Robust OFDM Synchronization

Bryan Hehn

John Hoffmann

Jim Schroeder

Harris Corporation

Government Communication Systems

Melbourne, FL 32902-0037

Abstract

A previous paper [5] presented techniques that

allow compatibility with the existing 802.11a

standard, and also provide a robust mode for

protected communications. We demonstrated the

advantages of remapping subcarriers over each

symbol interval combined with applying a Fast

Hadamard Transformation (FHT) prior to the

application of an Inverse Fast Fourier

Transform (IFFT) to create the time domain

OFDM waveform. The FHT operator reduced

the average power spectral density. This

technique, combined with Frequency Hopped

(FH) subcarriers utilized the entire time-

frequency space available within an OFDM

system to improve the robustness to interference

and reduce the signal detection probability.

The 802.11a synchronization process is

susceptible to jamming. We simulate an

alternative synchronization pattern [1] to reduce

the Packet Error Rate (PER) in the presence of

jamming. Simulation results will be used to

demonstrate the advantages of this

synchronization method as compared to

conventional 802.11a OFDM.

I. Introduction

Orthogonal Frequency Division Multiplexing

(OFDM) is of interest for many wireless systems

due to its robustness to multipath delay and its

potentially high data rate transmission capability.

Unfortunately, OFDM systems are more

sensitive to synchronization errors than single

carrier systems. A number of approaches have

been proposed for estimating the time and

frequency offset [1-4].

For this paper we are interested in 802.11a

synchronization. Since the 802.11a

synchronization process is susceptible to

Jamming, we propose an alternative

synchronization pattern to reduce the Packet

Error Rate (PER) in the presence of jamming.

Simulation results will be used to demonstrate

the advantages of this synchronization method as

compared to conventional OFDM.

II. 802.11a Synchronization Review

The preamble field that is used for

synchronization in the IEEE 802.11a standard

consists of 10 short symbols and 2 long symbols

as defined in Fig. II-1.

Fig. II-1 IEEE 802.11a Preamble

Synchronization Definition

The short symbol, S, modulated onto 52

subcarriers (12 non-zero subcarriers), is given by

+++

+−−−−

+−−−−

+−−+

=−

0,0,

1,0,0,0,1,0,0,0,1,0,0,0,

1,0,0,0,1,0,0,0,1,0,0,0

,0,0,0,0

,

1,0,0,0,1,0,0,0,1,0,0,0,

1,0,0,0,1,0,0,0,1,0,0

6/1326,26

j

jjj

jj

j

jjj

jj

S

An IFFT creates the time domain signal as

defined by

∑=

−=

∆=

2/

2/

2)()(

Nk

Nk

Ftkjk eStwtr

π

with a .8 µsec period (3.2 µsec / 4) repeated 10

times for a total short symbol period of 8 µsec.

A long training symbol is generated by

modulating 53 subcarriers using the sequence

Transformed into the time domain via

∑=

−=

−∆=

2/

2/

)(2)()(

Nk

Nk

TtFkj

kGeLtwtr

π

where TG is the guard interval of length 1.6 µsec.

The total long symbol time is then 1.6 + 2(3.2) =

8 µsec.

III. Synchronization Simulation Results

Short Code – 802.11a

The short code is relatively robust against

jamming, especially if a simple frequency

domain notch filter is applied. The frequency

domain notch filter performed much better than

applying an LMS algorithm as no convergence

time is required. We illustrate used of the LMS

algorithm in simulations using symbol domain

long code sequences.

The Autocorrelation Function (ACF) of the

802.11a time domain short code is shown in Fig.

III-1.

Fig. III-1. Autocorrelation Function of Time

Domain Short Code

The next plot, Fig. III-2., shows the Power

Spectral Density (PSD) of the short code with

four 12 dB sinusoidal jammers added plus 10 dB

AWGN.

Fig III-2. Short Sync PSD (Top), Short Sync +

Four 12 dB Jammers + 10 dB AWGN (Bottom)

In Fig. III-3. and Fig III-4. we plot time domain

waveform ACFs before and after frequency

domain notch filtering to show the potential

improvement in jammer resistance.

Fig III-3. Short Sync Jammed ACF

Fig III-4. Time Domain ACF of Notch Filtered

Short Sync

A comparison of Fig. III-1., the original time

domain ACF with Fig. III-4. the notch filtered

time domain ACF shows that the interference

has been effectively eliminated. Of course there

is more to the story than short sync

autocorrelation.

Short Code – Proprietary

The next step towards a realistic simulation is to

use the detection algorithm that is implemented

in the hardware prototype. In Fig III-5. we plot

the detection peak with no interference. This

preamble design is a modified version of the

IEEE 802.11a as given in [41].

Fig. III-5. Preamble Short Code Detection (Minn

Pattern) Without Interference

In Fig. III-6. we show the preamble short code

detection result with f our 12 dB Jammers Notch

Filtered.

Fig. III-6. Preamble Short Code (Minn Pattern)

Detection With Four 12 dB Jammers Notch

Filtered

Short Code – CAZAC

So called “Constant Amplitude Zero

Autocorrelation” (CAZAC) sequences were

originally developed in the early 1060s [78] for

use in radar system. Subsequently they have

been studied for use in communications

waveform design [77]. CAZAC sequences have

found use in other Harris modem projects so we

developed a simple simulation to test their

jammer resistance.

In Fig. III-7. we plot the ACF of the time domain

short sync preamble without jammer interference

Fig. III-8. and Fig. III-9. we show the ACF in the

presence of 4 X 12 dB jammers before and after

notch filtering to demonstrate the improvements

obtained by filtering.

Fig. III-7. Time Domain ACF of CAZAC

Sequence

Fig. III-8. Time Domain ACF of CAZAC

Sequence With 4 X 12 dB Jammers

Fig. III-9. Time Domain ACF of CAZAC

Sequence With 4 X 12 dB Jammers and Notch

Filter Applied

Long Code – 802.11a

Test Case - LMS:

• J/S = 12 dB CW Jammer

• SNR = 10 dB AWGN

• Code: T1 T2 at 106 bits in length

• Input and reference aligned for LMS

algorithm

• NOTE: Unsynchronized LMS still

converged, but with loss of correlation

peak amplitude

• Results for perfect synchronization in

Fig. VI-10., VI-11., and VI-12.

Fig. III-10 Symbol Domain T1 T2 Long Code

Autocorrelation Function

Fig. III-11. Symbol Domain T1 T2 Long Code

Cross Correlation of Code plus Jammer plus

WGN with Stored Reference

Fig. III-12. Symbol Domain T1 T2 Long Code

Cross Correlation of Code plus Jammer plus

AWGN with Stored Reference after LMS

Filtering (Perfect Code Alignment Input to LMS

Algorithm)

Test Case - FFT:

• J/S = 4 X 12 dB CW Jammers

• SNR = 10 dB AWGN

• Code: T1 T2 at 106 bits in length

• Input and reference aligned for FFT

Notch Filter algorithm

• Results for perfect synchronization in

Fig. VI-13., VI-14., and VI-15.

Fig. III-13. Long Code Time Domain ACF

Fig. III-14. Long Code Time Domain ACF With

4 X 12 dB Jammers + 10 dB AWGN

Fig. III-15. Long Code Time Domain ACF With

4 X 12 dB Jammers + 10 dB AWGN, Notch

Filter Applied

IV. Packet Error Rate Simulations

Introduction

Tactical radios commonly use a standard 802.11a

waveform that is susceptible to narrowband

interference and frequency offset errors. This

paper discusses the current baseline performance

under interference conditions and some methods

from the open literature that can be used to

improve the performance. Both Matlab

simulations and lab measurements are shown.

To understand any improvements that may be

made the current implementation's baseline error

rates were simulated. The Eb/No and the jammer

to signal levels' were simulated. Throughout

much of this memo the Eb/No = 10dB case will

be used as a reference level.

Baseline Bit Error and Packet Detect rate vs

Eb/No

The plots below show the bit error rate and

packet detection rate Vs energy per bit to noise

ratio (Eb/No). The bit error rate is calculated by

comparing the known transmitted bits to the

decoded bits. The packet error rate indicates the

percent of packets that had 1 or more bit errors.

The simulation parameters are BPSK, ½ rate

code, 200 packets of 1,000 bytes each, 0 Hz

frequency offset, perfect timing.

Figure IV-1. Baseline Implementation Bit Error

Rate with ideal packet timing and frequency

offset calculation.

Note that the 11dB Eb/No level error rate was

about 10% packet error rate. This is the error

rate that all algorithm changes will reference and

will be shown on most BER plots.

Baseline Bit Error and Packet Detect rate Vs JSR

The plots in Figure IV-2 show the bit error rate

and packet detection rate Vs jammer to noise

ratio (JSR). In some cases a frequency offset

was applied to the transmitted packet. The bit

error rate is calculated by comparing the known

transmitted bits to the decoded bits. The packet

error rate indicates the percent of packets that

had 1 or more bit errors.

Figure IV-2 Baseline Implementation Error Rate

Vs JSR with ideal packet timing and frequency

offset.

Figure IV-3 Baseline Implementation Bit Error

Rate and Packet Detect Rate Vs JSR, Freq

Offset=500 kHz, non-ideal timing detector &

non-ideal frequency offset compensation

The above plots show that packets are never

detected reliably. A contributing factor to packet

detect rate is false detects. If a false detect

occurs before the actual packet then the packet is

declared lost and the packet detect rate for that

iteration is set to 1. The current implementation

is especially sensitive to very low signal levels

during the silence period. Also, the low level

jammers produce a lot of false detects.

Walsh Transform

This section shows the error rates when the

Walsh transform is turned on. The ideal packet

timing is given to the simulations so the effect of

the packet synchronization is eliminated.

The results are compared with the Walsh Off

simulations.

Figure IV-4 Baseline Implementation Bit Error

Rate with ideal packet timing and non-ideal

frequency offset calculation.

Figure IV-4 shows that the Walsh transform has

about a 1dB implementation loss. There may

need to be further analysis to determine why the

Walsh suffers from this implementation loss.

The magnitude of the Walsh transform shows

when a jammer is added. The figures below

show the error Vs JSR plots.

Figure IV-5 Error Rates vs JSR, ideal packet

timing and non-ideal frequency offset

(foff=0Hz) calculation at 15dB Eb/No.

The figures above show a 15dB improvement in

PER by using the Walsh in a jamming

environment.

Enhanced Short Sync

The previous plots assumed perfect timing

synchronization. However, the first and possible

most important process is packet detection. If a

packet is not even detected then there can be no

hope of recovering any bits or letting the

transmitter know that the link is noisy. Various

proprietary enhancements to the current short

sync detection process were made but none

showed and significant improvement over the

current method. It was determined that to

improve the packet detection under jamming

conditions a new short sync would need to be

designed. Reference [1] shows a simple change

to the current, 802.11, short sync. The method,

called "Minn", throughout this memo was

implemented and simulated.

Figure IV-6 shows the modification of the

current short sync pattern.

Figure IV-6 Diagram showing the construction

of the Minn L=8 short sync

The Minn short sync simply inverts or not group

of 16 samples in some pattern. On the receive

side there will be a longer correlation but there

will be a single peak that indicates the end of the

short sync.

The Minn pattern can be L=8 or L=4 where L is

the number of groups of 16 samples. L=8

showed the most improvement in detection rate

but it does increase the receive processing

complexity. Although the L=8 receive

processing complexity is more than the L=4 or

the current short sync received it should still be

able to fit in the current FPGA resources. The

Minn L=8 is thus chosen as the best candidate.

It might be possible to increase the L to 10 (or

more) to further improve packet detection.

However, it is desirable to keep the current short

sync time of 160 samples. Also the first two

groups of 16 samples are used for AGC settling

and diversity switching so these samples may be

unreliable.

The exact pattern used for the Minn short sync

was found by a computer search that looked for

the pattern yielding the highest peak to average

signal after the packet detector. All of the 2^8

patterns were iterated through and run through

the actual packet detection algorithm and the

highest peak to average waveform was found.

Also, a desirable feature of the correlation

pattern is if there is another peak in the

waveform it should be to the right of the highest

peak. With this peak is found the receiver could

then wait some number of samples to see if a

larger peak may be found.

Figure IV-7 shows some candidate

synchronization patterns and the chosen pattern

(55) for Minn L=8.

Figure IV-7 Some candidate Minn L=8 sync

patterns.

Figure IV-7 shows the packet detection

waveform for five different patterns. The pattern

number indicates the pattern converted to

decimal if the -1's mapped to 0. For instance

pattern number 0 is [-1 -1 -1 -1 -1 -1 -1 -1] and

pattern 255 would be [1 1 1 1 1 1 1 1].

Pattern 121 was used initially because it does

have the best peak to average. However, pattern

55 is now used because the second and third

highest peaks are closer to the main peak. This

feature makes the receiver a bit easier. The

reason is of the algorithm finds a peak it must

wait N samples to see if there is a larger peak.

With pattern 55 N could be made smaller than

with pattern 121. Pattern 121 may be used in

some simulation however this does not change

any relevant findings. During actual packet

detection implementation other pattern may be

tested to determine the optimal under real-world

environments.

The figures below show the error rates Vs JSR

with the Minn L=8 short sync and modified

packet detector.

Current Short Sync, 160 samples, 16 samples repeated 10 times

(16x10)

1

6

1

6

1

6

1

6

1

6

1

6

1

6

1

6

1

6

1

6

Minn L=8 Short Sync, 160 samples (16x10)

1 1 -1 1 1 1 1 -1 1 -1

X

=

8 groups of 16 samples

Figure IV-8 BER & packet detect rate vs JSR

using the Minn, L=8 short sync, freq offset=500

kHz, non-ideal timing detector and non-ideal

frequency offset comp

Figure IV-8 shows that the packets are reliably

detected up to JSR of -5dB. This is a significant

improvement over the original short sync where

packets were not reliably detected below -15 dB

JSR. The plot original short sync (from Figure

IV-3) and the Minn L=8 short sync packet

detections plots are shown below for

comparison.

Figure IV-9 Original Short Sync (left plot) and

Minn L=8 short sync packet detection error rate

vs JSR plots

This short sync has the added benefit of

improved packet detection even under AWGN

only conditions. See Figure IV-10.

Figure IV-10 Packet detect error rate vs Eb/No

with original short sync and Minn L=8 short

sync. Minn L=8 shows ~8dB improvement

V. Conclusions

We simulated two short sync code preamble

options: (i) Existing IEEE 802.11a Standard, (ii)

Modified IEEE 802.11a Standard and use of a

FHT for frequency spreading. Our PER and BER

simulations demonstrated that the selected

preamble design, a modified version as given in

reference [1] of the IEEE 802.11a standard

preamble, is robust to jamming and

computationally efficient. Additionally, we

quantified the performance improved that

resulted from using an FHT.

VI. References

1. H. Minn, V. K. Bhargava, and K. B.

Letaief, "A robust timing and frequency

synchronization for OFDM systems,"

IEEE Transactions on Wireless

Communications, vol. 2, no. 4, pp. 822-

839, 2003.

2. F. Tufvesson and M. Faulkner, “Time and

Frequency Synchronization for OFDM

using PN-Sequence Preambles,” IEEE

VTC 1999.

3. A. Kebo, I. Konstantinidia, J. J. Benedetto,

M. R. Dellomo and J. M. Sieracki,

“Ambiguity and sidelobe behavior of

CAZAC coded waveforms,” pp. 99 –

103, Radar 2007.

4. R. L. Frank and S. A. Zadoff, “Phase shift

pulse codes with good periodic

correlation properties,” IRE Trans. Info.

Theory, Vol. 8, No. 6, pp. 381 – 382,

1962.

5. C. Moffatt and J. Schroeder, “Protected

OFDM Waveform for Tactical

Networks,” Defense Applications of

Signal Processing Workshop,” Kauai,

HI, September 27 – 30, 2009.

6. D. C. Chu, “Polyphase codes with good

periodic correlation properties,” IEEE

Transactions on Information Theory,

Vol. 18, pp. 531 – 532, 1972.

7.M. J. Medley, “Interference Mitigation in

Spread Spectrum Systems Using Lapped

Transforms,” AFRL-IF-RS-TR-2002-96,

May 2002.

8. A. Coulson, “Bit Error Rate Performance

of OFDM in Narrowband Interference

with Excision Filtering,” IEEE Trans. On

Wireless Comm., pp 2484-2492, Vol. 5,

No. 9, September 2006.

9. S. C. Tyler, “The Design of a Frequency

Domain Interference Excision Processor

Using Field Programmable Gate Arrays,”

AFRL-IF-RS-TR-2005-24 In-House

Report, AFRL / ID, Rome, NY, January

2005.

10.Lowdermilk, R.W., and harris, f.j.,

“Design and Performance of Fading

Insensitive Orthogonal Frequency

Division Multiplexing (OFDM) Using

Polyphase Filtering Techniques,”

Asilomar’96, Pacific Grove, Calif., 3-6

November 1996.

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Beach, “Robust Timing Synchronisation

in Multipath Channels,” EURASIP

Journal of Wireless Communications and

Networking, Volume 2008, Issue 4,

Article No. 7, January 2008.

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frequency offset in OFDM systems,"

IEEE Transactions on Signal Processing,

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McLaughlin, "Robust OFDM timing

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