Transmitter

The IEEE 802.11n is known as multi-input-multi-output OFDM system (MIMO-OFDM), op-erating in both 2*2 and 4*4 and 8*8 antennas to transmit and receive data and support higher coding rate up to 5/6. Figure 3 shows transmitter data path. First use FEC encoder to encodes the source data. Then the bit stream is parsed into spatial streams, according to the number of trans-mit antennas. The interleaver provides a form of diversity to guard against localized corruption or bursts of errors. And then, the QAM mapping is used to modulate the bit stream. It supports BPSK, QPSK, 16 QAM, 64 QAM, 64 QAM or 256 QAM. After QAM mapping, the constella-tion points pass through Space Time Block Code (STBC) encoder. The STBC encoder spreads the constellation points of each spatial stream to any other spatial streams. IFFT is used to trans-fer signal from frequency domain to time domain. In 80MHz, there are 2048 frequency entries for each IFFT, or 2048 sub-carriers in each OFDM symbol, 1702 of them are data carriers, 142 of them are pilot carriers, other are null carriers. After Insert Guard Interval (GI), the signal is transmitted by RF.

Spatial streams parse

puncture

FEC encoder

Figure 3: IEEE 802.11n transmitter data path

Figure 4: IEEE 802.11n receiver data path 2.1.2 Receiver

Figure 4 shows receiver data path. The signal is received from the RF. FFT is used to transfer received signal from time domain to frequency domain. Sync is used for synchronization, in-cluding to find when exactly the packet start, the OFDM symbol boundary and the best sample phase. Channel effect will be estimated and compensated by Equalizer. IQ mismatch is also taken under consideration. After all estimation and compensation, STBC decoder is used to com-bine four bit streams into original. Then the bit streams are de-map, de-interleaver and merge to single data stream. Finally, it is decoded by FEC which includes de-puncturing, Viterbi decoder and de-scrambler.

2.1.3 Basic MIMO PPDU Format

A PHY protocol data unit (PPDU) is defined to provide interoperability. Figure 5 shows the PPDU format for the basic MIMO mode. Each packet contains a header (ex. L-STF, L-LTF) for detection, channel estimation and synchronization purposes. For preventing unintentional beam-forming, insertion of the cyclic shifts (CSD) is applied to the preamble and signal fields. First part is the L-STF which can be used for signal detection, coarse acquisition …etc. The L-STF is formed by the repetition of ten L-STS of 64 samples each; these samples have correlation proper-ties. In this thesis, correlation techniques will be applicable for packet detection, symbol boun-dary detection, and timing synchronization. A detail data structure of L-STF is shown as Figure 6.

2.2 Channel Model

There are many imperfect effects during transmitted signals through channel, such as Addi-tive White Gaussian Noise (AWGN), sampling clock offset (SCO), multipath, and so on. The block diagram of channel model is shown in Fig. 7.

2.2.1 Additive White Gaussian Noise

Wideband Gaussian noise comes from many natural sources, such as the thermal vibrations of atoms in antennas, "black body" radiation from the earth and other warm objects, and from celes-tial sources such as the sun. The AWGN channel is a good model for many satellite and deep space communication links. On the other hand, it is not a good model for most terrestrial links because of multipath, terrain blocking, interference, etc. The signal distorted by AWGN can be derived as

( ) ( ) ( )

r t  s t  n t

(2.1)

where

r t ( )

is received signal,

( )

s t

is transmitted signal,

( )

n t

is AWGN.

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 GI L1 L2

L-STF 8 µs

L-LTF 64 µs 72 µs

Figure 6: OFDM training structure include of L-STF and L-LTF

TX TX

Time invariance

multipath SCO AWGN

Figure 7: Block diagram of channel model

Figure 8: Block diagram of channel model 2.2.2 Multipath

Because there are obstacles and reflectors in the wireless propagation channel, the transmit-ted signal arrivals at the receiver from various directions over a multiplicity of paths, as shown in Figure 8. Such a phenomenon is called multipath. It is an unpredictable set of reflections and/or direct waves each with its own degree of attenuation and delay. Multipath is usually described by two sorts:

a. Line-of-sight (LOS): the direct connection between transmitter and receiver.

b. Non-line-of-sight (NLOS): the path arriving after reflection from reflectors.

Multipath will cause amplitude and phase fluctuations, and time delay in the received signals.

When the waves of multipath signals are out of phase, reduction of the signal strength at the re-ceiver can occur. One such type of reduction is called the multipath fading; the phenomenon is known as “Rayleigh fading” or “fast fading.” Besides, multiple reflections of the transmitted sig-nal may arrive at the receiver at different times; this can result in inter symbol interference (ISI) that the receiver cannot sort out. This time dispersion of the channel is called multipath delay spread which is an important parameter to access the performance capabilities of wireless sys-tems. For a reliable communication without using adaptive equalization or other anti-multipath techniques, the transmitted data rate should be much smaller than the inverse of the RMS delay spread. A representation of Rayleigh fading and a measured received power-delay profile are shown in Figure9.

Figure 9: Channel Frequency Response

The clock drift means the different between the sampling frequency of the digital to analog converter (DAC) and the analog to digital converter (ADC). Because of sampling frequency off-set, even if the initial sampling point is optimized, the following sampling points will still slowly shift with time. This model is using timing shift and cubic interpolation to cause the clock drift effect and its effect can be written as Eq. 2.

(2.2)

where R_preADC represents the ADC original output signal, δ represents SCO and to get R nT ( _s) signal by shift the ADC original output signal and interpolation the fractional part Y. Figure 10 shows the clock drift model effect. Initial can samples at optimum sampling points, then slightly incorrect sampling instants will cause the SNR degradation.

2.3 Problem Statement

Due to the explosive growth demand for wireless communication, the next-generation wire-less communication systems are expected to provide high-speed and high-throughput. However, high-speed transmission needs high sampling rate, which would cause wide sampling clock off-set.

In TABLE Ⅰ, it compares some methods of timing synchronization in the state of the art.

In those methods, the largest tolerance of SCO is 675ppm, which is not large enough. The above mention has said that the wide clock offset tolerance is the core of the development for high-speed transmission. Hence, the thesis works on the wide clock offset in very high through-put MIMO OFDM systems.

TABLE I:

THE STATE OF THE ART

[1] [3] [21] [25]

System Type OFDM OFDM +4-QAM

MIMO-OFDM +64-QAM

OFDM +16-QAM

Method N/A Phase

in Freq.

Non-PLL ADCM

(ADCM) Interpolator

Required Format Pilot Preamble Short Preambles Preamble

Tolerant Range 675 ppm 400ppm 400 ppm 100 ppm

Converge Cycle 3 symbols N/A 4 symbols 100 symbols

CHAPTER 3

FD-Timing Synchronizer

Timing synchronization is one of the most important things in wireless OFDM systems. The duty of the synchronization is to help the receiver to get information correctly. There are symbol timing offset and sampling timing offset that constitutes timing synchronization errors. The ADC is the first stage of baseband, so it dominates the receiving signal to noise ratio (SNR). To get the highest input SNR, the ADC is hoped to sample at the eye open position where it has the maxi-mum signal power. In this thesis, we will focus on the study of sampling timing offset.

In this section, a frequency-domain synchronizer is proposed for sampling timing offset. The synchronizer contains two parts: sampling phase offset and sampling clock offset. The 8*8 2048-FFT MIMO-OFDM system with complicated channel model is aimed.

3.1 Sampling clock offset estimation

Sampling clock offset means the different between the sampling frequency of the digital to analog converter (DAC) and the analog to digital converter (ADC). Because of the sampling fre-quency offset, even if the initial sampling point is optimized, the following sampling points will still slowly with time. In Eq. 3.1, the normalized sampling error is defined as ^{r t}

t

T T

 T

 where

T

t and T are the transmitter and receiver sampling period, and the sampling timing offset, _r n T t , increase with index n.

[ ] (

_r

) = ( (1 ) ) = (

_{t t t}

)

r n  r nT r n    T r nT  n T 

(3.1)

After DFT, the effect due to the clock offset is the phase rotate, as shown in Eq. 3.2 and Fig-ure 11.

2 the phase rotation occurred between different symbols and subcarriers. It is obvious that phase rotations increase with the increasing of symbol index and subcarrier index. When subcarrier in-dex is negative, the phase rotation is also negative.

Figure 11: The phase rotation on each subcarrier under SCO..

,

Rl k _k( )m ( ,m k )

Figure 12: Block diagram of the SCO estimation algorithm

Figure 13: The difference of the phase rotation on two short preambles

This algorithm of sampling clock offset estimation is based on the non-HT short training preamble, utilizing the correlation between the two same short preambles. Figure 12 shows the block diagram of the SCO estimation algorithm. Basing on Eq. 3.3, the value of the phase rota-tion



_{l k,} is proportional to subcarrier index and symbol index. First, we translate short pream-ble to frequency domain by N-FFT, where N is the number of samples in one short preampream-ble, as shown in Eq. 3.3. low SNR and multipath fading channel, as shown in Figure 13. In order to decrease the effect, we use some mechanisms to improve the accuracy of slope estimation.

The key construct of those mechanisms is to get rid of seriouslydestroyed data following positive one. The elements in the same group need to be with the same sign, so we use majority rule to delete the fewer elements, such as point A shown in Figure 13.

 Step2:

However, Figure 14 shows that the line composed by phase difference and subcarrier index is not perfect with the influences of AWGN and multipath, so we use the least square algorithm to get the optimal slope. According to the linear algebra theory, if ^x is the least square solution of the systemAxb, the ^x can be gotten using Eq. 3.6.

Using this algorithm, we can estimation a slope of a skew line which is closest to the experi-ment data.

Figure 14: The difference of the phase rotation on two short preambles

 Step3

After step1, some destroyed data have been deleted, but there are still destroyed data such as point B in Figure13. In the step, a trade-off of data hinges on the distance from data to the ap-proximation line which is estimated at step2. According to a threshold value, if the distance is larger than threshold, the data would be abandoned. Finally, we return to step2 to get the slope again.

( ,1) =2

^s

u

slope m mT

  T

 

(3.7)

Figure 14 shows the improvement of slope estimation after those steps. The line (original) is in AWGN and multipath channel, and it is a zigzag line. If we directly compute the approxima-tion line using the rough data, we will get the red dotted line. The dotted line is not near enough for sampling clock offset estimation. After step1, the approximation line becomes the line (delete A) which is near the ideal line. In TABLE Ⅱ, it is obvious that the slope passing those steps be-comes more correct.

TABLE II:

SLOPE IN DIFFERENT STEPS

Original Step1~2 Step1~3 Ideal

Slope 0.0958 0.1327 0.1308 0.1256 SCO(ppm) 15200 21000 20800 20000

As a result, the final equation for estimating the sampling clock offset can be expressed by

( ,1) = 2 2

u

s s

u

slope T m

mT mT

T

 

 

  

(3.8)

3.2 Sampling phase acquisition

After RF down conversion and without SCO effect, all preambles and datum are sampled by using a fixed clock phase which may be not the optimal sampling phase, as shown in Figure 15(a).

The received short preamble is





Figure 15: (a) Phase adjustment-based multiphase A/D sampling

(b) The proposed timing detection in frequency-selective fading.

 

in time domain. Then, we utilize the N-FFT to get the short preamble in frequency domain.

1 2

Signals which are sampled at the optimal phase have the maximal autocorrelation power. So we use the autocorrelation power as timing detection (TD). The autocorrelation can be obtained by

Due to different clock phases causing various timing errors as shown in Figure 15(b), the co-herent clock phase can be found via “step-by-step” scan per preamble in maximizingTD( ) . Yet, this process increases cycles. Unfortunately, most wireless systems have not sufficient preambles.

Hence, the objective of this study is to assure fast and robust recovery.

Figure 16: The state diagram of sampling phase acquisition

TABLEIII

DECISION CRITERIA OF EIGHT REGIONS Region

Figure 16 is the state diagram of the proposed algorithm. Now, we utilize an M-phase clock to control A/D sampling per symbol. The first step is to adjust the A/D sampling clock with

thspecifies the direction of clock offset.

Secondly, compute the slope of

TD ( ) 

such as Eq. 3.12

According to the characteristic cure of TD and the relation of dir1 and dir2, we divided the sampling error (~) into eight regions, as show in TABLE III.

The different condition of each region is described in Table III.

Then, every region corresponds to a mapping-phase which is center of the region, as the following Eq. 3.13.

(3.13)

Based on decision rule of dir1 and dir2, we can find the region where initial

phase (ε) is in and get a mapping-phase to be a estimation phase of the acquisition algorithm.

Because the interval of the region is

4

 and the mapping phase cut the region by half, the phase error will converge to

16

M after timing acquisition, as shown in Figure 17.

[ ~ ]

Figure 17: PDF of sampling phase error

3.3 Combine sampling phase acquisition and SCO estimation

Sampling phase acquisition and SCO estimation algorithm both need to utilize short pream-bles, but wireless systems have not sufficient preambles to supply. Hence, we combined the two algorithms to share the preambles. In this work, there are two problems as follow:

Problem 1:

Sampling phase acquisition algorithm needs to adjust sampling phases at different preambles.

However, the action will cause the phase rotation, _k( )h , which is also proportional to subcar-rier index k, as shown in Eq. 3.14. In the equation, h is the adjustment of phase. The differ-ence of phase between different subcarriers changes degrades the accuracy of SCO estimation algorithm.

( ) 2

k

h h k

 M 

   

(3.14)

Problem 2:

Successive preambles would be sampled with different phases due to the wide SCO. In the other hand, every symbol have different initial phase offset. However, in sampling phase acquisi-tion, the relation of sampling phases between preambles is important. The relation would be un-expected with the influence of wide SCO.

For those problems, we use some mechanisms to improve the performance of proposed algo-rithm. Figure 18 shows that the algorithm utilizes six short preambles to solve sampling clock offset and sampling phase offset in the same time. First, use two short preambles to rough esti-mate SCO and compensate SCO1. After the step, there are still residual SCO, so we would encounter the above two problems in next step.

For problem2, delay sampling phase acquisition algorithm one symbol and utilize 3^th and 4^th symbol to estimate the residual SCO. Through, the estimation may be not correct enough, due to the distance between two symbols is close, but it can use to reduce the effect of problem2. Basing on SCO3, compute the phase shift cased by residual SCO and adjust the phase M1、M2 to maintain the relation needed by sampling phase acquisition.

In Figure 18, symbol5 adjust sampling clock with M1 phase changes. At the moment, prob-lem1 is present. According to Eq. 3.14, the phase rotation of symbol5 increases with the value

( 1)

k M



 .Then, the phase difference,_k(2), between symbol3 and symbol5 will also increase as show in Eq. 3.15.

Figure 18: Block-diagram of six preambles

Figure 19: PDF of sampling phase error (a) without solving problems (b) solve problems

To maintain the linear relation between _k(2)and  , use the new value _k(2) ' to subs-titute _k(2).

(2) ' (2) ( 1)

k k k

M

  

    

(3.16)

Passing six short preambles, SCO and sampling phase offset have been estimated. There is one thing particularly noteworthy that the estimate phase is the initial phase offset of symbol4 not the original phase offset ε. Hence, the phase shift which is caused by residual SCO until sym-bol4 needs to be taken out. Figure 19 shows the performance of solving the above problem.

3.4 Compensation

As mentioned before, most methods use interpolation techniques or ADPLL 、ADDLL to recover analog-to-digital converters (A/D) sampling. In the proposed algorithm, we compensate sampling phase offset and SCO in time domain with the multiphase technique which are

imple-Figure 20: The state diagram of compensation

mented by all-digital clock management (ADCM).

In the aspect of sampling phase acquisition, the algorithm outputs a estimation phase to phase control. However, SCO estimation algorithm outputs a value of normalized sampling clock offset ( ^{r t}

t

T T

T

 ) , so we need a phase translator to get the phase correspond with the value of SCO,

as shown in Eq. 19, where n is the data index and M is the number of multiphase.

_ ( )

_ ( )

(1 )

r s

r s

s s

s

nT SCO phase n nT SCO phase n nT nT

n T nT

n T n M



 

 

 

  

     

(3.17)

Finally, phase control combines the two phases to ADCM.

CHAPTER 4

SIMULATION

We use simulation to evaluate the receiver’s performance with the AWGN, multipath fading and sampling clock offset.

4.1 Simulation Platform

MATLAB is chosen as simulation language, due to its ability to mathematics, such as matrix operation, numerous math functions, and easily drawing figures. A MIMO-OFDM system based on IEEE 802.11n Wireless LANs, TGn Sync Proposal Technical Specification [22], is used as the reference simulation platform. The major parameters are shown in TABLE IV.

4.2 Simulation Result

As mention before, the multiphase generator is used to generate 32 phases between one clock cycles. In other word, the phase error 32 means that signal is delay one cycle, and the phase error 0 means that sign is at ideal phase. With different initial phase error and SNR=14, after timing synchronizer, the final phase errors are convergence into 4 phases, as shown in Figure 21. In TABLE V, the value of root mean square error is more and more larger with SCO increasing, but the probability density function still is Gauss distribution and mean is near to zero .

TABLE IV SIMULATION PARAMETERS

Parameter Value

MCS Set 86

Antenna No. 8*8

Modulation 64 QAM

Coding Rate 2/3

PSDU Length 4096 Bytes

Carrier Frequency 2.4 GHz

Bandwidth 80 MHz

IFFT / FFT Period 25.6 s (2048-FFT)

TABLE V

RMS OF SAMPLING PHASE ERROR

SCO(ppm) 10000 20000 30000 40000

RMS 1.9882 1.8237 2.2410 3.8890

Variance 3.8919 3.3043 4.1429 7.1407 Figure 21: PDF of sampling phase error

To compare with perfect synchronization at 8% PER, SNR losses are about 0.29 dB of SCO=0ppm and 0.51dB of SCO=40000ppm, as shown in Figure 22.

Figure 22: The system performance with 64-QAM SNR=14-dB, 100-ns RMS delay spreading

Figure23 shows the root mean square of sampling errors. No synchronization sample means without an algorithm to fix the error of an unknown initial phase. Those initial phase is random to generate and its RMS is about 9.1~9.5 (phase). The value of RMS is decreasing with the increas-ing of SNR and converges to 2 phases.

The required packet-error rate (PER) is 8% under a packet length of 4096 byte, 64 QAM, IEEE frequency-selective fading with an RMS delay spread of 100 ns. Figure 24 displays the offset tolerance with various SNR and modulations which can be as high as 40000~-30000-ppm, much larger than the 25 ppm in most wireless standards.

Figure 23: The root means square error of sampling phase with 64-QAM SNR=14-dB, 100-ns RMS delay spreading

Figure 24: Offset tolerance with SNR=14-dB, 100-ns RMS delay spreading

在文檔中 應用於超高速傳輸多天線系統(MIMO-OFDM)頻域上之高時脈誤差容忍時間同步器 (頁 13-0)