zadoff-Chu,
Frank-Zadoff, and Milewski sequences (sometimes they are called CAZAC
sequences). Polyphase sequences are much more appealing for frequency
domain processing than in time domain, and 802.16 OFDM mode uses
polyphase sequence. At Nyquist sample rate, the PAPR of polyphase
sequences are 0dB and it degrades slightly with oversampling (which
happens when we have null subcarriers).
A particular family of GCL sequence we like is when the length (P) is a
prime number. In this case, we can have up to P-1 different sequences
whose pairwise cyclic cross correlation property is optimal (i.e., the
amplitude of correlation at all lags are the same that equals to
1/sqrt(P)). The optimal cross correlation holds for any pair of such
designed GCL sequences. But for other sequences such as a PN sequence,
the correlation at some lags can be much larger than 1/sqrt(P) and at
some other lags can be much smaller. It is then difficult to say
whether a significant tap detected is the true channel or caused by the
interference. Due to oversampling, among the P-1 sequences, some GCL
sequences in time domain will have a better PAPR than the others, so we
an choose those with the best PAPR. If the desired length is not a prime
number, we can truncate from the GCL sequence whose length is the prime
number closest to the desired length. The properties still hold well.
This is a systematic design for any sequence length and the sequence can
either be generated on the fly or stored. It is much more difficult to
hand craft PN sequences to give both low PAPR and good cross
correlation. And a good correlation is particularly difficult to get if
the PN sequence is short (see PAPR and cross correlation comparison
provide in our previous power point contribution)
Compared with using a BPSK PN sequence, the added complexity for GCL
sequence detection and channel estimation is that a complex-valued
multiplication is involved at each pilot subcarrier (or a phase rotation
if converted to polar coordinates). However if the correlation is
performed in the time domain directly (say a sliding correlator for
timing synchronization), both PN and GCL sequences will have
complex-valued coefficients.
Sometimes, people mention that cell ID can be detected with correlating
the frequency domain samples (i.e., post-FFT) with the PN. But note the
fading across subcarrier can be very significant (20-30 dB variation).
If half of the subcarriers are faded more than the rest half, such a
frequency domain correlation may be unsatisfactory.
Best Regards,
Jeff Zhuang
Motorola