Chapter 3 The Proposed Design
3.2 Adaptive Channel Estimation
3.2.3 Feedback Decision-directed Channel Error Tracking 42
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 or no one can handle that situation. The so called cycle slip occurs when the carrier frequency changes from one edge to another edge quickly, e.g. from -50 ppm to 50 ppm with 100 kHz. In this situation, even we have good algorithm can still not save the performance loss.
Table 4.4 Comparison of the tolerance without and with phase noise detection.
Estimation property
Figure 4.8 Performance without phase noise detector and the profile when PER = 1.
Figure 4.9 Performance with phase noise detector and the profile when PER = 1.
Chapter 5
THE PROPOSED ARCHITECTURE
5.1 Architecture of Adaptive Equalization
The whole architecture of the proposed adaptive equalization can be divided into three parts, the CFR error tracking, the property measurement and the others. The architecture of the algorithm is depicted in Figure 5.1. At first, distorted long preamble is divided the known training symbols in advance. We obtain the initial CFR and put it into the 5-tap smooth filter. The smoothed CFR will be used for data compensation. The CFR error tracking loop contains five components. The upper adder and multiplier are used to calculate normalized de-mapping error vector. Then the results representing the mean of normalized constellation error vectors will be stored in the accumulator. After multiplying the smoothed CFR, the residual estimation error is induced. The most important part of this architecture is the property measurement which consists of two pairs of MSE calculator and a comparator. The MSE calculator is composed of one adder, square device, four shift registers and the summation block. As implied by the name, it computer the MSE of the equalized pilots and the desired pilots. In the end, the comparator will decide if we should update the CFR, since this output of the property measurement controls the multiplexer for equalization. The hardware cost listed in Table 5.1 includes four multipliers, four adders and about 162 kilo-bytes memory space.
Figure 5.1 The hardware architecture of adaptive equalization.
Table 5.1 Hardware complexity of the proposed adaptive equalization.
Multiplier Adder Register (B)
Quantity 4 6 1.6 k
5.2 Architecture of Phase Noise Detection
Figure 5.2 shows the architecture of the phase noise detection. In the beginning, the residual frequency offset, C0,l, and the corresponding OFDM symbol number, l, are delivered form PR. We use the remaining frequency offset to calculate the tendency of the wave came of phase noise as described in section 3.3. The search window is implemented with ten 1-bit shifter registers. The half of the registers is added then compared with the error threshold for search peak. Here the threshold is set to 3 over 5, which mean we can declare the peak is found if there are at least three in five taps.
As soon as peak is found, the corresponding symbol number is passed to the table for estimating loop time constant, Δω. Then we use the result for estimating another parameter. The difference of the remaining frequency offset, their corresponding symbol numbers and the estimated loop time constant are the input of the table containing formula for computing loop bandwidth. The comparator of upper one is used to control the switch of tracking mechanism. Another comparator is used to avoid the loop bandwidth out of bound and will make B dispersing. The hardware cost of the proposed phase noise detector listed in Table 5.2 includes four adders and 109 bytes memory space in rough. The compensation architecture here is ignored because it only needs to fix the NCO table for adding sine calculation.
Figure 5.2 The hardware architecture of phase noise detection.
Table 5.2 Hardware complexity of the proposed phase noise detection.
Multiplier Adder Register (B)
Quantity 0 4 109
Chapter 6
CONCLUSION AND FUTURE WORK
6.1 Conclusion
This thesis proposes a novel scheme for channel equalization in OFDM receivers. The proposed algorithm can use de-mapping results and pilots to adjusting estimate channel frequency response in singular multipath environments. From simulation results, the average estimation error of the proposed algorithm is small enough for little system performance loss under different multipath channel. And the convergence speed is much faster at the same time. Besides, the proposed method is suitable for implementation issue compared with the reference designs.
By the way, a phase noise with CFO model is also constructed in this thesis. It is found that the joint effects of phase noise and CFO degrade the system performance dramatically. Thus we propose a novel estimation algorithm and a robust compensation scheme which is shown to work well under loop bandwidth 11 ppm, loop time constant 25 kHz, and maximum CFO tolerance 50 ppm at 2.4 GHz carrier frequency. All of the estimations are done in the known pilots.
Therefore, the proposed algorithm can enhance the performance of OFDM systems and is possible to achieve both small and low-cost systems.
6.2 Future Work
In the future, high QAM constellation which will be more sensitive to non-ideal effects such as CFO and phase noise may be used for higher data rate. Multi-input
multi-output OFDM (MIMO-OFDM) systems are also gaining prominence in high data rate applications. However, the above problem in this thesis will limit the system performance. That means a more robust scheme has to be applied to overcome these impairments. Although the CFO estimation mechanism is good enough, it still needs some adjustment when IQ mismatch occurs [8]. Besides, computation in low-SNR points for CFO estimation can be eliminated for high performance and low complexity, i.e. coarse tune using two autocorrelations with 4 point per short symbol and fine tune using one autocorrelation with 32 points per long symbol [10].So some extensions to the research presented in this thesis will be included in our future work.
A. In the future, the work is to improve the detection range of the proposed method. Additionally, we will need some mechanism for special case in the proposed method.
B. This thesis proposed the phase noise estimation in single-input single-output OFDM (SISO-OFDM) system. In the future, we will try to derive a model for the effect of phase noise and CFO in MIMO-OFDM system and develop a compensation technique for the impairment.
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