Receiver Architecture

One of the major drawbacks of OFDM systems is its high sensitivity to synchronization errors. Without accurate synchronization algorithm, it is not possible to reliably receive the transmitted data. In a MB OFDM system, the preamble is used for the sake of synchronizing OFDM signals. In the following section we will introduce the receiver architecture of the MB OFDM system, as shown in Figures 3.4, in detail [20].

3.2.1 Synchronization

Synchronization is a fundamental assignment for any communication system and should be done before the other work like channel estimation and data demodulation. Synchronization has two parts: timing synchronization and frequency synchronization

Packet Detection

Packet detection is the task of finding an approximate estimate of the start of the preamble of an incoming data packet as best it can. Because it is the first synchronization algorithm, the rest of the synchronization process is dependent on good packet detection performed. Fortunately, the preamble of the MB OFDM system has been designed to help the detection of the start edge of the packet. The cross-correlation method takes advantage of the periodicity of the synchronization symbols at the start of the preamble. As shown in Figure 3.5, the matched filter with the coefficient of the preamble sequence is proposed to correlate the received symbols. The preamble sequence is pre-assigned by the piconet channel of MAC layer. When some threshold of correlation is exceeded by the output power of the post-matched filter, the receiver will declare a packet detection. The commonly used value of the threshold is more than 250.

Symbol Timing Estimation

When the start of the preamble of an incoming data packet has been captured, the following job is symbol timing estimation finding the precise moment of when individual OFDM symbols start and end. The result of symbol timing estimation will circumscribe the DFT window, and the DFT result is then used to demodulate the subcarriers of the symbol. MB OFDM receiver has knowledge of the preamble available to them, which enables the receiver to use simple cross-correlation based symbol timing algorithm. According to an estimate of the start edge of the packet provided by packet detector, the symbol timing estimation algorithm improves the estimate to sample level precision, as shown in Figure 3.6. The refinement is performed by calculating the cross-correlation of the received signal r and a _n known reference s . The known reference _k s can be the end of the _k

synchronization symbols or the start of the channel estimation symbols. Equation 3.11 shows how to calculate the cross-correlation. The value of n that corresponds to maximum absolute value of the cross-correlation is the symbol timing estimate.

1 2

where the length L of the cross-correlation determines the performance of the algorithm. Larger value improves performance, but also increases the amount of computation required.

Frequency Synchronization

OFDM is highly sensitive to carrier frequency offset. It results in two main phenomena: reduction of amplitude of the desired subcarrier and ICI caused by nearby subcarriers. The first phenomena results from that the desired subcarrier is not sampled at the peak of the sinc function. The reason of second phenomena is that adjacent subcarriers are not sampled at the zero-crossings of their sinc function. The degradation in dB can be approximated by

( )

where f_∆is the frequency error as a fraction of the subcarrier spacing and T is the sampling period.

Frequency Offset Tracking

The data-aided algorithm is appropriate for the MB OFDM system. The preamble allows the receiver to use efficient maximum likelihood algorithm to estimate and correct for the frequency offset, before the actual information portion of the packet starts.

We introduce the algorithm that operates on the received time domain signal as

shown in Figure 3.7. First, the transmitted passband signal is

2 tx

j f nT n n s

y =s e ^π (3.13)

where s is the baseband signal and_n

ftxis the transmitter carrier frequency. The received signal rn is

f is the receiver carrier frequency and rx

tx rx

f_∆ = f −f is the difference between the transmitter and receiver carrier frequencies. Let D be the delay between the identical samples of the two repeated symbols. Then, the frequency offset estimator is developed as follows, starting with an intermediate variable z

( )

We observe that an angle of z is proportional to the frequency offset, and the frequency offset estimator is obtained by

ˆ 1

2 _s

f z

πDT

∆ = − ( (3.16)

where the (zoperator takes the angle of its argument

Carrier Phase Tracking

There is always some residual frequency error, because the frequency estimation is not accurate. The residual frequency offset results in constellation rotation. This is the reason why the receiver has to track the carrier phase after data symbols are received.

Data-aided tracking of the carrier phase is simple method for MB OFDM system. There are twelve predefined subcarriers among the transmitted data. These special subcarriers are referred to as pilot subcarriers. The receiver can exactly track the carrier phase with these pilots, symbol by symbol. After the DFT of the nth received symbol, the pilot subcarriers R are equal to the product of channel _{n k,} frequency response H and the known pilot symbols _k P_{n k,} , rotated by the residual

Assuming as estimate H_k of the channel frequency response is available, the phase estimate is

If the channel estimate is perfectly accurate, we get the estimator

2 2 2 2 2

There is no the phase ambiguity problem, because the pilot data are known at receiver. However, the channel estimation is not perfectly accurate, thus they contribute to the noise in the estimate.

3.2.2 Channel Estimation

In wideband communication systems, under the assumption of a slow fading channel, in which the channel transfer function is stationary within a packet duration, preambles or training sequences can be used to estimate the channel response for the following OFDM data symbols in the same packet. The channel estimation symbols in the preamble facilitate an powerful estimate of the channel frequency response for all the subcarriers. The quality of the channel estimation can be improved by averaging the two channel estimation symbols, because they are entirely identical symbols. the two received channel estimation symbols R1,k andR2,k are a product of the channel estimation symbol Xk and the channel Hk plus additive white Gaussian noise Nl,k

, , 1,2

l k k k l k

R =H X +N l = (3.20)

Thus the channel estimate can be calculated as

( )

where the channel estimation data power have been selected to be equal to one. The noise samples N1,k and N2,k are statistically independent, thus the variance of their sum divide by two is a half of the variance of the individual noise samples.