Chapter 2 System Platform
2.2 Channel model
2.2.4 Sampling Clock Offset
The interfaces of RF and baseband data are digital to analog converter (DAC) in the transmitter and analog to digital converter (ADC) in the receiver side. The oscillators used to generate the DAC and ADC sampling instants at the transmitter and receiver will never have exactly the same period. The ADC is the first stage of baseband, so it dominates the receiving SNR. To get the highest input SNR, the ADC is hoped to sample at the eye open position where it has the maximum signal power.
However, the initial sampling phase could be anywhere in the eye diagram, so timing synchronization is necessary. The ADC has two kinds of clock source: free running clock and PLL output clock. With free running clock, this method also called non-synchronous sampling or fix sampling, clock frequency and phase are fixed.
Once timing error estimated, the compensation would be performed with interpolator.
With PLL output clock, also called synchronous sampling or dynamic sampling, it receives the timing error and adjusts its frequency and phase to compensate the error.
There is a need to maintain synchronization while the accuracy and stability of the original clock reference in the receiver may not be ideal. These tasks are the responsibility of a specific module Delay Lock Loop (DLL). Figure 2-12 shows an example of oversampled signal with SCO.
Figure 2-12 An example of oversampled signal with SCO
In the MATLAB platform, the model of clock drift is built using the concept of interpolation. The input digital signal and the shifted sinc wave can interpolate the value between two sampling points. The sampling phase can be written as nTS-ΔPN. And then we get the ADC output signal R(nTS) by convoluting the ADC input signal RpreADC(nTS) and shifted sinc wave. The received signal after ADC can be derived as equation where (2.3) l is the sampling point index.
( ) ( ) sin ( )
SCO brings a slow shift of the symbol timing point, which rotates subcarriers. And a loss of SNR due to ICI generated by the slightly incorrect sampling instants. The shift of sampled phase in time domain will induce the linear phase error in frequency domain. Figure 2-14 shows the frequency domain behavior of SCO model in the system platform. When clock cycle increases, the range of linear phase error will increase.
Figure 2-13 Clock drift makes constellation dispersed
Figure 2-14 The phase rotation on each subcarrier under SCO environment
Chapter 3
Proposed Algorithm
N this chapter, we propose an algorithm to tolerate Wide Clock Offset. The 2*2 MIMO-OFDM system with Wide Clock Offset is aimed. To simplify the problem, we fixed the SCO ppm from 0 to 10000 of thousand multiplier. In the standard of 802.11n , each MIMO OFDM symbol has ten Legacy Short Training Sequences (L-STS) of 16 samples as we mentioned in the section 2.1.3 .To achieve our goal we extend the number of Legacy Short Training Sequences from 10 to 51.
The first three short preambles are for packet detection and boundary detection , and the rest of them are for Coarse and Fine timing synchronization of Wide Clock Offset . Figure 3-1 is the scheme of the proposed algorithm. Our algorithm includes Coarse and Fine estimation of SCO. The main goal of Coarse compensation is to bound the residual SCO to the range of SCO from 0 to 3000 ppm of thousand multiplier. After each estimation we’ll send a signal to DAC to compensate the SCO that we estimated.
Received signal
Figure 3-1 Flowchart of the proposed algorithm
I
3.1 Coarse timing synchronization of Wide Clock Offset
In order to estimate SCO of wider scope, we have to find a way to separate the SCO from different quantity. Firstly we try to solve it by the radical ten L-STF.
However it’s too few to accumulate the difference between each distinct SCO quantity.
We found that we can use much more L-STF to achieve it. So we extend the amount of legacy short preamble from ten to fifty-one. We use twenty-four short preamble to do Coarse SCO estimation and each eight short preambles we define as an Basic unit here. We collect three basic unit with different SCO quantity. Figure 3-2 shows the three basic unit. We control DAC to let the different Basic unit has distinct SCO quantity.
Basic unit 1 Basic unit 2 Basic unit 3
+5000ppm
-5000ppm
Figure 3-2 The three basic unit of Coarse SCO estimation
The way we will introduced can separate SCO quantity from 6000 to 16000 ppm of thousand multiplier. Because the parameter of R+5000 and R-5000 will have apparent diversity from 6000 to 16000 ppm of SCO. And that is why we need to add pseudo SCO quantity of 6000 ppm to the Basic unit 1. In order to distinguish SCO from different quantity we let the Basic unit 2 and Basic unit 3 have different SCO quantity as Figure 3-2 illustrated. Basic unit2 and Basic unit 3 both differentiate positive and negative of SCO quantity of 5000 ppm from Basic unit 1. The difference between Basic units of SCO “5000 ppm” is accrued by a great deal of dissimilar
simulation. With this distinct SCO quantity between each Basic unit we can achieve our goal. After the collection of the three Basic units, we can start the Coarse SCO estimation. Since each Basic unit has 8 L-STF so it has 128 points in it. We define Rij as the point of ith Basic unit and jth position. From equation (3-2) (3-3) (3-4) we can get R+5000 , R-5000 , R+－5000diff .
By the three parameters we can accomplish the coarse SCO estimation. Figure 3-3 is the simulation result of R+5000 and R-5000 from 0 to 10000 SCO ppm of 10000 packets. From this figure we can see that there is evident discrepancy between R+5000
and R-5000. This property lead us to discriminate SCO from different quantity precisely.
Since we know how to calculate these three parameters , we do some simulation to get them and analysis these simulation results.
The simulation environment below is based on the following conditions:
z MIMO-OFDM system in 20 MHz z packet no. is 10000
z PSDU is 1024 bytes z MCS is 13 SNR is 24
z Decoder using soft Viterbi decoder
z Multipath Model : TGnE (rms delay spread 100 and tap numbers 15) z Decoder using soft Viterbi decoder
Original SCO Value of R+5000 Value of R-5000 Value of R+-5000diff 0 8.4852≦R+5000≦94.6259 13.861≦R-5000≦64.4957 -29.19≦R+‐5000diff≦79.96
1000 73.8958≦R+5000≦146.36 1. 2780≦R-5000≦58.0144 55.52≦R+‐5000diff≦129.44
2000 131.1874≦R+5000≦185.5 1.6382≦R-5000≦58.6763 108.92≦R+‐5000diff≦182.38
3000 182.9915≦R+5000≦226.2 2. 3877≦R-5000≦47.6644 152.34≦R+‐5000diff≦212.54
4000 201.9628≦R+5000≦251.8 2. 6223≦R-5000≦45.6039 166.46≦R+‐5000diff≦242.22
5000 192.1705≦R+5000≦241.3 2. 4401≦R-5000≦48.1522 155.50≦R+‐5000diff≦235.65
6000 172.3893≦R+5000≦224.2 2. 4665≦R-5000≦54.2802 138.17≦R+‐5000diff≦214.72
7000 135.6931≦R+5000≦197.1 82.6823≦R-5000≦135.635 18.11≦R+‐5000diff≦95.35
8000 131.6822≦R+5000≦195.3 210. 9979≦R-5000≦251.52 -103.71≦R+‐5000diff≦-28.01
9000 139.427≦R+5000≦203.73 278. 0854≦R-5000≦309.71 -157.94≦R+‐5000diff≦ -83.0
10000 144.7336≦R+5000≦213.8 174. 9550≦R-5000≦220.14 -57.04≦R+‐5000diff≦18.11
Table 3-1 The value of R+5000, R-5000 and R+－5000diff in each different SCO quantity
Decision Condition Est_Sco_coarse
Table 3-2 Decision criteria of Coarse SCO estimation
Original SCO Estimation result
0 77 errors, 70 packets 10000,7 packets 1000 1000 69 errors, 40 packets 0 , 29 packets 2000 2000 206 errors, 5 packets 1000 , 201 packets 3000 3000 54 errors, 35 packets 2000 , 19 packets 4000
4000 3962 errors, 3962 packets 3000
5000 10000 errors,7 packets 2000 , 8680 packets 3000 1313 packets 4000
6000 10000 errors, 167 packets 4000, 9843 packets 3000
7000 No errors
8000 1 error, 1 packet 10000
9000 No errors
10000 2790 errors, 2740 packets 8000, 50 packets 0 Table 3-3 Coarse SCO estimation of 10000 packets
Table 3-1 is the simulation result of R+5000, R-5000 and R+－5000diff in each distinct SCO quantity of 10000 packets. Each value of these three parameters in each SCO quantity all has a range. After analyzing Table 3-1 we can find out the colored content is useful. There are some overlap between the Table 3-1 even the colored contents. So we must adjust these range of useful value for the good of differentiating SCO from different quantity. Table 3-2 is the result after analyzing and modifying of colored content in Table 3-1. By the value of Table 3-2, it becomes the decision criteria of our coarse SCO estimation. Because when Original SCO equals to 5000 or 6000 ppm, the value of the three parameters will overlap with others. So we can’t tell them from each other. Table 3-3 is the result of Coarse SCO estimation. From this result we can see that when Original SCO equals to 7000 or 9000 ppm , the estimation is perfect without errors. The worse condition is when Original SCO equals to 5000 or 6000 ppm, they will be recognized as the SCO ppm ranging from 2000 to 4000 ppm.
Obviously, there may be some Residual SCO exist after our coarse SCO compensation. Residual SCO can be acquired by equation (3-5). The range of the Residual_SCO is almost from 0 to 3000 ppm. The Residual Sco will be compensated after the Fine SCO estimation.
Residual_Sco Original_Sco Est_Sco_Coarse= − (3-5)
3.2 Fine timing synchronization of Wide Clock Offset
Residual SCO (28~35th L-STF)
Residual SCO + 8000 ppm (36~43th L-STF)
Residual SCO – 8000 ppm (44~51th L-STF)
Basic unit 1 Basic unit 2 Basic unit 3
+8000ppm
-8000ppm
Figure 3-4 The three basic unit of fine SCO estimation
Figure 3-5 R+8000 and R-8000 in each SCO quantity of 10000 packets
Figure 3-4 is the three basic unit of fine SCO estimation. It quiet similar to the figure 3-2. The only difference is that the SCO gap of basic unit 2 and basic unit 3 with basic unit 1 is 8000 ppm but not 5000 ppm. We do much simulation to decide the SCO gap of Coarse and Fine SCO estimation. By equation (3-1) (3-2) (3-3) (3-4) we can also calculate R+8000 , R-8000 , R+－8000diff three parameters in the same way. Because the Residual SCO we focused only in the range of 0 to 3000 ppm. So we also show the value of three parameters in these SCO ppm. Figure 3-5 is the simulation result of R+8000 and R-8000 with 10000 packets in the SCO range from 0 to 3000.
Original SCO Value of R+8000 Value of R-8000 Value of R+-8000diff 0 116.37≦R+8000≦211.00 175.62≦R-8000≦258.28 -101.06≦R+‐8000diff≦0
1000 237.45≦R+8000≦304.54 199.42≦R-8000≦279.58 0≦R+‐8000diff≦70 2000 126.473≦R+8000≦208.94 20.76≦R-8000≦120.05 70≦R+‐8000diff≦176.8608 3000 86.40≦R+8000≦185.24 268.96≦R-8000≦315.06 -215.67≦R+‐8000diff≦-101
Table 3-5 Decision criteria of Fine SCO estimation
Table 3-4 is the value of three parameters with 10000 packets. After analysis and modification of Table 3-4 we can get new range of the three parameters in Table3-5. The content of Table 3-5 is the criteria of Fine SCO estimation. By the result of Table 3-5 we can start to Fine SCO estimation. Table 3-6 is the simulation
result of Fine SCO estimation with 10000 packets.
Residual SCO Estimation result
0 3 errors
1000 95 errors
2000 155 errors
3000 10 errors
Table 3-6 Fine SCO estimation of 10000 packets
From Table 3-6 we can see that the result of fine SCO estimation is acceptable. The error rate of fine SCO estimation is about 1.55% at most. By equation (3-6) we can calculate out the Sco_to_DAC. We’ll alert a control message to the DAC to let the rest data has the SCO quantity of Sco_to_DAC. Obviously , if the Sco_to_DAC equals to zero then the compensation of the SCO will be correct. In the next chapter we’ll show the system performance with our proposed algorithm.
Sco_to_DAC = Residual_Sco - Est_Sco_Fine (3-6)
Chapter 4
Simulation result
To evaluate the proposed algorithm, a typical MIMO-OFDM system based on IEEE 802.11 wireless LANs, TGn sync proposal technical specification is used as
a reference-design platform. We chose MATLAB as our simulation language, due to its ability to mathematics, such as matrix operation, numerous math functions, and easily drawing figures as our simulation result to illustrate the performance.
4.1 Simulation Environment
The simulation environment below is based on the following conditions:
z MIMO-OFDM system in 20 MHz z PACK no. is 1000
z PSDU is 1024 bytes z MCS is 13
z Decoder using soft Viterbi decoder
z Random SCO from 0 to 10000 of thousand multiplier
Multipath Model : TGn-E and relative rms delay and Tap number will be shown in table 4-1.And the MCS set will be shown in table 4-2.
Mode rms delay spread Tap numbers
A 0 ns 1 B 15 ns 2 C 30 ns 5 D 50 ns 8 E 100 ns 15 F 150 ns 22
Table 4-1 TGn Multipath Specifications
MCS Index Modulatin Antenna No. Code Rate
8 BPSK 2 1/2 9 QPSK 2 1/2
10 QPSK 2 3/4
11 16 QAM 2 1/2
12 16 QAM 2 3/4
13 64 QAM 2 2/3
14 64 QAM 2 3/4
24 BPSK 4 1/2
25 QPSK 4 1/2
26 QPSK 4 3/4
27 16 QAM 4 1/2
28 16 QAM 4 3/4
29 64 QAM 4 2/3
30 64 QAM 4 3/4
Table 4-2 MCS set
4.2 Simulation Result
Figure 4-2 Error Rate VS SNR of the proposed algorithm
10 12 14 16 18 20 22 24
Figure 4-3 RMSE VS SNR of the proposed algorithm
-10000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 0.1
PER of Each SCO ppm in different SNR
SCO(ppm)
Figure 4-4 PER of Each SCO ppm in different SNR
Fiigure 4-5 Error Probability Distribution
(a) (b)
Figure 4-6 Constellation of SCO 1000 ppm under 2x2 MIMO-OFDM system (a) w/o SCO compensation (b)with SCO compensation
Figure 4-7 Constellation of SCO 5000 ppm under 2x2 MIMO-OFDM system (a) w/o SCO compensation (b)with SCO compensation
Figure 4-8 Constellation of SCO 10000 ppm under 2x2 MIMO-OFDM system (a) w/o SCO compensation (b)with SCO compensation
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
4.3 Simulation analysis
1000 2
1
(Residual_Sco - Est_Sco_Fine) RMSE =
1000
Packet=
∑
(4-1)
From figure 4-1 we can see that the system performance PER will degrade about 0.2 dB with the proposed algorithm. We proposed a novel scheme for the estimation of Wide Clock Offset. From figure 4-2 we can see that the pure error rate of the proposed algorithm is acceptable(less than 8%) when SNR is bigger than 16.
This illustrates that we can estimate SCO correctly under SNR 19 dB. Figure 4-3 is the RMSE of the proposed algorithm. From this simulation we can see that the RMSE will converge at SNR 24 dB. This is because all the R value we evaluated is at SNR 24 dB. Figure 4-4 shows the performance in Each SCO ppm with different SNR. We can see that when SNR bigger than 19 the packet error rate will be much closer.
Figure 4-6、4-7、4-8 are the constellation of SCO effect of 1000 ppm 、 5000 ppm and 10000 ppm. From this simulation result we can see that the constellation will disperse severely with the SCO ppm turns to be bigger. And after the compensation of our algorithm, we’ll eliminate this phenomenon.
Chapter 5
The Proposed Architecture
The whole architecture can be divided into two main parts, Coarse SCO estimation and Fine SCO estimation. The compensation of SCO only needs to send a signal to DAC to compensate the rest data of estimation result. The most importance of the proposed SCO estimation is to calculate out the three parameters as we mentioned in section 3-1 and 3-2. Since the behavior of the coarse and fine estimation is the same, so we can share the hardware of them.
Figure 5-1 Block diagram of the proposed algorithm
Three parameters generator Estimate SCO
Figure 5-2 Block of SCO estimation
EST_SCO
MUXMUXMUX Two’s Complement Two’s Complement
1(tan)−1(tan)− MUX10 MUX10 Buffer
CounterTo 96 Buffer MUX10 MUX10 SCO Estimator
MUXMUXMUX Two’sComplement Two’sComplement
1(tan)−1(tan)− MUX10 MUX10 Buffer
CounterTo 96 Buffer MUX10 MUX10 SCOEstimator EST_SCO
Figure 5-3 Architecture of three parameters generator
Chapter 6
Conclusion and Future Work
6.1 Conclusion
In this thesis, a novel Sampling Clock Offset estimation of Wide Scope based on IEEE 802.11n is proposed. This is based on short training field of the preamble. We can combat SCO from 0 to 10000 ppm of thousand multiplier. In order to distinguish the Wide SCO from different quantity we extend the number of L-STF from ten to fifty-one. By this changes we can have good performance on SCO estimation. From the simulation result we can see that the packet error rate degrade about 0.2 dB from the perfect condition. We also can correctly estimate the SCO under SNR 19 dB of the perfect compensation. From the result we can see that our algorithm can tolerate Wide SCO in the presence of AWGN and Multipath. Table 6-1 shows the comparison result of performance in the presence of SCO with other methods. From this table we can see that only our algorithm can tolerate SCO quantity bigger than 1000 ppm.
Ref [14] Ref [17] Ref [19] Proposed WORK
System SISO 2x2 MIMO SISO 2x2 MIMO
Modulation 16 QAM N/A OFDM
64 QAM
OFDM 64 QAM Sampling Method Non-
Synchronous
Non- synchronous
Non-
synchronous Synchronous Architecture Interpolator Interpolator Interpolator Non-PLL/DLL
(ADCM)
Sampling Rate 1x 1x 4x 1x
Converged Cycle 32 symbols 20 symbols N/A 48 symbols
SCO Range 100 ppm 500 ppm ±200 ppm
0~10000 ppm of thousand
multiplier Table 6-1 Comparison with other methods
6.2 Future work
The proposed algorithm in this thesis can have good performance in the SCO ppm from 0 to 10000 of thousand multiplier as we supposed. So our future work is to tolerate SCO not only those quantity as we mentioned above. Or we can use fewer numbers of short preamble to achieve Wide SCO estimation. The trade-off between cost and performance must be a critical consideration.
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