802.11a OFDM Long Preamble Cyclic Prefix

Question

im currently looking at an implementation of the preamble for OFDM in the 802.11a standard, as shown in the pic below

What I dont understand is the cyclic prefix (labelled GI2). Based on this picture we have the two long preamble symbols (Labelled T) each of which are 64 symbols long, and then a length 32 cyclic prefix which adds up to 160 symbols, as expected. However, all the other CPs in this standard are length 16 (i.e. for data symbols, and even the short preamble is easily implemented this way), which contradicts this length 32 CP.

I understand this sorta works if you treat the long preamble as a single length 128 symbol, with a length 32 CP, but in terms of hardware implementations this would mean using a different length FFT for this one symbol which doesn't make sense to me.

Instead, I would have expected the orientation of the long preamble symbols to be more like

+---------------+---------------------+--------------+---------------------+
|               |                     |              |                     |
|  length 16 CP | 64 Data Symbols (T) | Length 16 CP | 64 Data symbols (T) |
|               |                     |              |                     |
+---------------+---------------------+--------------+---------------------+

Now I question, does it actually make a difference? i.e. the actual data symbols are the exact same in both cases, it's just the location of the CP and what's in the CP which is different (in the standard its the last 32 symbols of the second T, whereas in my example its the last 16 of T copied twice).

But then, looking at schmidl and Cox's original paper (Part III http://home.mit.bme.hu/~kollar/papers/Schmidl2.pdf) it seems the requirement is to have a long preamble in which the two halves of the symbol are the same in order to properly take advantage of their method of decoding - so perhaps my idea wouldn't work?

I guess what im asking is, is there a way to use the same OFDM Modulator (i.e. one which does the cyclic prefix automatically) for the short preamble and for the long preamble? For the short preamble it works well because each of the 10 short preambles are length 16, and the CP is also length 16, so when you chop 16 off the end of the symbol and add it to the start it takes the OFDM symbol from having 4 short preambles (in its original length of 64) to 5 preamble symbols (in its new length of 80) ... then you just repeat this and you have your 10 short symbols - but that same logic doesn't follow for the long preamble.

Alternatively, can I just use one long preamble symbol which has 32 repeated symbols and a length 16 CP. I understand this isn't to spec but what would the performance deficit be between having 1 or 2 long preamble symbols?

I hope someone can help me out here

Thanks!

Answer 1

The spec defines the LTF just like you're showing in the time domain.

There is no need to use a different OFDM modulator, simply produce time-domain symbol T with the usual modulator, then concatenate the last half of the symbol with 2 more copies of T (or equivalently cyclically read out T starting half way through the symbol for 8us worth of samples).

As for replacing the LTF with two cyclically prefixed copies of the symbol T, obviously that would not comply with the standard. It also undermines the apparent cyclic convolution property you are trying to achieve with the prefix (although the channel really shouldn't be so long that a double length CP is necessary, the extra length is helpful for timing recovery). And yes, just about every 802.11 receiver out there will rely on this behavior in the LTF and will fail badly without it.

As for using a long preamble symbol that has 32 repeated samples, that simply would not have the frequency resolution necessary to establish a channel estimate for every subcarrier, but it would work with a roughly 3dB worse channel estimate for a hypothetical non-802.11 protocol.

If you're still having trouble seeing how this construction works, I'd recommend rereading the standard starting at Eq. 17-8. The terms of Eq 17-9 are exactly the cyclically time shifted coefficients of a length 64 IFFT (no need for a separate length ifft), and given that there are nonzero odd frequency domain coefficients, the periodicity of this signal is the same as the periodicity of exp(j * 2 * pi * delta_f), 3.2us or 64 20MHz samples.