Computationally-Efficient, Low-Order Filtering Technique for TETRA Release 2 Synchronization

Kasra G. Nezami , Peter W. Stephens Sepura plc

St. Andrews Road, Cambridge, CB4 1GR, UK kasra.nezami@sepura.com peter.stephens@sepura.com

Stuart D. Walker Department of Computing and Electronic Systems,

University of Essex, Wivenhoe Park,

Colchester, Essex, CO4 3SQ, UK stuwal@essex.ac.uk

Abstract— The new TETRA Release 2 standard aims to increase the data throughput of the current TETRA 1 standard by a factor of 10. However there are serious issues with the cross-correlation based timing recovery, as specified in the standard. In this paper, we highlight the TETRA Release 2 timing recovery issues in narrow-band mode as well as the adjacent channel interference (ACI).

A computationally efficient method, based on low-order filtering of the adjacent channel with low peak rejection has been proposed in this paper, which not only completely removes the adjacent channel impact, but substantially reduces the dependence of timing extraction on Signal to Noise Ratio (SNR) level in the region of interest.

Keywords- TETRA Release 2; Frame synchronization; Complexity theory; Correlation; Adjacent channel interference

I. INTRODUCTION Frame-alignment, timing and frequency recovery are an

integral part of any wireless telecommunication system. In multi-carrier transmission systems, based on Orthogonal Frequency Division Multiplexing (OFDM), this has been intensively investigated. Special preambles are exploited in [1], [2] and [3], while cyclic prefixes on the OFDM symbols are used in [3] and [4] to synchronize by means of cross-correlation.

Unlike OFDM, cyclic-extension-less Filtered Multi-Tone (FMT) ([5]), modulated signals have pulse-shaping filters with impulse responses significantly longer than the symbol period and hence require symbol timing recovery. Blind time and frequency synchronization by exploiting the ramp-up characteristics of the pulse shaping filter are discussed in [6]. In [7], a blind Maximum-Likelihood timing recovery technique for Filter-Bank Multi-Carrier Modulation (FBMCM) is introduced , in which the Timing-Error-Detector (TED), uses two sets of filter-banks (one with the actual filter coefficients and the other with their derivatives) to derive the timing-offset. An Early-Late gate (EL-TED) timing recovery method is proposed in [8], while a decision directed symbol timing recovery scheme based on preambles is discussed in [9].

Unlike OFDM, all the FMT synchronization techniques discussed above should receive their TED result via a loop

filter. This is not suitable for the multi-carrier Terrestrial-Trunked-Ratio (TETRA) Release 2 (an ETSI standard) [10]. The FBMCM-based TETRA Release 2 (TR2) receiver is expected to be synchronized with the transmitter on the first frame, received at the beginning of the session, which renders the techniques discussed above unusable.

In the absence of any dedicated timing synchronization bursts, the standard has allocated the first two symbols of the burst to special pilot-symbols, also known to the receiver. The idea is that the multi-carrier modulation of these pilot symbols takes a consistent synchronization waveform, which can be used by the receiver as a training sequence for cross-correlation in time-domain [11]. Hence in theory, the Filter-Bank Multi-Carrier Demodulator (FBMCD) can start demodulation instantly from a synchronized position.

However there are unique characteristics associated with this standard, which may either result in the synchronization producing a very poor cross-correlation performance or needing a computationally expensive architecture.

In section II of this paper, the TR2 multi-carrier transmission system model is discussed. The inefficiency of the TR2 recommended synchronization method in some TR2 modes and the sensitivity of the system to timing estimation error are presented in section III. In section IV, we propose a low-complexity, high performance cross-correlation-based synchronization architecture, suitable for all TR2 modes and across the SNR range. The performance results are given in section V and the paper concludes in section VI.

II. TETRA RELEASE 2 TRANSMISSION MODEL In FMT modulation systems, the input n-QAM sequences

{ }1,...,1,0),( −= NkmYk are grouped in blocks of size N , where k is the sub-carrier index after modulation and m is the multi-carrier symbol number. Each sub-carrier is up-sampled by a factor D and separately shaped with a root-raised-cosine (RRC) Nyquist filter, whose impulse response, { })(ngo , has a roll-off factor of α . Then they are frequency up-converted by multiplication by the complex exponential

{ }1,...,1,0,/2 −= Nke Nknj π. The multiplication results are

This work has been sponsored by Sepura plc., Cambridge, UK

1525-3511/08/$25.00 ©2008 IEEE

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then summed to produce the composite multi-carrier modulated sequence:

����

�� −=

= mok

N

k

Nknj mDngmYeN

ny )()(1)(0

/2π (1)

The TR2 transceiver architecture is shown in Fig. 1. After digital-to-analogue conversion (and RF processing), the multi-carrier modulated signal is transmitted through the multi-path fading channel and analogue to digital converter (ADC) at the receiver before the multi-carrier demodulation. At the demodulator, the received composite sequence { })(nx is frequency down-converted to base-band by multiplying it by the complex exponential { }1,...,1,0,/2 −=− Nke Nknj π and passing the result through the RRC filter, whose impulse response { })(ngR is matched to the transmitter filter:

)()( * ngngoR = (2)

The parallel outputs of the matched filters are then down-sampled by a factor of D to produce the sequence{ })(mX k , which after channel equalization provides { })(ˆ mYk , the best estimate of the transmitted data:

( )Nnkj

mrk enxnmDgmX /2)()()( π− −= (3)

Figure 1. FMT-based TR2 multi-carrier modulation transceiver

In the TR2 standard, the number of sub-carriers can be any of 8,16,32 or 48 for channel bandwidths of 25,50,100 and 150kHz, respectively. The RRC filter roll-off factor α is set to 0.2 and symbol rate ( T

1 ) is 2.4kHz.

The sub-carriers are spaced 2.7kHz apart in order to reduce the interference from/on the adjacent channel and achieve a computationally efficient multi-carrier transceiver architecture based on a poly-phase filter bank and FFT [12].

It also specifies very strong adjacent channel interference (ACI), 47dB higher than the in-band signal at receiver sensitivity (-113dBm), as shown in Fig. 2 below. NDB8, in Fig. 2, refers to Normal Downlink type Burst with 8 sub-carriers in the 25kHz channel. TR2, with its variable channel bandwidth and very tough adjacent specification, demands a level of selectivity not realizable by an analogue/RF sub-system.

Hence all the selectivity needs to be realized in the digital/base-band domain [13]. Fortunately, this selectivity can readily be realized using a multi-carrier filter demodulator, with minimal complexity, by setting it to operate always at the maximum bandwidth.

We show in the next section that the adjacent channel significantly degrades the synchronization performance beyond use, in addition to its already poor performance in narrow-band modes.

III. SYNCHRONIZATION IN TETRA RELEASE 2 The sensitivity of the TR2 system to synchronization timing

error and the issues surrounding cross-correlation based synchronization are discussed in this section.

A. TETRA 2 Sensitivity to Timing Estimation Error Timing estimation error at the input to the multi-carrier

demodulator has the following two adverse effects.

1) Non-optimal sampling point selection by the multi-carrier demodulator.

2) Per sub-carrier phase rotation, proportional to the sub-carrier frequency and delay.

Figure 2. Adjacent Channel as Specified for the 25 kHz channel

47dB

25kHz TR2 signal

-113dBm

-66dBm

25kHz TR1 Interferer

DAC S/P

Multipath Channel

Nk

kπϖ 2=

nje 0ϖ )(0 mY

ADC P/S

)(mX k

)(1 mY

)(1 mYN −

)(ngo

)(ngo

)(ngo

)(ng r

)(ng r

)(ng r

nje 1ϖ

nj Ne 1−ϖ

)(mYk

D

D

D

nje 0ϖ−

nje 1ϖ−

nj Ne 1−− ϖ

D

D

D

)(ny

)(nx

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The standard requires that the internal time base of the Mobile Station (MS) to be adjusted to that of the signals received from the Base Station (BS) with a timing difference not exceeding 125/9µs. This timing accuracy is required to be met at 3 dB below the reference sensitivity level [10].

There are different levels of reference sensitivity defined by the standard for 4-QAM, 16-QAM and 64-QAM modulation techniques as well as channel conditions; i.e. static reference sensitivity for AWGN channel (Additive White Gaussian Noise) and dynamic reference sensitivity for TU50 (Typical Urban at 50km/h) and HT200 (Hilly Terrain at 200km/h) channel conditions.

Table I indicates that 4-QAM modulation in 25 kHz channel bandwidth requires the highest sensitivity level. The values in the table are used to benchmark the cross-correlation for different TETRA 2 channel conditions.

B. Cross-Correlation Based Synchronization The reference waveform, produced from the multi-carrier

modulation of the pilot symbols of the first two multi-carrier symbols of the burst, is cross-correlated with the received noisy signal to identify the frame edge and optimum-sampling point prior to the FBMCD unit. Fig. 3 shows an example of the cross-correlation of the reference vectors with the received data for NDB8 type Burst.

TABLE I. 4-QAM REFERENCE SENSITIVITY LEVELS AND TIMING ACCURACY

Figure 3. Cross-Correlation Result (Bottom) of the Noise Free NDB8 Signal (middle) with the Reference Vector (top)

The Fig. 3 assumes no channel AWGN or ACI. Successful cross-correlation is expected to be achieved in all channel conditions (i.e. Static, TU50 and HT200) and different levels of signal to noise ratio.

Fig. 4 shows the timing accuracy of cross-correlation based synchronization for a NDB48 type burst under Static and HT200 channel conditions.

Here the Root Mean Square (RMS) of the estimation error is presented for different SNR levels. Perfect timing estimation can be achieved in a static channel for all SNR levels. In HT200 channel at 3 dB below the reference sensitivity (i.e. 7dB) the RMS error is marginal. The residual error floor observed in the HT200 is due to the multi-path delay spread.

C. TETRA 2 Cross-Correlation Issues The NDB8 type burst has a lower number of pilot symbols

modulated to form the reference cross-correlation vector (i.e. 1/6th of the NDB48), which results in lower quality cross-correlation performance as shown in Fig. 5.

While the error observed in the Static channel is negligible, the HT200 channel error is much higher and outside the levels specified by the standard. Also the error floor has increased (compared to NDB48) and needs improvement.

The other issue is the cross-correlation performance in the presence of the ACI. In a multi-carrier modulation system, the channel selectivity is achieved by the receiver’s multi-carrier demodulator. So in theory, no filtering of the ACI prior to FBMCD would be needed to ensure correct operation of the demodulator.

But since the time domain cross-correlation is performed prior to the multi-carrier demodulator, the ACI severely affects the performance of the correlator as demonstrated in Fig. 6. The Es/No, in Fig. 6, is set 50dB to eliminate the channel noise impact on timing estimation error. As the adjacent channel power is increased from 10dB below signal power to 47dB above (as specified by the standard), the timing estimation RMS error increases sharply, beyond use.

Figure 4. NDB48 Cross-Correlation Results

Figure 5. NDB8 Cross-Correlation Results

Channel BW/Burst Type

Static Sensitivity (dBm)

Dynamic Sensitivity (dBm)

25 kHz / NDB8 -113 -108 150 kHz / NDB48 -105 -101

Channel BW/Burst Type

Es/No at Static Sensitivity (dB)

Es/No at Dynamic Sensitivity (dB)

25 kHz /NDB8 5 10

150 kHz / NDB48 13 17 Required -3dB level for timing accuracy

2dB 7dB

Reference sensitivity levels for 4-QAM in 25kHz and 150 kHz channels as defined in the standard (Top); Equivalent Es/No levels (Middle); Es/No level at which synchronization is required to be met

(Bottom)

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Figure 6. NDB8 Cross-Correlation: Signal Energy to Adjacent Channel Interference Ratio (dB)

It is imperative to filter out the ACI prior to cross-correlation. Alternative filtering solutions are:

1) Analogue domain filtering of adjacent channel interference: This is not a viable approach as it requires almost brick-wall variable bandwidth analogue filters to support different TETRA 2 bandwidths.

2) Finite Impulse Response (FIR) filtering the signal stream of data from the ADC: There are two issues with the second approach. Firstly, the filter effectively repeats the selectivity function of the FBMCD. The second problem is the high complexity of this approach as described below in terms of the number of Multiply and Accumulate operations (NMAC) needed per burst.

940,032 234)(72192 Q) & (Ilength)(burst (taps) NMAC

=×××=××=

(4)

Filtering out the interference without distorting the in-band signal, destined to both the FBMCD and the correlation function, dictates the use of a high filter order (192 taps), hence the computational complexity (CH) in terms of Million Operations Per Second (MOPS) would be as follows:

MOPS 66.2 0.0142 / 940032 T) /(34)(N C MACH

===×= (5)

To put the above figures in perspective, it is almost twice the FBMCD’s complexity. This is a very high complexity level for effectively a redundant function.

Next we propose a low complexity, highly efficient modification of the cross-correlation based synchronization.

IV. SYNCHRONIZATION BASED ON SHORT PERIOD, LOW SPEC. FILTERING

A low complexity cross-correlation based synchronization is presented in this section. Here we first address the ACI issue by proposing a low complexity filtering strategy, only for the purpose of cross correlation. We then address the poor performance of the cross-correlation at low signal to noise ratio levels by using the magnitude of the cross-correlation peak as a measure of reliability of the estimate. Fig. 7 shows the architecture for the proposed solution.

Figure 7. Reference Cross-Correlation Generation Block-Diagram

A. Periodically Active Low-Order Filtering In order to remove ACI for the purpose of the cross-

correlation, the out of band interference must be filtered out and reduced to below the signal level. Our analysis indicates that the cross-correlation is relatively insensitive to slight attenuation of the outer sub-carriers (droop). So as long as a reasonable cross-correlation is achieved, the specification of the filter, dealing with the ACI, can be relaxed. Fig. 8 shows an example of such filter. The lower plot in Fig. 8 shows a reduced ACI (of Fig. 2) using a very short filter (only 32 taps) which also reduces the wide-band noise level. The 10dB droop in the in-band signal region is due to the gradual roll-off of the low order filter and can be tolerated.

To further reduce the complexity of the proposed low order filter, it needs to be active only for the duration of the two symbols, which contain the reference sync signal, plus a limited search window, during which the cross-correlation peak is expected. With a search window of 200�s (�T/2 ), the total time the filter needs to be active is T×5.2 .

Figure 8. Low Order Filter Freq. Response (top); NDB8 Spectrum with Reduced Adjacent Channel after Filtering(bottom)

*

Low Order Filter

FBMCD & Channelization & ACI rejection

Full-Band ��-ADC with no ACI rejection

Full-band multi-carrier demodulator

�� ADC

Active for a short window

refCross-Correlation

> thrz -1

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B. Rejection of the Low Reliability Peaks The second strategy we have adopted here is to use the

magnitude of the cross correlation peaks (see Fig. 3) as a measure of the reliability of the estimation. An example of the cross-correlation peaks of 18 consecutive NDB8 bursts is shown in Fig. 9. At 25 dB SNR, the peaks consistently produce the correct result, while at 5dB, it is visually clear that the low magnitude peaks are incorrect. By ruling these low magnitude peaks out, a highly accurate estimation, even at low SNR levels can be achieved.

By means of simulation we can determine a threshold level, below which the estimated values will be ignored. This is shown in Fig. 10.

Figure 9. NDB8 TU50 Cross-Correlation Peaks: at SNR=5dB (top); at SNR=25dB (bottom)

Figure 10. NDB8 Cross-Correlation Threshold Levels

In Fig. 10, the RMS timing error based on different threshold levels are presented in different fading channels and for different SNR levels (lower plots), while the percentage of the accepted cross-correlation peaks are presented in the upper plots.

Although choosing a high threshold level can improve the performance, the acceptance rate drops sharply. Using a small number of peaks in the calculations reduces the synchronizer’s response to sudden changes in the channel; hence there is a trade-off here.

We can see that setting the threshold level to 0.45 results in a low RMS error level, while more than 50% of the peaks would be accepted.

V. PERFORMANCE AND COMPLEXITY ANALYSIS

A. Performance Using a low-order filter prior to the correlator in order to

reduce the ACI effects, and setting the rejection threshold of the normalized correlation peaks to 0.45 produces the lowest RMS timing estimation error as shown in Fig. 11 below. We can see that in both channel modes and across the SNR range the RMS error is consistently very small and nearly equal to the minimum achievable level, which performance-wise is even better than when there was no ACI involved.

B. Complexity The proposed filtering method has the following

complexity in terms of the number of Multiply-and-Accumulate (MAC) operations.

,52011 2)5.2(7232 Q) & (Indow)(Search Wi(taps) NMAC

=×××=××=

(6)

Hence the filtering complexity of the proposed architecture (CL) in terms of MOPS is as below:

MOPS0.810.0142/ 11520T) /(34)(N C MACL

===×= (7)

The 0.81 MOPS complexity is more than 80 times less complex than a brute force filtering described in section III.C.

Figure 11. NDB8 Cross-Correlation RMS Error with Filtered Adjacent Channel and Low-Peak Rejection

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VI. CONCLUSION We demonstrated in this paper that the time-domain cross-

correlation of the received signal with reference vectors can be used on its own to acquire and track timing-offset, for wide-band TETRA 2 modes, but it underperforms in narrow-band modes and at presence of the adjacent channel interference.

A low-order filtered adjacent channel with low-peak rejection method has been proposed. The main advantages of the proposed approach are as follows:

1) Adjacent channel interference reduction only for the cross-correlation function

2) Using a low-order filter to reduce the interference. (32 taps only)

3) Filtering only for the duration of the cross-correlation search window.

4) Achieving a low timing RMS error for all channel conditions and across the SNR range.

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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings.

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