Frequency and Timing Requirements

Chapter 2 Overview of WiMAX System

2.8 Frequency and Timing Requirements

Timing Requirements

For any duplexing, all SSs shall acquire and adjust their timing such that all uplink OFDMA symbols arrive time coincident at the BS to an accuracy of ±25% of the minimum guard interval or better. For example, this translates into ±8 samples in the case of 1024-FFT OFDMA.

Frequency Requirements

At the BS, the transmitted center frequency, receive center frequency, and the symbol clock frequency shall be derived from the same reference oscillator. At the BS, the reference frequency accuracy shall be better than ± ×2 10⁻⁶.

At the SS, both the transmitted center frequency and the sampling frequency shall be derived from the same reference oscillator. Thereby, the SS uplink transmission shall be locked to the

BS, so that its center frequency shall deviate no more than 2% of the subcarrier spacing, compared to the BS center frequency.

During the synchronization period, the SS shall acquire frequency synchronization within the specified tolerance before attempting any uplink transmission. During normal operation, the SS shall track the frequency changes by estimating the downlink frequency offset and shall defer any transmission if synchronization is lost. To determine the transmit frequency, the SS shall accumulate the frequency offset corrections transmitted by the BS (for example in the RNG-RSP message), and may add to the accumulated offset an estimated UL frequency offset based on the downlink signal.

Chapter 3 Decision Directed Channel Estimation

This section describes some channel estimation schemes to deal with different environments. After finding the packet starting point, channel estimation is performed to recover the channel frequency response. In this Chapter, the channel estimation will be introduced in detail. Then, we give a brief overview of the relevant technique.

3.1 Channel Estimation Structure

The simple structure of the channel estimation is show as Fig. 3-1. The received signal is modeled as ^{Y m}

( )

⁼^{H m X m}

( ) ( )

⁺^{N m}

( )

, Y is the received signal, X is QPSK i.i.d.

transmitted signal, H is with zero mean complex Gaussian distribution, N is white Gaussian noise, and m is subcarrier index.

Rx_signal

Initial Channel

Iteration-Decision directed

Final result ˆH H Y

Fig. 3-1 Channel estimation structure

There are two operations in the structure. One is the initial channel response estimation, the other is the iteration steps to refine the channel response until convergence.

3.2 Obtain The Initial Channel

We have some different choices to obtain the initial channel responses, namely, Pilot Symbol Aided, Linear Prediction, and Linear Interpolation.

Pilot Symbol Aided [17][18]

We add pilots X_Np to a symbol block. Denote N as the pilot numbers, and _p reasonably assume pilots X_Np are known. We can obtain the initial channel H_Np, then put the initial channel H_Np into a low pass filter. The output of the low pass filter is the final result ˆH .

Linear Prediction [15][16]

Suppose the last p s symbol channels are known perfectly, we predict the ' p+ 1 channel from the previous 1 ~ p channels.

Linear Interpolation

We need a buffer to save a block of data. We use Pilot Symbol Aided in the first and last symbol to obtain channel, and the initial channels of the other symbols are obtained by the Linear Interpolation.

3.2.1 Pilot Symbol Aided

Channel estimators usually need some kind of pilot information as a point of reference. A

pilot

Fig. 3-2 Pilot Symbol Aided

fading channel requires constant tracking, so pilot information has to be transmitted more or less continuously. Decision-directed channel estimation can also be used. But even in these types of schemes, pilot information has to be transmitted regularly to mitigate error propagation. The structure of the Pilot Symbol Aided is show as the Fig. 3-2. The channel of every symbol was estimated by pilot. The initial channel estimation of every symbol was shown in the follow description,

( ) ( ) ( )

The illustration is shown in Fig. 3-3

( )

⁰

Fig. 3-3 Initial channel H_Np

W is the DFT matrix. N is the pilot numbers. The sub-carrier index _p m is in the pilot

The complete channel estimation ˆH of all the sub-carriers is computed from h_L+₁ by

( ) ¹

The operations of the equations are the same as a low pass filter [23]. The equation is shown as Fig. 3-4 Low pass filter

IFFT

The parameter N has large correlation with the length of the channel impulse response _p

L and cyclic prefix length N . Now, we discuss the relationship of the pilot number _cp N , _p the channel length L , and the cyclic prefix length N .If the real channel impulse response _cp and channel frequency response are shown as Fig. 3-5 and Fig. 3-6

0 1 2 L M −1

Fig. 3-5 Real channel impulse response

0 1 2 m M −1

Fig. 3-6 Real channel frequency response

0 1 2 L M −1

Fig. 3-7 Initial channel impulse responseh_Np ( )⁰

Fig. 3-8 Initial channel frequency responseH_Np

In OFDM system, we assume the channel impulse responses are time invariant during a symbol time, and the cyclic prefix length N is always larger than channel impulse _cp

response length L . Because we want to reduce the inter-symbol interference (ISI) perfectly, so, the cyclic prefix length N is larger than the channel length L always. Than we just _cp discuss the relationship between N and _cp N during a symbol time. _p

N_cp ≤N_p

According to the sampling theory, the relationship between channel impulse response and channel frequency response can be shown in Fig. 3-7 and Fig. 3-8. According to the figures, we know that the initial channel H_Np through to the low pass filter still close to the

real channel impulse response.

N_p <N_cp

Similarly, the relationship between channel impulse response and channel frequency response are shown as Fig. 3-9 and Fig. 3-10.

We know that, if sampling rate is smaller than Nyquist frequency in frequency domain, the aliasing will happen, in the time domain.

According to Fig. 3-9 and Fig. 3-10, we know that the initial channel H_Np through to the low pass filter not close to the real channel. Because there will be aliasing on impulse

0 1 2 L M−1

0 n

( )

⁰

( )

h L

0 0 0

Fig. 3-9 Initial channel impulse responseh_Np

( )

⁰

H ^{H m}

( )

0 1 2 m M −1

0 0 0 0 0 0 0 0 0

Fig. 3-10 Initial channel frequency responseH_Np

0 1 2 L M−1

Fig. 3-11 Final resource of the channel impulse response.

response. According to the discussion, the parameter pilot number Np must be large than

N or equal to cp N . _cp

3.2.2 Linear Prediction

In this section, we introduce autoregressive (AR) model. When the p th-order AR (AR

( )

^p ) hypermodel for the frequency-selective fading channel is employed, we obtain a linear dynamic system which can be described by the following state-space model, the structure of the Pilot Symbol Aided is show as the Fig. 3-12

, , , ,

pilot

Fig. 3-12 Linear Prediction

is the Gaussian process noise, and it is assumed to be circular and independent of the receiver noise n. Because multi-path are independent and uncorrelated, so the weight numbers a _{l i}_, are calculated separately. We want to predict the t th symbol channel the from p th-order channel h_{l t}_{, 1}₋,h_{l t}_{, 2}₋ ,h_{l t}_{, 3}₋ ,...,h_{l t p}_,₋ as

( ) ( ) ( ) ( )

The above optimality equations are called the Wiener-Hopf equations for linear prediction. It can be rewritten in matrix form as

[ ] [ ] [ ]

Optimal solution is given by

[ ] [ ] [ ]

Toeplitz (square) matrix Any square matrix of the form

0 1 1

Is said to be Toeplitz.

3.2.3 Linear Interpolation

If we have B symbols in an OFDM block, we use Pilot Symbol Aided in first symbol of the block, and obtain this symbol channel. Than, we need a buffer to save a block data, and the first symbol of the next block. The initial channels of the other symbols are obtained by the Linear Interpolation. The structure is shown as Fig. 3-13

The first channel of the block1 is ˆH t , the first channel of the block2 is

( )

0 ˆH t . We save

( )

Fig. 3-13 Linear Interpolation

(

) (

)

After the last action, the initial channel is obtained. If the OFDM system active without the iteration step, just take the initial channel as a final result, the result is not close to the real channel. If the initial channel is obtained by Pilot Symbol Aided, the final result is not very terrible. But if the linear prediction is used, the error between initial channel and real channel will be accumulating to next initial channel. So, we do some iteration to close the real channel.

We have two difference choice to use. One is Decision directed, the other is Expectation Maximization (EM) Algorithm.

3.3 Iteration- Decision Directed

The iteration processing was introduced as follows. Before doing the iteration, the input of the lowpass filter is called the initial channel estimation H , but after the iterative is used, the ^{( )}⁰ output of the lowpass filter is the pth iterativel result ˆH^{( )}^p . The iteration process is shown in the Fig. 3-14. The initial channel estimation H is the input of the iteration processing, pass ^{( )}⁰ by lowpass filter, some of the AWGN is reduced. The receiver signal Y and the output of the lowpass filter ˆH are used to calculate the detection signal ^{( )}⁰ ˆX . The detection signal ^{( )}⁰

( )0

ˆX are used to be new pilots. After p times iteration, the output of the LPF ˆH⁽^p+¹⁾ is the final channel. The next iterative result of the detection signal is ˆX⁽^p+¹⁾.

LPF ^Quantize

Fig. 3-14 Decision directed iteration process

The iteration stop until the channel estimation ˆH⁽^p⁺¹⁾ is stable.

3.4 Decision Directed Channel Estimator

Base on the last discussion, we have three methods to obtain the initial channel, and two iteration methods.

Initial channel

1. Pilot Symbol Aided 2. Linear Prediction 3. Linear Interpolation

Iteration- Decision directed

We combine the methods to be six channel estimators 1. Decision directed Pilot Symbol Aided (DD Pilot) 2. Decision directed Linear Prediction (DD AR) 3. Decision directed Linear Interpolation (DD LI)

3.5 Channel System Environment

In this section, we first show the simulation environment for our study, including the system parameters and channel environments.

3.5.1 System Parameters

We have to specify the system parameters from all usable values provided by 802.16e so that the simulation environment could be constructed. The standard is very flexible in choice of bandwidth and cyclic prefix length. However, it would be difficult to conduct the simulation and implementation study without some particular sets of parameters. Hence we pick some sets of parameters shown in this section. The system profile we select is Wireless random generated binary data. The frame duration could be 5, or 10ms. Other parameter values are

Table 3-1 System Parameters Used in Our Study

Parameters Values

System Channel Bandwidth (MHz) 10 10 20

Sampling Frequency (MHz) 11.2 11.2 22.4

FFT Size 1024 2048 2048

Sub-carrier Spacing (kHz) 10.94 5.47 10.94

Useful Symbol Time (μsec) 91.4 182.8 91.4

Guard Time (μsec) 11.4 22.8 11.4

OFDM Symbol Time (μsec) 102.9 205.7 102.9

in Table 3-1

3.5.2 Channel Environments

Typical models of the wireless communication channel include additive noise and multi-path fading. For channel simulation, noise and multipath fading are described as random processes, so they can be algorithmically generated as well as mathematically analyzed.

3.5.2.1 Gaussian Noise

The simplest kind of channel is the additive white Gaussian noise (AWGN) channel, where the received signal is only subject to added noise. A major source of this noise is the thermal noise in the amplifiers which may be modeled as Gaussian with zero mean and constant variance. Incomputer simulations, random number generators may be used to generate Gaussian noise of given power to obtain a particular signal-to-noise ratio (SNR).

Table 3-2 Terrain Type vs. SUI Channels

Terrain Type SUI Channels

A: hilly terrain, heavy tree SUI-5, SUI-6 B: between A and C SUI-3, SUI-4 C: flat terrain, light tree SUI-1, SUI-2

Table 3-3 General characteristics of SUI channels

Doppler Low delay spread Moderate delay spread High delay spread

Low SUI-1, SUI-2, SUI3 SUI-5

High SUI-4 SUI-6

3.5.2.2 Slow Fading Channel

In slow fading, multipath propagation may exist, but the channel coefficients do not change significantly over a relatively long transmission period. The channel impulse response over a short time period can be modeled as

( )

parameters are time-invariant in a short enough time period.

3.5.2.3 Fast Fading Channel

With sufficiently fast motion of either the transmitter or the receiver, the coefficient of each propagation path becomes time varying. The equivalent baseband channel impulse response can then be better modeled as

( )

^{( )}

( )

Note that α_l and θ_l are now functions of time. But τ_l is still time-invariant, because the path delays usually change at a much slower pace than the path coefficients. The channel coefficients are often modeled as complex independent stochastic processes. If there is no line-of-sight (LOS) path between the transmitter and the receiver, each path may be made of the superposition of many reflected paths, yielding a Rayleigh fading characteristic. A commonly used method to simulate Rayleigh fading is Jakes’ fading model, which is a deterministic method for simulating time-correlated Rayleigh fading waveforms.

Table 3-4 SUI-1 Channel Model

Relative delay ( sμ or sample number) Average power