Chapter 2 Overview of WiMAX System
2.4 Summery
Specification of IEEE 802.16 system has been introduced in this chapter. Unlike the CDMA-based 3G systems, which have evolved from voice-centric systems, WiMAX is designed to meet the requirements necessary for the delivery of broadband data services as well as voice. The Mobile WiMAX physical layer is based on Scalable OFDMA technology. The new technologies employed for Mobile WiMAX result in lower equipment complexity and simpler mobility management due to the all-IP core
network and provide Mobile WiMAX systems with many advantages over CDMA based 3G systems. We also introduce some key transmit techniques and their operations. By using these transmit techniques, the capacity and range of the system can be improved significantly.
Chapter 3
Channel Estimation and
Synchronization for WiMAX System
In this chapter, channel estimation and synchronization schemes are introduced. In real situations, synchronization and channel estimation should be done before data detection. First, two channel models corresponding to static or mobile environments are introduced in Section 3.1. Second, a jointly designed timing and frequency synchronization scheme is proposed in Section 3.2 and then computer simulations will be showed to confirm the performance of the proposed scheme. In Section 3.3, two channel estimation schemes are introduced to deal with different environments. Finally, Section 3.4 will describe the phase estimation and the residual frequency offset estimation scheme, and then computer simulations show that more accurate frequency synchronization can be obtained after compensating the residual frequency offset.
3.1 Channel Model
Wireless propagation channels have been studied for more than 50 years, and a large number of channel models are already available. The signal that has propagated through a wireless channel consists of multiple echoes of the originally transmitted signals; this phenomenon is known as multipath propagation. The different multipath components are characterized by different attenuations and delays. The correct modeling of the parameters describing the multipath components is the key point of channel modeling.
In first generation systems, a super-cell architecture is used where the base station and subscriber station are in LOS condition and the system uses a single cell with no co-channel interference. For second generation systems, a scalable multi-cell architecture with NLOS conditions becomes necessary. In WiMAX system, the wireless channel is characterized by:
¾ Path loss (including shadowing)
¾ Multipath delay spread
¾ Fading characteristics
¾ Doppler spread
The main channel models were considered here: Stanford University Interim (SUI) channel models [11] and International Telecommunication Union (ITU) channel models [12]. Each channel model was parameterized in order to best fit the particular channel characteristics. SUI channel models can be used for simulations, design, and testing of technologies suitable for fixed broadband wireless applications. However, ITU channel models are applied for the measurement based channel model. Even though multipath parameters are fixed in a measurement based channel model, it is useful to reflect the real operating channel conditions.
3.1.1 SUI Channel Model for Fixed Wireless Application
SUI channel models were proposed in [11] to model a statistic environment in IEEE 802.16d. There are many possible combinations of parameters to obtain different channel descriptions. A set of 6 typical channels were selected for the three terrain types that are typical of the continental US. The channel parameters are related to terrain type, delay spread, and antenna directionality and each channel model has three taps with distinct K-factor and average power. Table 1 shows an example of time domain attribute of the SUI-3 channel, which is chosen to evaluate the proposed algorithm.
Table 3.1: Parameters of SUI-3 channel models
Multipath Delay Profile
Due to the scattering environment, the channel has a multipath delay profile. It is characterized by τrms (RMS delay spread of the entire delay profile) which is defined as
2 2
( )
rms jPj j avg
τ =
∑
τ − τ 2 (3.1)where
avg jPj j
τ =
∑
τ ,τ is the delay of the jth delay component of the profile and j Pj is given by
P = (power in the jth delay component) / (total power in all components) j
RMS delay spread
A delay spread model was based on a large body of published reports. It was found that the RMS delay spread follows lognormal distribution and that the median of this distribution grows as some power of distance. The model was developed for rural, suburban, urban, and mountainous environments. The model is of the following form
rms T d y1 ε
τ = (3.2)
where τrms is the RMS delay spread, is the distance in km, is the median value of
d T1
τrms at d = 1 km, ε is an exponent that lies between 0.5-1.0, and y is a lognormal variant. Depending on the terrain, distance, antenna directivity and other factors, the RMS delay spread values can span from very small values (tens of nanoseconds) to large values (microseconds).
Fading distribution, K-factor
The narrow band received signal fading can be characterized by a Ricean fading.
The key parameter of this distribution is the K-factor, defined as the ratio of the “fixed”
component power and the “scatter” component power. The narrow band K-factor distribution was found to be lognormal, with the median as a simple function of season, antenna height, antenna beamwidth and distance. The model for the K-factor (in linear scale) is as follows:
s h b o
K =F F F K d uγ (3.3)
where
F is a season factor; s F =1.0 in summer; 2.5 in winter s F is the received antenna height factor h
F is the beamwidth factor b
K and o γ are regression coefficients
u is a lognormal variable which has 0 dB mean and a standard deviation of 8 dB.
Using this model, one can observe that the K-factor decreases as the distance increases and as antenna beamwidth increases.
Doppler spectrum
The random components of the coefficients generated in the previous paragraph have a white spectrum since they are independent of each other. The SUI channel model defines a specific power spectral density (PSD) function for these scatter component channel coefficients called “rounded” PSD which is given as
2 4
0 0
1 1.72 0.785
( ) 0
f f
S f ⎧ − +
= ⎨⎩
0 0
1 1 f f
≤ (3.4)
>
where 0
m
f f
= f . In fixed wireless channels the shape of the spectrum is therefore different than the classical Jake’s spectrum for mobile channels. Figure 3.1 shows that its shape of Doppler spectrum is convex.
Figure 3.1: Doppler spectrum of SUI channel models
Antenna correlation
The SUI channel models define an antenna correlation, which has to be considered if multiple transmit or receive elements, i.e. multiple channels, are being simulated.
Antenna correlation is commonly defined as the envelope correlation coefficient between signals transmitted at two antenna elements. The received baseband signals are modeled as two complex random processes X(t) and Y(t) with an envelope correlation coefficient of
( { } ) ( { } )
{ }
{ { }
2} { { }
2}
env
E X E X Y E Y E X E X E Y E Y ρ
− − ∗
=
− −
(3.5)
Note that this is not equal to the correlation of the envelopes of two signals, a measure that is also used frequently in cases where no complex data is available.
Antenna gain reduction factor
The use of directional antennas requires to be considered carefully. The gain due to the directivity can be reduced because of the scattering. The effective gain is less than the actual gain. This factor should be considered in the link budget of a specific receiver antenna configuration.
Denote as the Gain Reduction Factor. This parameter is a random quantity which dB value is Gaussian distributed with a mean
GBW
Δ
μgrf and a standard deviation
σgrf given by
(0.53 0.1I) ln( / 360) (0.5 0.04I)( ln( / 360))2
μgrf = − + β + + β (3.6)
(0.93 0.02I) ln( / 360)
σgrf = − + β (3.7)
where
β is the beamwidth in degrees
I = 1 for winter and I= -1 for summer
In the link budget computation, if G is the gain of the antenna (dB), the effective gain of the antenna equals . For example, if a 20-degree antenna is used, the mean value of
G− ΔGBW
GBW
Δ would be closed to 7 dB.
3.1.2 ITU Channel Model for Mobile Wireless Application
As we know, for fixed wireless application such as IEEE 802.16-2004, the SUI channel models are recommended for simulation. However, for mobile wireless application like IEEE 802.16-2005, the recommendatory channel model is not proposed at present. Here we choose International Telecommunication Union (ITU) channel model [12] for mobile and fixed use.
ITU channel model is a measurement based channel model proposed for the 3GPP WCDMA system. Delay and average power of each multipath for the ITU channel models are summarized in Table 3.2. Four or six multipath signals are generated in the wireless channel depending on the channel type as shown in Table 3.2 respectively. The ITU channel model can be modeled as
1
( ) ( ) ( )
N
n n n
n
w t p g t z t τ
=
=
∑
− (3.8)where z(t) and w(t) denote the complex low pass representations of the channel input and output respectively, p is the strength of the nth weight and n (t) is the complex Gaussian process weighting the nth replica.
gn
Table 3.2: Parameters of ITU channel models
As shown in Table 3.2, ITU channel model includes two environments. For the pedestrian test environment, this environment is characterized by small cells and low transmit power. Base stations with low antenna height are located outdoors, and pedestrian users are located on streets, inside buildings or residences. Its path loss is defined by
10 10
40log 30log 49
L = R+ f+
f
(dB) (3.9) where R denotes the separation (km) between the base station and the mobile station and f is carrier frequency.
For vehicular environment, it is characterized by large cells and higher transmit power. The model is applicable for in urban and suburban areas outside the high rise core where the buildings are of nearly uniform height. Its path loss is written as
L = 40 (1− ×4 10−3Δhb)log10R−18log10Δ +hb 21log10 +80 (dB) (3.10) where
R is the separation (km) between base station and mobile station f is carrier frequency
hb
Δ is base station antenna height (m), measured from the average rooftop level
The path loss model is valid for a range of Δ from 0 to 50 m. hb
The ITU channel model uses Doppler spectrum of classical Jake’s spectrum. As shown in Figure 3.2, the Doppler spectrum is concave.
Figure 3.2: Doppler spectrum of ITU channel models
3.2 Timing and Frequency Synchronization
A joint design of timing and frequency synchronization scheme is proposed in this section [13], [14]. Synchronization should be done before the rest work like channel estimation and data detection. Here, we consider three steps to complete the timing and frequency synchronization:
(i) adjust the window size according to the known preamble structure and compute the delay correlation outputs;
(ii) use the delay correlation outputs to perform the timing synchronization;
(iii) use the corresponding delay correlation outputs to perform the frequency synchronization.
Before performing the timing and frequency synchronization algorithms, the received signal is passed through a matched filter. The delay correlation outputs can be obtained by correlating the received signal and the known preamble over a window of v
samples. The window size depends on the preamble structure. Here, CP length is configured to be 1/4 of FFT length for simplicity. The delay correlation outputs ψ L and ψ of the ith received samples can be written as R preamble respectively, v is equal to half of short preamble length, f equals short preamble length, and n equals 1, 2, 3, and 4. There are 8 delay correlation outputs will be stored in each received samples.
sL sR
In the following paragraphs, timing and frequency synchronization schemes which make use of the delay correlation outputs to achieve synchronization will be introduced.
z Timing synchronization: Timing synchronization involves finding the most significant path and the best possible time instant of the start of received data.
After collecting groups of 8 delay correlation outputs obtained in Equation (3.11), the best timing instant can be detected by choosing the peak value of which is computed by where represents the timing acquisition metric, and z is the number of delay correlation outputs for the ith received samples and equals 8. Once the best starting position of the received signal is detected, frequency synchronization can then be performed.
( )i Ψ
z Frequency synchronization: Frequency synchronization deals with finding a wider range of the frequency offset between the transmitter and receiver local oscillators.
The frequency offset estimation is developed by choosing the delay correlation
outputs that make a peak value of Ψ . Hence a frequency offset estimate can be ( )i found based on the phase of the delay correlation outputs as follows:
Δ =f 2π1T ∠
{ }
φdopt (3.13)/ 2 1 / 2 1
* *
, , 1 , , 1
1 1
1 ( ) ( ) ( ) ( )
2
z z
L n L n R n R n
n n
i i i
T ψ ψ ψ ψ
π
− −
+ +
= =
⎧ ⎫
= ∠⎨ + ⎬
⎩
∑ ∑
i ⎭where T is the duration of the short preamble, dopt is the optimum timing acquisition instant, and z is the number of delay correlation outputs for the ith received samples. Although the residual frequency offset still exists, it can be estimated by using the pilot subcarriers embedded in the data symbols that will be introduced in Section 3.4.
Computer simulations for the joint design of timing and frequency synchronization scheme are shown in Figures 3.3 and 3.4. First, Figure 3.3 shows the matched filter output of the proposed timing synchronization algorithm in a SISO-OFDM system. The simulation is carried out in the environment of ITU Vehicular B channel and simulated at Eb/N0 = 0 dB. As seen in Figure 3.3, the jointly designed algorithm with timing synchronization gives satisfactory result in the mobile and Rayleigh fading channel. The start of the received signal can be estimated directly by detecting the peak of the timing acquisition metric Ψ . ( )i
0 5 10 15 20 25 30 35 0
0.5 1 1.5 2 2.5 3 3.5x 105
Match filter output
Figure 3.3: Matched filter output of the jointly designed algorithm for timing synchronization under ITU Vehicular B channel model (at Eb/N0 = 0 dB)
Sample index
Figure 3.4 shows the MSE of the frequency offset estimate as a function of Eb/N0
in a SISO-OFDM system. SUI-3 channel model is used in this simulation. With the frequency offset estimation method, the average MSE is about . For the scenario in which the oscillator offset is 20 kHz (about 10 ppm of the carrier frequency), the error of the frequency offset estimation method is just 60 Hz, which is much smaller than the subcarrier spacing.
3 10× −3
Figure 3.4: MSE of the jointly designed algorithm for frequency synchronization under SUI-3 channel model
0 5 10 15 20 25
10-4 10-3 10-2 10-1 100
Eb/No
mean square error
3.3 Channel Estimation
This section describes two channel estimation schemes to deal with different environments. After finding the packet starting point, channel estimation is performed to recover the channel frequency response. Preamble-aided channel estimation is suitable for static environment. However, pilot-aided channel estimation provides better performance than preamble-aided channel estimation in mobile environment. In the following we introduce the operations of two schemes [15], [16].
Long preamble (T) Impulse response Received LP (T)
Long preamble (F) Frequency response Received LP (F)
FFT FFT FFT
Known Unknown Known
Known
Known Known
Time Domain
Frequency Domain
*
Long preamble (T) Impulse response Received LP (T)
Long preamble (F) Frequency response Received LP (F)
FFT FFT FFT
Known Unknown Known
Known
Known Known
Time Domain
*
Frequency Domain
z Preamble-aided channel estimation: Preamble-aided channel estimation is carried out by using the long preamble. Owing to the same symbol structure as data symbols, long preamble becomes the best candidate for performing this job. After removing CP, a receiver can perform channel estimation by taking FFT of the received long preamble to obtain the LS channel estimate
LP LP
{ }
LPH R
FFT l
= (3.14)
where RLP is the received long preamble after taking FFT and lLP is the known long preamble. As shown in Figure 3.5, after taking FFT of received long preamble, we also require to transform the original long preamble into frequency domain. Thus, the channel frequency response can be obtained simply by dividing the FFT output of received long preamble and the FFT output of the original long preamble.
Figure 3.5: Preamble-aided channel estimation scheme
z Pilot-aided channel estimation: Pilot-aided channel estimation is based on LS criteria together with channel interpolation based on piecewise-linear interpolation method. The pilot arrangement of WiMAX systems is comb-type pilot arrangement. The estimate of pilot signals in the sth OFDM symbol based on LS criterion is given by
R represents the pilot subcarriers in the sth received symbol after taking FFT,
l = 1, 2, …, . After the estimation of the channel frequency response of pilot subcarriers, the channel response of data subcarriers can be interpolated according to adjacent pilot subcarriers. Piecewise-linear polynomial interpolation method is used here. Two successive pilot subcarriers are used to determine the channel response in between the pilot subcarriers. For data subcarrier k,
Np
Known pilot data Ps
Received
Known pilot data Ps
Received where M is the number of data subcarriers in between the adjacent pilot subcarriers and j = 1, 2, …, . The process of pilot-aided channel estimation is illustrated in Figure 3.6.
Np
Figure 3.6: Pilot-aided channel estimation scheme
3.4 Phase Estimation
Phase estimation can be regarded as a remedy after over-compensating the received signals by estimated frequency offset mentioned in Section 3.2 [24], [27]. The pilot subcarriers embedded in the data symbol can be used to estimate the rotating phase due to the residual frequency offset. The phase estimator can be expressed as
^ *
2
_ _
( ) ( ) j f sTr b
s k k
k pilot subcarrier index
q H P s R s πΔ
=
⎛ ⎞
=
∑
⎜⎝ ⋅ ⎟⎠ =Y es (3.17) where represents the known pilot data at the kth subcarrier in the sth OFDM symbol,k( ) P s
H ˆ
is the channel estimate of preamble in the frequency domain, R s k( ) represents the received data at the kth subcarriers in the sth OFDM symbol, and andTb
fr
Δ denote one symbol time and the residual frequency offset respectively. If there is any residual frequency offset, it is reflected in the phase estimator and we can obtain the rotating phase as φˆs =arg
{ }
qs = Δ2π frsTb. Therefore, we may have the information for phase tracking on a symbol-by-symbol basis. Furthermore, the residual frequency can be estimated easily via the phase estimator. According to q , s qs+1, where L denotes the number of symbols in a frame. After the residual frequency is compensated, we can perform channel estimation again to obtain the more accurate channel estimates.Figure 3.7 shows the MSE of the residual frequency offset estimate as a function of Eb/N0 in a SISO-OFDM system. The channel model used in this simulation is SUI-3 channel. Compared with the frequency offset estimation method mentioned in Section 3.2, the residual frequency offset estimation method provides better accuracy of
estimation. However, the frequency offset estimation method mentioned in Section 3.2 trades accuracy for a wider range of estimation. So the residual frequency offset estimation method can co-work with the frequency offset estimation method to obtain a wider range and better accuracy of estimates.
0 5 10 15 20 25
10-5 10-4 10-3 10-2 10-1 100
Eb/N
o
mean square error
jointly design algorithm for frequency synchronization
residual frequency offset compensation
Residual frequency offset compensation
Jointly designed algorithm for frequency synchronization
Figure 3.7: MSE of the residual frequency offset estimate under SUI-3 channel model
3.5 Summary
In this chapter, we first introduce two channel models: the first is SUI channel model which is used to form a set of channel models suitable for IEEE 802.16 fixed wireless applications and the second is ITU channel model which is used for mobile wireless applications. After that, we introduce the requirement tasks at the receiver.
Synchronization is first introduced and we propose a joint design of timing and frequency synchronization algorithm to lower the computational complexity. Then, channel estimation, phase estimation and residual frequency offset estimation are introduced in the rest part of the receiver. Furthermore, we compare the MSE of the frequency offset estimates after performing residual frequency offset estimation.
Computer simulations of the overall system will be showed in Chapter 4 and the proposed algorithms can work as expected.
The receiver functional blocks that are introduced in this chapter are basic blocks.
In order to adapt to different modes, some receiver functional blocks require to be modified. All the modification and more detailed experimental results will be given in Chapter 4.
Chapter 4
SC-OFDM-OFDMA SDR Architecture
Wireless communication standards are evolving rapidly. WiMAX now is an emerging suite of air interface standards for combined fixed, portable and mobile broadband wireless access. To meet the requirements of different standards, SDR technologies enable dynamic reconfiguration on the same platform and minimize the hardware variants. In this chapter, we propose a SC-OFDM-OFDMA SDR system to support the various air-interface standards specified by IEEE 802.16-2005 in a single SDR system. In this way, the system possesses as many common components as possible for these three modes, and the transmitter and receiver can be switched among the three modes via SDR operation. The rest of this chapter is organized as follows.
Concept of SDR will be described in Section 4.1. The transmitter architecture of the
Concept of SDR will be described in Section 4.1. The transmitter architecture of the