Chapter 2 System Platform
2.2 System Block Diagram
2.2.3 Receiver
2.2.3.3 Phase Recovery
In our proposed synchronization method, the remaining CFO and SCO compensation are solved at the same time in the frequency domain. Because the estimation and compensation method are all performed by estimating and compensating the data phase, this partition can be called as “Post-FFT Phase Compensator”.
According to the equation (2.21) and (2.x), the remaining CFO and SCO will present some symptoms at the carrier phase. However, there are some different between the two effect. From equation (2.21), we know that the remaining CFO will induce a phase rotation to all the carriers in an OFDM symbol. The SCO will induce a linear phase rotation shown in the equation (2.x). The jointed effect of the two offsets
is shown in Figure 2.22. Here we will propose a compensation method which can mitigate these two effects. We compensate the two effects at the same time in frequency domain and the signal upsampling and feedback to time domain control are not needed.
Figure 2.22 Phase rotation of each subcarriers in an OFDM symbol.
From above figure, the behavior of the carrier phase suffered from effect of the remaining CFO and SCO can be modeled as a linear equation (2.22). The k means the subcarrier’s indexes, the θl,k is the phase rotation of the lth symbol kth carrier and C0l, C1l are two coefficients.
, 0 1
l k C l C kl
θ = + (2.22)
0
1
k k
C = M
∑
θ (2.23)1 2 k k
k
k
C k
θ
⋅
=
∑
∑
(2.24)The problem of the remaining CFO and SCO is that the phase distortion will cause decision error if the rotation angle is larger than the decision boundary. The most direct compensation method is to compensation the rotation angle with the opposite direction directly. Each subcarrier’s rotation angle can be calculated using the equation (2.22). And the least squares algorithm is used to estimate these two coefficients. The angle of the pilot data can be used to perform the estimation.
Because of channel noise and ICI, some estimation results are not very stable. In our design, weighting function and moving average are needed for a more stable compensation. Figure 2.23 is the phase recovery block diagram.
Figure 2.23 The phase recovery block diagram.
The θ0 is equal to the mean phase term C0 in equation (2.22). The θ1 is the linear phase term which is equal to the C1‧k. The θ0,comp and θ1,comp are the estimation phase having to be compensated to each subcarrier. The θ0’ and θ1’ are the estimation phase of the last symbol. W0 and W1 are weighting coefficients for the θ0 and θ1. NTS
is the OFDM symbol time including GI.
Because the pilot phase has been subtracted by θcomp’ before phase error estimation, the estimated phase error can be described as below where the θr,0 and θr,1
are the mean and the linear phase error of pilots. The following equations explain the
behavior of Figure 2.23.
At first, the recently received pilots have to be compensated with the phase error in previous estimation. The estimated phase error outputted from the least squares estimator has to be jointed into the weighting function to estimate the latest phase error. The latest phase can be used to compensate the other carriers’ data. It is also input into the storage for the estimation of the next symbol. Equation (2.28) and equation (2.29) are the estimated mean phase error and the linear phase error. They are the compensated angle, too.
We also use some mechanisms to avoid making a wrong estimation. The first one is to add an evaluation time. At the start of a transmission, we have to observe several symbols to get a more correct tendency. The symbol number is Ncomp. From equation (2.25) to equation (2.29) and Figure 2.23, we know that if the symbol index is smaller
than Ncomp, the SCO compensation is stopped. In the evaluation time, the estimation is continuous and the weighting functions are different. The second method is to judge if the estimation result is reasonable. If these slops between different pilots’ phase have the same trend, the estimation result will be accepted. In a low SNR environment, the noise will make a violent change on each pilot. Accepting the estimation hastily may cause an excessive response and need a long time to mitigate the memory effect of wrong estimation in the feedback loop. In chapter 5, the mechanism will be implemented upon an application.
Chapter 3
THE PROPOSED DESIGN
In this section, adaptive channel equalization and phase noise compensation scheme will be proposed. The target OFDM system is the packet-based and burst synchronization scheme. In a real system, several synchronization issues must be taken care including frame detection (FD), multipath cancellation, and other channel effects. In our design, we will considerate not only our function blocks but also the whole system.
The total compensation scheme contains two partitions. One is the adaptive channel equalization for singular channel condition. The other is phase noise acquisition and compensation to make up the overall system require. This chapter is the distinguishing feature in the thesis.
3.1 Singular Channel Problem
Although there have been already many frequency domain deconvolution techniques [20], they are still not suitable in our situation because multipath may be composed of severe selective fading and unstable poles instead of convergent filtering. Besides, these existing frequency domain methods which produce aliasing CFR require more hardware cost. Another issue is the problem of traditional one-tap equalization, which noise would be enhanced largely on very deep channel frequency response. This effect shown in Figure 3.1 makes the performance unpredictable. As a result, we are going to propose a novel adaptive frequency domain approach to overcome the
significant issue.
Figure 3.1 Noise would be enhanced largely on very deep CFR.
3.2 Adaptive Channel Estimation
In OFDM systems, instead of TDE, FDE is used to remove the influence of multipath fading channel, which requires less computation. In an ERP-OFDM of 802.11g packet, the received long preamble, YL(k), is used for CFR estimation, where the estimated CFR, HE(k), can be derived as
( ) ( )
XL(k) indicates the known long preamble data. Owing to the AWGN in long preamble, equalization is not perfect and causes data drift. Time domain CFO and SCO acquisition are also influenced by AWGN. These residual offsets after time domain compensation still causes received data incorrect. To remove the imperfect factors left in frequency domain, a joint scheme is proposed to remove the equalization error, residual CFO and SCO simultaneously with channel equalization.
The adaptive CE using smooth filter (SF) and decision-directed channel error tracking (DDCET) is proposed for high performance and low design complexity. SF has been applied to provide high performance and low complexity for CE [7], but the noise floor problem degrades performance in high SNR conditions. Combining SF and DDCET can enhance the total performance. The block diagram of the proposed scheme is given in Figure 3.2.
Figure 3.2 Block diagram of the adaptive EQ with PR.
For channel estimation, the inverse of known preamble, XL-1(k), is selected to multiply with the received preamble, YL(k). Smooth filter is then used to reduce the AWGN of estimated CFR, HE(k) . For basic channel equalization, received data, Xe(k), is multiplied with the estimated CFR, HA(k). However, in order to remove the CE error, residual CFO and SCO, an error estimator is applied to trace the compensation value. The estimator includes a feedback decision-directed channel estimation (DDCE), which is used to trace the equalization error by using the de-mapping information of the received data; and a weighted phase recovery, which is used to trace the residual CFO and SCO by using the phase information between the received pilots, Pe(k), and the known pilots, PD(k). A joint compensation value is then feedback to the equalization operation; remove imperfect factors of the next OFDM symbol altogether with the original equalization multiplier. That is, CE error, residual CFO, and SCO are compensated with equalization simultaneously. Detail algorithms are discussed below.
3.2.1 Fixed-coefficient Smooth Filter
The proposed smoothing filter is a finite impulse response (FIR) filter with exponential-decay power. The smoothing function is described as
( )
After estimation by dividing long preamble, the estimated CFR, HE(k), will be convoluted by the proposed smoothing filter. The convolution equation is listed as
(3.3)
After the filter, each subcarrier of CFR will be weighted summation of itself and nearby subcarriers within 2WS+1 bandwidth. And the weighting function is equal to filter coefficient ℓ·RS. Since additive noise is zero-mean, the weighted summation will decrease the noise power. Assume that H(k) is the true CFR; WL(k) is the frequency-domain additive noise in long preamble; and εHS(k) is the noise of smoothing filter. The smoothed CFR, HS(k), can be described as
( ) ( ) ( ) ( ) ( )
In low SNR regions, smoothing noise, εHS(k), can be deal with the additive noise, WL(k)/ XL(k), efficiently. In high SNR regions, however, the additive noise power will be neglected and the smoothing noise will dominate the estimation error and degrade the estimation performance. Thus we can find
( ) ( )
From equation (3.5), we find the estimation error will saturate to smoothing noise in high SNR regions. Thus the smoothing filter is suitable for low SNR regions. And in high SNR regions, the proposed adaptive channel manager will detect the error saturation and select estimated CFR, HE(k), instead of smoothed CFR, HS(k), for
equalization.
3.2.2 Adaptive Channel Manager
In high SNR regions, since the smoothing noise degrades the estimation performance, adaptive channel manager will select estimated CFR as the adapted CFR, HA(k). It detects saturation of estimation error by receiving the information, LSNR, about SNR from AGC. We can get the SNR criterion, L0, with the saturation noise from the simulation. Dependent on L0, the adapted CFR will be selected as
(3.6)
From the algorithm, adaptive channel manager use the SNR criterion for selection of adapted CFR. The adapted CFR can be described as
0
By means of adaptive channel manager, channel estimation error will never saturate in high SNR regions and the performance is enhanced. After receiving preamble, adapted CFR will be inversed and stored in inversed CFR buffer. The residual estimation error, εHA(k), will be traced and removed in decision-directed tracking loop described in the following section.
3.2.3 Feedback Decision-directed Channel Error Tracking
Feedback DDCET is applied for high performance and low complexity.
Computation-save control (CSC) is applied in DDCET to reduce redundant tracking.
Channel error tracking can be turned off after several OFDM symbols cause the tracking error is converged to a very small value. The feedback DDCET estimates the CFR error by the de-mapping result of data subcarriers. In data transmission, the equalized data subcarriers with CFR, HA(k), can be shown as
( ) ( ) ( ) ( ) [ ( ) ( )] ( )
where Wi(k) indicates the frequency-domain additive noise in data subcarriers. The estimated CFR error, ΔH(k), causes the de-mapping error vector between the equalized carrier, Xe(k), and the predicted de-mapping signal, XD(k). This error vector can be derived as
For CFR error estimation, this DDCET uses the mean of normalized constellation error vectors to eliminate the zero-mean additive noise, Wi(k). The mean of the normalized constellation error vectors during l OFDM symbols is listed as
( )
Unlike the feedforward compensation method, we use feedback scheme to get better performance and less compensation complexity. In the feedback loop, the CFR, HA(k) is adjusted by the running average of estimated CFR error, ΔH(k).
(3.11)
( ) ( ) ( )
l A
H k H k m kε
Δ ≈ − ⋅
After that, we compare the equalized pilots with the known one and compute the mean-square error as the error function. Then we judge if this corrected CFR is suitable. If the MSE of the equalized pilots, MSEcomp, is greater than the MSE of the pilots before compensated, MSEori, we discard this CFR. Otherwise, the old CFR will be replaced by the suitable one. The algorithm of this feedback loop is
2
where M is the number of pilots and μ is the step size of the adaptive tracking loop.
Under the feedback tracking algorithm which adjusts the CFR directly instead of compensating the data subcarriers only, we can get more accurate data subcarriers to
make more precise estimations of CFR error, residual CFO and SCO, hence a better system performance.
Table 3.1 Summary of the proposed equalizer.
Initialization: ( )
For each new OFDM symbol arriving at the equalizer Smoothing: HA( )k =HE( )k ⊗S k( )
De-mapping error vector: ( )ε k = X ke( )−XD( )k
Mean of normalized constellation error vectors: ( )
( ) ( )
3.3 Phase Noise Detection and Compensation
When phase noise occurs, the accuracy of CFO estimator will descend following the performance degradation. The phase deviation in frequency domain is not linear anymore. One reason is that the increased remaining frequency offset makes the ICI playing an important role in the effect of CFO. Besides, the additional phase noise, BsinΔωt, causes extra phase shift in each OFDM symbol. That means the phase
difference between two repeat OFDM symbols is not the same. In frequency domain, phase gain between two adjacent OFDM symbols can be described as
(3.15)
Obviously, we can not calculate the exact remaining frequency offset from equation (3.19) because the phase shift increases in some OFDM symbols and decreases in other OFDM symbols.
Hence, we need a new mechanism against the degradation due to phase noise.
The proposed phase noise detection algorithm can be separate into two steps. Step one is phase noise acquisition. In this stage, we record the tendency of remaining CFO which we can get from PR. A search window storing 2c results is used for searching peak of fluctuating wave caused by phase noise. The minimum error tolerance for peak decision is e/c. Once detecting peak, keep the corresponding OFDM symbol number, l. After the second peak obtained, we can estimated loop time constant, Δω, with equation (3.20). Figure 3.3 shows the search window with error tolerance and
phase deviation arise from phase noise.
Figure 3.3 Search window of the proposed phase noise detection.
The other parameter, loop bandwidth, can be estimated by relationship between loop time constant and phase difference of peaks.
0, 0, 1
After phase noise parameters are calculated, the correct data can be obtained from the time domain before FFT. The compensation architecture starts to generate sin wave joint with estimated CFO to correct the phase of the received data. The block diagram is shown in Figure 3.4.
Figure 3.4 Block diagram of the proposed design.
Although the compensation engine started, the high frequency noise makes the phase of the received data drifting. Therefore, step two – phase noise tracking is turn on. From section 2.2.3.2, we know that the remaining CFO will be limited in 1 ppm.
If the detected value is more than that after phase noise compensation, we can assert that the acquisition is not accurate enough. Assume the loop time constant has more credit (error rate > 90%), we adjust loop bandwidth, B, in binary search to approach the real value. The initial margin can be obtained by equation (3.22).
0, 0, 1
If the current remaining CFO, C0, is larger than last one, C0,old, increase B. On the other hand, decrease B with the estimated bandwidth error, ΔB. When the fixed bandwidth is out of range (> 50 ppm), we discard the result and return to acquisition stage. With the help of binary search, the loop bandwidth will finally converge and
loop time constant will be refined at the same time. The estimated parameters will be store and update for the next packet, so the compensation mechanism can directly modify the received signal after first packet. Correctly speaking, not only the AFC but also other synchronization blocks can avoid suffering from distortion of phase noise.
The compensation step of each field in OFDM packet is shown in Figure 3.5.
Figure 3.5 Compensation engine of the proposed design.
Chapter 4
PERFORMANCE ANALYSIS
To satisfied system requirement, system PER is simulated under the highest data rate of IEEE 802.11g, which is the 54 Mbps mode with 64-QAM modulation and 3/4 FEC coding rate [3]. In simulations with multipath channel, IEEE Rayleigh-fading channel is used with different RMS delay spread and 13 independent taps. We also assume a fading channel varying from packet to packet; i.e., it is static within each packet, and the required performance is measured at a PER of 10%. In below performance analysis, system PER of the proposed adaptive equalization and phase noise detection will be discussed and compared with the conventional approaches.
4.1 Adaptive Channel Equalization
Table 4.1 SNR degradation under different modulation with singular channel.
Modulation BPSK QPSK 16-QAM 64-QAM
SNR degrade (dB) 3 5 7 10
Comparison of the conventional feedforward equalization and the proposed adaptive equalization is shown is Figure 4.1. From this figure, we know that the conventional method needs additional compensation hardware. On the other hand, the proposed algorithm adjusts the channel frequency response instead of fix compensation. The approach not only saves cost but also maintains accuracy.
Figure 4.1 (a) The proposed feedback DDCET.
(b) Conventional feedforward DDCET
The brilliant performance of the proposed adaptive equalization in IEEE channel with RMS delay spread 25, 50 and 100 ns is shown in Figure 4.2 to 4.6. The singular channel which exists the very deep point in the CFR is 30% in the real world. And the other 70% channel we call them general or ordinary channel in the thesis. The singular channel which has low point in CFR degrades the performance larger as the modulation order increase. The result is shown in Table 4.1. From these simulation results, we can see that the proposed method has little help in the ordinary channel but obviously has a lot of improvement in the singular channel. And it even can resist the delay spread up to 100 ns while the traditional methods fail.
Figure 4.2 Performance of adaptive CE in IEEE rms 25 general channel.
Figure 4.3 Performance of adaptive CE in IEEE rms 25 singular channel.
Figure 4.4 Performance of adaptive CE in IEEE rms 50 general channel.
Figure 4.5 Performance of adaptive CE in IEEE rms 50 singular channel.
Figure 4.6 Performance of adaptive CE in IEEE rms 100 general channel.
Table 4.2 Comparison of the adaptive CE in different channel.
Channel
Method
Ordinary (rms 50)
Singular (rms 50)
Perfect 18.3 22.7 This work 18.9 25.1
[7] 19.7 31.5
1-shot 20 34.8
In the proposed scheme, instead of estimating the compensation value of present OFDM symbol directly, the increasing rate estimation of compensation value is applied to predict the data drift of the present OFDM symbol using the information of the past symbols. In Figure 4.7, the estimated values of OFDM symbol index are shown. After about 20 OFDM symbols, tracking error is converged to a small value.
Then the channel error tracking can be turned off.
Figure 4.7 Convergence of the proposed adaptive equalization.
Table 4.3 lists some adaptive equalization in the world. Most of the details are discussed in chapter 1. In short, we are the best of all.
Table 4.3 Comparison state-of-the-art adaptive equalization.
ISCAS 2005
[12] ICCS 2004 [13] TCSET 2004 [14] Globecom
2004 [15] This work Operating
Domain Time Time Time Time Frequency
Method Weighted RLM Reduced-rank
modified LMS MOE LMS Feedback DD
Property
Utilization Preamble Pilot GI GI Pilot
Modulation N/A QPSK N/A QPSK 64-QAM
Channel
Cycle 300 (sample) 400 (sample) N/A 500 (symbol) 20 (symbol)
Characteristic Capable of error level and the faster convergence
4.2 Phase Noise Detection
Figure 4.8 shows the performance without the proposed phase noise detection and the profile of PER = 1. Figure 4.9 is the same condition except with our design. Compare these two figures, we can find that the phase noise tolerance is surprisingly improved.
Note that the phase fluctuates dramatically over boundary (±π) when loop bandwidth is larger than 6 ppm, so performance degrades fast. Another thing deserve to be mentioned is that the detection algorithm doesn’t work when loop time constant is less than 7 kHz when packet length equals to 1000 since it needs two peaks. Although the tolerance of our method is not enough large, the serious condition won’t happens
Note that the phase fluctuates dramatically over boundary (±π) when loop bandwidth is larger than 6 ppm, so performance degrades fast. Another thing deserve to be mentioned is that the detection algorithm doesn’t work when loop time constant is less than 7 kHz when packet length equals to 1000 since it needs two peaks. Although the tolerance of our method is not enough large, the serious condition won’t happens