**CHAPTER 1 Introduction**

**1.4 O UTLINE OF T HIS T HESIS**

In this thesis, Chapter 2 introduces the simulation platform and system specification, including IEEE 802.11a WLAN, LDPC-COFDM UWB system, and multi-band Viterbi COFDM (MB-OFDM) UWB system. The proposed algorithms according to different system requirements will be described in Chapter 3 and Chapter 4. In Chapter 3, we focus on a common throughput (less than 100MHz) frame synchronizer and use IEEE 802.11a WLAN for case study. In Chapter 4, we focus on a high throughput (greater than 500MHz) frame synchronizer and use LDPC-COFDM

8

and MB-OFDM UWB system for case study. The simulation result and performance analysis of our proposed design will be discussed individually in Chapter 5 for three different system platforms introduced in Chapter 2. Chapter 6 shows the architecture of proposed design and its hardware implementation result. Finally, conclusion and future work will be given in Chapter 7.

9

**CHAPTER 2 ** **System Platform **

**CHAPTER 2**

**System Platform**

In this chapter, system platforms used for our case study will be introduced. The first is constructed according to IEEE 802.11a physical layer (PHY), finalized by IEEE 802.11 Wireless LAN committee in November 1999. It is an indoor wireless local area work (LAN) data communication in the 5GHz band. Others belong to OFDM based UWB system, including LDPC-COFDM system [8] and MB-OFDM system [7]. The system specifications of the two system platforms will be introduced individually.

**2.1 IEEE 802.11a PHY **

**2.1 IEEE 802.11a PHY**

**2.1.1 System ** **Platform **

The system platform diagram of our IEEE 802.11a transceiver PHY is shown as FIG 2.1. The transmitter contains two main function blocks：OFDM modulation and forward-error correction (FEC) coding. The OFDM modulation has 64-point DFT with 4 kinds modulation methods listed in TABLE 2.1. The FEC coding supports three coding rates: 1/2, 2/3 and 3/4. The receiver contains three main function blocks: synchronization, OFDM demodulation and FEC decoding.

Synchronization compensates the received signals degraded by channel effects. The detail channel effects will be discussed in section 2.3. After synchronization, the OFDM demodulation transfers time domain signals into frequency domain sub-carriers and FEC decoding corrects the error data caused by channel effects.

10

**AGC****AGC** **AFC****AFC**

**Multi-path**

**insertion** **IFFT****IFFT** **Preamble & GI**
**insertion**

FIG. 2.1 IEEE 802.11a system platform

The major system parameters of IEEE 802.11a PHY are listed as TABLE 2.1. It required 20MHz bandwidth to transfer data. With 4 kinds modulations and 3 coding rates, the supported data rates are from 6M bits/s to 54M bit/s. The detail modulation parameters of supported data rates are listed as TABLE 2.2. For each transferred OFDM symbol, it has 48 data sub-carriers and 4 pilot sub-carriers, total 52 used sub-carriers modulated by 64–point FFT/IFFT. The last 16 points of IFFT outputs will be appended to the OFDM symbol as guard interval to retain the cyclic prefix property of FFT symbol. The performance requirement is less than 10% packet error rate (PER) according to the IEEE 802.11a SPEC.

11

Required bandwidth 20MHz

Date rate (Mbits/s) 6, 9, 12, 18, 24, 32, 48, 54

Modulation method BPSK, QPSK, 16QAM, 64QAM

Error correct code K=7(64 states convolutional code) FEC coding rate (R) 1/2, 2/3, 3/4

FFT size (N) 64

Number of used sub-carriers (NST) 52 Number of data carriers (NSP) 48 Number of pilot carriers (NSD) 4

OFDM symbol duration 4.0 us

IFFT/FFT period (TFFT) 3.2 us

GI duration (TGI) 0.8us (TFFT/4)

Packet Error Rate (PER) performance ≦10%

TABLE 2.1 IEEE 802.11a PHY system parameters

Data rate (Mb/s)

Modulation Coding Rate

TABLE 2.2 IEEE 802.11a PHY data rate dependent parameters

12

**2.1.2 Frame ** **Format **

FIG 2.2 shows the format of the PLCP protocol data unit (PPDU) used for IEEE 802.11a PHY.

It comprises PLCP preamble, PLCP header and data field. The PLCP preamble is used for synchronization, including 10 short symbols and 2 long symbols. The short symbols are used for automatic-gain control (AGC), coarse timing detection and coarse frequency offset estimation.

The long symbols are used for fine timing detection, fine frequency offset estimation and channel estimation. The detail PLCP preamble format and its timing parameters are shown in FIG 2.3 and TABLE 2.3. After the PLCP preamble is the PLCP header. It conveys information about coding rate, modulation type and the data length of PLCP service data unit (PSDU). The last component is data field contains variable number of OFDM symbols by the PSDU length.

### PLCP Preamble SIGNAL DATA FIELD

RATE Reserved LENGTH Parity Tail SERVICE PSDU Tail Pad

### PLCP header

### Coded/OFDM (1/2,BPSK)

### Coded/OFDM (indicated in SIGNAL)

FIG. 2.2 PPDU frame format of IEEE 802.11a PHY

T_{LONG }: long training sequences

GI

SIGNAL OFDM symbol

GI

DATA
OFDM
symbol
t_{1} t_{2} t_{3} t_{4} t_{5} t_{6} t_{7} t_{8} t_{9} ^{t}_{10} T_{1} T_{2}

### PLCP preamble

T_{GI2}

Tshort : short training sequences

FIG. 2.3 PLCP preamble format

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TABLE 2.3 Timing parameters of PLCP preamble

**2.2 Ultra-Wideband System **

**2.2 Ultra-Wideband System**

**2.2.1 System ** **Platform **

In recent years, UWB communication has received much attention as a high speed, low cost wireless LAN implementation in short distance. To promote UWB technology, FCC allowed spectrum from 3.1GHz to 10.6GHz, total 7.5GHz band for UWB devices in 2002. Since UWB system has not been standardized; two baseband systems has been proposed. One is impulse radio based, transmitting nano-second time domain pulses over a wide bandwidth [17~18]. The other is OFDM based, dividing spectrum into several sub-bands and use one OFDM modulation to transfer data. In this paper, we focus on two OFDM based UWB systems for case study. The first is LDOC-COFDM system, having 528MHz bandwidth, 128 point FFT, and low density parity check (LDPC) codec with 120Mb/s~480Mb/s data rates. The detail system spec and system requirement for 8% PER are listed in TABLE 2.4 and TABLE 2.5. The second is MB-OFDM system, transmitting OFDM symbols across three time-interleaved sub-bands. An example of

TPREAMBLE: PLCP preamble duration 16 us (TSHORT + TLONG) TSHORT: Short training sequence duration 8 us (10 × TFFT/4) TLONG: Long training sequence duration 8 us (TGI2 + 2 × TFFT ) t1~t10 : Short symbol duration 0.8 us (10 × TFFT) T1~T2: Long symbol duration 3.2 us (TGI2 + 2 × TFFT ) TGI2: Training symbol GI duration 1.6 us (TFFT/2)

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timing-frequency coding (TFC) for the MB-OFDM system is shown as FIG 2.4. TABLE 2.6 lists the SPEC of MB-OFDM system and TABLE 2.7 lists the system requirement for 8% PER.

TABLE 2.4 LDPC-COFDM system SPEC

TABLE 2.5 Requirement for 8% PER of LDPC-COFDM system

Symbol Length 312.5 ns

Band Period: 937.5 ns Frequency: MHz

3168

3696

4224

4752

pre-guard interval: 60.6 ns OFDM symbol: 242.4 ns guard interval: 9.5ns

FIG. 2.4 An example of MB-OFDM system for TFC (1、2、3、1、2、3)

Data Rate (Mb/s) FFT Bandwidth (MHz) FEC Coding Rate Spreading Gain

120 128-point 528 3/4 4

240 128-point 528 3/4 2

480 128-point 528 3/4 1

Data Rate (Mb/s) Required Distance (m) Required Eb/N0 (dB) Required SNR (dB)

120 10 12.91 7.55

240 4 18.35 16

480 2 20.5 21.1

15

TABLE 2.6 MB-OFDM system SPEC

TABLE 2.7 Requirement for 8% PER of MB-OFDM system

The system block diagram of OFDM based UWB system shown as FIG 2.5. It comprises transmitter, channel model and receiver. Transmitter sends transferred signals meet system SPEC.

Channel model simulates channel interference and RF effects. At receiver, frame synchronizer detects the valid packet and FFT-window boundary. Then received signals are sent to demodulation, FEC decoder and finally it’s sent back to MAC.

Data Rate (Mb/s) FFT Bandwidth (MHz) FEC Coding Rate Spreading Gain

53.3 128-point 528 1/3 4

80 128-point 528 1/2 4

110 128-point 528 11/32 2

160 128-point 528 1/2 2

200 128-point 528 5/8 2

320 128-point 528 1/2 1

400 128-point 528 5/8 1

480 128-point 528 3/4 1

Data Rate (Mb/s) Required Distance (m) Required Eb/N0 (dB) Required SNR (dB)

110 10 12.9 7.1

200 4 18.34 15.2

480 2 20.5 21.1

16

QPSK spreading IFFT preamble insert

FIG. 2.5 System block diagram of OFDM based UWB system

**2.2.2 Frame ** **Format **

**PLCP preamble** **PLCP header** **Data**

**2. Preamble**
** format :**

**30 sync symbols**

**Sync Sequences (128 points )**

**Pre - GI** ^{Post}_{-GI}

**3. Sync symbol**
** format :**

**9.375ns**

FIG. 2.6 Frame format of MB-OFDM UWB system

The Frame format of OFDM based UWB system is shown as FIG 2.6 [19]. One packet is constructed from PLCP preamble, PLCP header, and data field. The PLCP preamble duration is 9.375ns. It has 30 sync symbols, including 21 packet-sync symbols (PS), 3 frame-sync symbols (FS), and 6 channel estimation symbols (CES). One sync-symbol can be divided into pre guard

17

interval, sync sequences and post guard interval. The sync sequences have one hundred and twenty-eight points with constant amplitude (1 or -1). The pre guard interval is the cyclic prefix of sync sequences with 32 points. The guard interval is inserted for transmitter and receiver to switch the carrier frequency to next sub-band.

**multi-path**

FIG. 2.7 Channel model data flow of simulation platform

**2.3 Simulated Channel Model**

**2.3 Simulated Channel Model**

The channel effects flow of our platforms in simulation are shown as FIG 2.7, including multipath fading channel, additive white Gaussian noise(AWGN), carrier frequency offset effect, and sampling clock offset (SCO) effect. We will introduce how these channel effects distorts the transferred data in detail as follows:

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**2.3.1 Multi-Path Fading Channel **

In wireless communication, the transmitting signals may collide with some obstacles and result other time-delay, power-decay reflected paths received by antenna. It is called multi-path interference, as shown in FIG 2.8. In time domain, the multi-path interference causes inter-symbol interference (ISI) from succeeding symbols; and in frequency domain, it causes frequency-selective fading when delay spread is longer than symbol period. In our platform, we model the multi-path interference by the linear convolution of corresponding channel impulse responses as

. In IEEE 802.11a PHY, the channel impulse response is established from the IEEE 802.11a channel model [20]. An example of the IEEE channel impulse response for 100 ns RMS delay spread is shown in FIG 2.9. In UWB system, we use Intel channel model [21] for LDPC-COFDM system and IEEE 802.15.3a channel environment from CM1 to CM4 model [22] for MB-OFDM system. FIG 2.10 shows an example of the UWB channel impulse of Intel channel model for 9ns RMS delay spread.

**RX**

FIG. 2.8 Multi-path interference and ISI effect

19

FIG. 2.9 IEEE 802.11a channel impulse response

FIG. 2.10 UWB channel impulse response

20

**2.3.2 AWGN ** **Model **

At receiver antenna, the transferred signals will be interfered by non-predicted noise. In our
*platform we use AWGN model to simulation the non-predicted noise. The AWGN signal w(t) is *

generated by MATLAB as follows:

*RMS*

*Where L is the length of data signals and RMS is the normalized root mean square power *
defined as:

### 10

^{(}

^{P}

^{data}

^{SNR}^{)}

^{/}

^{20}

### 2 *RMS* =

^{−}

Where *P**data* is the power of data signal ands SNR is the SNR ratio between data signals and
AWGN signals.

**2.3.3 Carrier Frequency Offset Model **

Carrier frequency offset (CFO) is happened due to the difference of carrier frequency

between transmitter RF and receiver RF. The CFO effect in time domain can be represented as follows:

Where *f*_{1} is the carrier frequency of transmitter and *f*_{2} is the carrier frequency of receiver.

The parameter *T* is the period of sample clock. In IEEE 802.11a PHY, the sample clock rate is
20MHz and *T *equals to 50ns. In OFDM-based UWB system the sample clock rate is 528MHz

and *T *equals to 1.894ns .It clearly shows CFO effect will cause linear phase shift in time domain
as Fig 2.11.

21

FIG. 2.11 Linear phase shift caused by CFO

With the linear phase shift in time domain decaying the orthogonality of subcarriers, CFO induces inter-carrier interference (ICI) in frequency domain by moose’s law [23]. ICI effect can be represented as follows：

### [ ] ( )

**2.3.4 Sampling Clock Offset Model **

As shown in FIG 2.7, sample clock offset (SCO) is caused by the variances of sampling frequency between digital to analog converter (DAC) in transmitter and analog to digital converter (ADC) in receiver. In time domain, SCO results time shift from practical sampled points and ideal

22

sampled points. Without compensating SCO effect, the time shift error will be accumulated. It leads ADC to sample the received signal at wrong time and fails receiver behavior. The SCO distortion also makes a linear phase error in frequency domain as FIG 2.12. Thus, we use pilot sub-carriers to estimate the linear phase error caused by SCO to recovery the transferred data.

FIG. 2.12 SCO effect in Time domain and frequency domain

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**CHAPTER 3 **

**CHAPTER 3**

**A Low Complexity Frame Synchronizer ** **for OFDM Application **

**A Low Complexity Frame Synchronizer**

**for OFDM Application**

In this chapter, a low complexity frame synchronizer used for OFDM system is proposed. It mainly chooses the most-significant taps of matched filter used for FFT window detection to reduce correlation complexity of frame synchronizer. To explain our study clearly, the IEEE 802.11a PHY introduced in chapter 2 is selected as our system platform. The detail algorithm, analysis and simulation results will be shown in the following.

**3.1 Frame Synchronizer Data Flow **

**3.1 Frame Synchronizer Data Flow**

**Packet**
**Detection**

**Coarse**
**AFC**

**FFT**
**Window**
**Detection**

**Fine**
**AFC**

**From ADC** **To FFT**

**Long Preamble**
**Detection**

**Frame Synchronizer**

FIG. 3.1 Frame synchronizer data flow

The data flow of proposed frame synchronizer is shown in FIG 3.1. In the initial, packet detection detects the valid packet through normalized auto-correlation algorithm in short preamble.

A decision threshold is chosen to compare with the normalized auto-correlation value. The valid

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packet will be asserted when the normalized auto-correlation value is greater than decision threshold. Then, coarse frequency compensation uses residue short training symbols to compensate CFO ≦ ±4ppm(±20KHz). At the same time, frame synchronization detects the end of short preamble by another decision threshold. Next, FFT window detection finds out start boundary of FFT window by comparing with one long training sequence (cross-correlation algorithm). After deciding the FFT window boundary, fine frequency compensation compensates remain CFO ≦ 0.8ppm(4KHz) and channel equalizer estimates channel response by another long training sequence.

**3.1.1 Packet ** **Detection **

In 802.11a PHY, the valid packet can be detected by depending the periodic data property of PLCP preamble. As mentioned in 2.1.2, short preamble is constructed by ten repeating short symbols and each short symbol has period ‘Ts’ (0.8us). Thus we make a comparison of received signals R(t) and R(t+Ts) by the normalized auto-correlation scheme [24-25] depicted as follows:

*

In the above equation: C*k* is the auto-correlation value and P*k* is the corresponding symbol power.

The parameter ‘N’ is the number of sample points in a short period ‘Ts’ equaling to 16.

25

Normalizing the auto-correlation value C*k *with symbol power P*k ,* we can get a new decision value
λ*k. *The normalized auto-correlation valueλ*k* can detect the valid packet independent with
receiver power level. Thus packet detection begins working without AGC turning the correct RF
receiver gain. In IEEE 802.11a PHY, AGC, packet detection, diversity selection and Coarse CFO
estimation are required to be complete in short preamble duration. The number of short symbols
needed for packet detection should be as less as possible. In our design, since AGC and packet
detection can work simultaneously, they can share short symbols with each other and get longer
estimation time to increase performance. The proposed decision value Λ*k* are defined as
following equation: it uses three short symbol pairs for normalized auto-correlation algorithm.

2

FIG. 3.2 Example of Packet Detection in Proposed Design

26

FIG 3.2 shows an example of packet detection. Noise signals with 5us are added before the
valid packet. The testing channel condition is SNR=0dB, CFO=200KHz(40ppm) and multipath
delay spread=150 ns. The vertical axis is the proposed normalized auto-correlation value Λ*k*. To
detect the valid packet, a pre-defined threshold is needed to compare with Λ*k*. Once the
normalized correlation value is greater than pre-defined threshold, detection of packet will be
asserted. It is clearly under low SNR regions, the normalized auto-correlation value of noise signal
varies extremely. To reduce the error rate of false announcement, a decision window is defined to
test packet assertion. When Λ*k *is greater than pre-defined threshold, the decision window starts
to check the following correlation values. Packet detection only announce when all correlation
values in decision window are also greater than the pre-defined threshold. If not, the packet
assertion will be canceled and packet detection returns the initial state, as shown in FIG 3.2. * *

.

**3.1.2 FFT Window Detection **

In our proposed design, FFT window detection finds the correct FFT window boundary by the known-data property [26]. It compares the received data with the ideal long training symbol data in a pre-defined searching window. The data comparison is based on the cross-correlation algorithm shown as follows：

1 2

In the above equation, ‘R’ is the received data from ADC, ‘C’ is the corresponding compared element of long training symbol. ‘Ln’ is the total number of elements in one long training symbol.

In 802.11a standard, Ln is the same as FFT size equaling to 64. Δ(k) is correlation value of the

27

kth index of pre-defined searching window. Thus the maximum cross-correlation value represents which most similar to the ideal long training symbol, declared as the FFT window boundary.

FIG. 3.3 FFT window detection in AWGN and multi-path channel

28

An example of FFT window detection in AWGN channel and multi-path channel with 150 ns RMS delay spread is shown as FIG 3.3. It is clearly in the AWGN channel, the maximum cross-correlation index will be the start of FFT window as we expected. However in the multi-path channel, the delay spread of other arrival paths makes the maximum cross-correlation value locate in the later samples compared with the ideal FFT window boundary, and the correct FFT window boundary becomes the 2th or 3th peak cross-correlation value in the searching window. A common resolution is choosing the index earlier N points (N is an integer modified by designer) than the maximum cross-correlation value index as preferred FFT window boundary. However, the early catching will reduce the effective GI and degrades system performance in severe multi-path channel [27]. To solve this problem, the TOP ‘M’ pre-cursor searching scheme in [3] was referenced. It defines the index of maximum ‘M’ cross-correlation values as boundary candidates.

The ‘N’ samples before the peak cross-correlation value is pre-cursor window. If there are more than one boundary candidates locating in the pre-cursor window, chooses the earlier index as our preferred FFT window boundary. Otherwise, chooses the peak cross-correlation value index as our preferred FFT window boundary. FIG 3.4 is the FFT window boundary distribution between using pre-cursor searching scheme (In our design, M=5 and N=5) and conventional design (without pre-cursor searching scheme) in multi-path channel with RMS delay spread=150 ns. For the perfect boundary cutting (index=0 at FIG 3.4), using pre-cursor searching scheme has correct probability twice the conventional design. Also the boundary distribution of pre-cursor searching scheme is more centralized, meaning less early catching points needed to retain effective GI.

Comparing the simulation curves in SNR=0dB and SNR=10dB, since increasing SNR can’t reduce

29

multi-path interference, the boundary distribution of conventional design choosing the maximum correlation value in different SNR region are almost the same. However, SNR improvement can reduce probability of error boundary candidates in pre-cursor searching scheme caused by AWGN noise. Thus SNR improvement of pre-cursor searching scheme leads to better boundary distribution centralization (index=0) and less early catching (index from –4 to -1).

FIG. 3.4 FFT window detection in AWGN and multi-path channel

**3.2 Proposed Algorithm **

**3.2 Proposed Algorithm**

**3.2.1 Most-Significant ** **Taps ** **Scheme **

In 802.11a PHY, the most hardware cost of frame synchronizer is FFT-window detection. To

30

implement the cross-correlation scheme (Eq 3.3), matched filter with 64 taps are used to calculate the timing metric Δ(k), meaning 64 complex multipliers(each complex complier has four multipliers and two adders) are needed. Therefore, the most efficient approach for hardware saving is reducing required taps compared in FFT window detection. However, matched filter is based on ML estimation, its compared accuracy has positive relation with input data power. And decreasing tap number of matched filter may result in performance degradation. To reduce required taps of matched filter with the least performance loss, the most-significant taps schemes is proposed.

2

1

* ] [ ])

[

### )

(### ( ∑

= +

### ×

### =

### ∆

^{N}*m*

*m*
*S*
*m*

*S*

*k*

*C*

*R*

*k*

_{ (Eq }

_{3.4) }

In Eq 3.4, the parameter C is the matched-filter coefficient from C0 to C63, corresponding to the 64 taps. S is the index-sorting matrix from the maximum element of C to the minimum element. For example, S[1] represents index of the 1st maximum element of C and S[2] represents index of the 2nd maximum element. The parameter N is the number of used taps modified by user in demand. FIG 3.5 shows the power distribution of matched-filter coefficients in time domain and reorders them by power ratio.

FIG. 3.5 Power distribution of C0~C63 and S[1]~S[64]

31

The contents of index-sorting matrix S is listed as follows:

S≣{15、51、1、33、25、41、30、36、46、20、54、12、35、31、39、27； (1st~16th) 59、7、62、4、45、21、26、40、2、64、16、50、3、63、55、11； (17th~32th) 8、58、60、6、28、38、48、18、43、23、57、9、34、32、49、17； (33th~48th) 44、22、19、47、53、13、14、52、42、24、37、29、10、5、61 } (49th~64th)

FIG. 3.6 Analysis of most significant tap number versus power ratio

In 802.11a standard, the matched-filter coefficients are generated from the long OFDM training symbol transferred into time domain, resulting great power ratio variance between the coefficients. In the most-significant taps scheme, the least power ratio coefficients will be seen as redundant taps and removes from matched-filter. Thus the most-significant taps scheme can reduce

In 802.11a standard, the matched-filter coefficients are generated from the long OFDM training symbol transferred into time domain, resulting great power ratio variance between the coefficients. In the most-significant taps scheme, the least power ratio coefficients will be seen as redundant taps and removes from matched-filter. Thus the most-significant taps scheme can reduce