**Chapter 3 Packet detection and some timing synchronization issues**

**3.2 Packet detection basic issues**

OFDM can be used in the context of continuous mode and packet-mode transmission networks. The two transmission schemes require somewhat different approaches to the synchronization problem. Continuous-mode systems transmit data continuously, so a typical receiver can initially spend a relatively long time to acquire the signal and then switch to tracking mode. On the other hand, the synchronization has to be acquired within a very short time after the start of the packet to archive high data rates for packet-mode systems. In MB-OFDM systems, the transmitted signals are OFDM symbols carried by a sequence of carrier frequencies depending on the TFC. Beside the usual OFDM synchronization tasks including packet detection, carrier frequency synchronization, and timing recovery, the MB-OFDM systems also need a band alignment procedure which aligns the transmitter time-frequency sequence.

**3.2 Packet detection basic issues **
**Basic scheme **

In MB-OFDM systems, there are 30 preambles as training sequences to train the receiver, as mentioned in 2.2. The four patterns for each channel have low cross correlation property to each other. And for each of the preamble, the autocorrelation is close to a delta function. Just like the direct sequence spread spectrum, the preamble can be used to channelize piconet. So the proposed packet detection scheme is a match filter (MF), as shown in figure 3.2.2. For the simplicity of implement, the match filter coefficients are the signs of the preamble, therefore there will be no multiplier in the match filter. The MF is proposed to match the preamble pattern corresponding to the channel which the receiver is going to access. The match filter output is compare to a threshold to determine if the signal comes. For power saving purpose, a constant threshold is preferred in the system. If a proper threshold is setting, the packet detection will be robust to interference and noise.

figure 3.2.2 MF structure

**Interference **

When there are two or more piconets operating at the same time, collision will happen in some band. Unfortunately, sometimes the power of interference is stronger than the desired signal. To simplify the detection algorithm, the MF collects the signal of single band. And the packet detection algorithm must be designed robustly to the interference.

First of all, the interference should be modeled in mathematical form to formulate the statistic property of MF output. Take a look at the OFDM symbol,

### ∑

^{−}

−

=

= ^{/}^{2} ^{1}

2 /

2 _{0}

) (

*N*

*N*
*n*

*t*
*nf*
*j*
*n**e*
*a*
*t*

*s* ^{π} , which can be represented as

### ∑

^{−}

−

=

= ^{/}^{2} ^{1}

2 /

) (

*N*

*N*
*n*

*n*
*n**w*
*a*
*t*

*s* , a weighted sum

of modulated data. If the data are taken as random variables and N is large, s(t) is close to a Gaussian process based on the central limit theorem (CLT).

The OFDM symbol of MB-OFDM systems is composed of 128 tones and each tone carries a QPSK symbol of power equal to unity and tones of indexes {0 64 65 66 67 68} are null tones. The power spectrum density of the MB-OFDM symbol is as shown in figure 3.2.3. And based on Weiner-Khinchin theorem, the autocorrelation of an OFDM symbol is the inverse Fourier transform of the PSD.

The autocorrelation is as figure 3.2.4. The autocorrelation function is approximately equal to delta function which means the Gaussian process is uncorrelated.

figure 3.2.3 PSD of MB-OFDM symbol

figure 3.2.4 Autocorrelation of MB-OFDM symbol

The OFDM symbol of MB-OFDM can be modeled as white Gaussian noise with zero mean because the DC tone is null. It will simplify the analysis of the MF output statistic property while the interference can be modeled as white Gaussian.

**Simulation model **

There are two kinds of simulation model, the first is to take the SOP interference as white noise and pass through a multipath channel then add to the received signal. In the second model, the received signal is the desired signal incorporated with thermal noise and the signal generated from another piconet.

As shown in figure 3.2.5.

figure 3.2.5 SOP simulation model

**Threshold setting **

The setting of the threshold is an import part of the detection algorithm. A simple setting method based on AWGN channel is derived.

The received signal after sampling is *r** _{i}* =

*s*

*+*

_{i}*n*

*, where si is the transmitted*

_{i}The value of Ai depends on the cross-correlation of the symbol and pattern as
shown in figure A-1, it is reasonable to assume Ai equal to 0 if the received
sequence is not match the pattern desired. And wi is a random variable with
distribution *N*(0,σ_{v}^{2}), where σ_{v}^{2} =*N*σ^{2}. So defined two hypotheses, H0 and H1,
where

H_{0} : *m** _{i}* =

*w*

_{i}H_{1 }: *m** _{i}* =

*A*+

*w*

*(3.2.2)*

_{i}Based on the proposal of MB-OFDM system, the value of Ai is 1300 when the
received signal matches the pattern. So the value of mi is a random variable of
Gaussian distribution with variance Nσ^{2} and bias 0 or 1300 depending on the
excess of boundary. The threshold can be set according to the desired false alarm
rate or missing rate, as shown in figure 3.2.6. In figure 3.2.6, the SNR is -10 dB
for which the noise power is ten times lager than the signal power, and

77

figure 3.2.6 The PDF of MF output

Due to the co-band interference of SOP, the SINR might get negative value in dB which means the power of interference is stronger than that of desired signal.

The packet detection algorithm in MB-OFDM systems should be robust to this kind of interference. It is important to how much noise the algorithm can tolerate.

A plot of the missing rate versus SNR is shown in figure 3.2.7. As shown in this figure, the false alarm rate and missing rate is greatly increasing when SINR lower than -3dB. It is desirable to design another more robust algorithm.

figure 3.2.7 FAR/Missing rate versus SNR of MF scheme

figure 3.2.8 FAR/Missing rate versus threshold of MF scheme