Advanced global navigation satellite system receiver design (797918), страница 14

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An integer or integer and ahalf number of cycles are allowed in each chip interval. The received BOC signal canbe modelled as follows.u BOC (t ) = A × cos(ω0t + φ ) × b(t − τ ) × d5-23For simplicity we consider receiving only a single noiseless BOC signal with no othersignal in phase quadrature. The BOC correlator architecture when employingcorrelation techniques used for conventional PSK receivers is shown in Figure 5-12.wII∫wIQ∫wQQ∫wQIb(t − τˆ)cos(ω0t + φˆ)uBOC(t)∫sin(ω0t + φˆ)~b (t − τˆ)b(t − τˆ)Figure 5-12, BOC correlator using conventional PSK architectureThe correlation results can be written compactly as wIIW =  wQITwIQ cos1 = ∫ u BOC (t )ω0t + φˆwQQ sinT0()Tb (t − τˆ ) ~ dtb (t − τˆ ) 5-24where the orthogonal BOC code sequence is defined as91Receiver theory~T  T b (t − τˆ ) = b t − τˆ + DC  − b t − τˆ − DC 2  2 5-25The result of the integrals in Equation 5-24 can be written as follows.(τˆ − τ ) × dwIQ(τˆ − τ ) × dwQIwQQThe ‘( )≈ A × cos(φ − φˆ ) ×≈ A × sin (φ − φˆ ) ×≈ A × sin (φ − φˆ ) ×wII ≈ A × cos φ − φˆ ×5-26(τˆ − τ ) × d(τˆ − τ ) × d’ symbol represents the multi-peaked BOC correlation function which can bewritten as(τˆ − τ ) = trc(τˆ − τ ) × Λ(τˆ − τ )5-27where the trc( ) function is a continuous triangular cosine waveform wheretrc(τˆ − τ ) → ±1 as τˆ → τ + n × TS , shown in Figure 5-13.trc(τˆ −τ )+1−2TS−TSTS2TS^τ-τFigure 5-13, Triangular cosine functionThe ‘’ symbol represents the BOC discriminator function, equivalent tosubtracting separate early and late correlations, written as follows.92Receiver theory(τˆ − τ ) =T τˆ − τ − DC  −2 T τˆ − τ + DC 2 5-28The wII correlation for a BOC(2×fC, fC) modulated signal is shown in Figure 5-14.

Inorder to locate the BOC signal the search process must remove the dependency oncarrier phase error, this can be accomplished using the conventional PSK searchcorrelation given in Equation 5-9. However, the multiple peaks and troughs of theBOC correlation function introduce nulls across the correlation interval, which reducethe probability of detection. For PSK ½ chip code search bins results in a minimumcorrelation gain of -6dB from the peak gain. For BOC system a minimum correlationgain of -6dB is only achieved with search bins of ½ a sub-chip.10.510.510.500.5100.5-0.51-11Code error (chips)0Phase error (rads)010.5-0.5-1Code error (chips)Figure 5-14, wII for BOC(2×fC, fC) against code error (chips) and carrier phase error(rads)Implementing a standard serial search technique BOC modulation increases the searchtime compared to PSK by a factor of twice the ratio of sub-carrier frequency to coderate (a factor of 4 for BOC(2×fC, fC), or a factor of 12 for BOC(6×fC, fC)).

When FFTacquisition is employed BOC modulation has an equivalent impact on the number ofpoints required. Again compared to PSK the number of FFT points required toachieve equivalent correlation loss increases by a factor of twice the ratio of sub-93Receiver theorycarrier frequency to code rate. Along with increasing code lengths and sampling ratesthis poses an unacceptable overhead on the receiver hardware. Therefore, for reliablefast acquisition of BOC signals it is necessary to form a single peak across thecorrelation interval for the search process.Creating a single correlation peak for BOC search requires additional receiverhardware.

To achieve this we consider two different approaches proposed in theliterature, each with different receiver hardware requirements.The first technique ‘single sideband (SSB) acquisition’ was first proposed by Betz in[Betz 1999]. This method treats each of the two BOC sidebands as separate PSKsignals. This requires independent filtering of each sideband. In addition, eachsideband must have a separate carrier demodulation stage, requiring an additionallocal oscillator to be implemented in the receiver’s correlator architecture.

Figure5-15 shows the receiver hardware required for BOC acquisition using the SSBtechnique. The BOC sidebands can be separated using analogue filters. However,either a multiplexed or additional ADC stage will be required. Using digital filtersimposes considerable demands on the receiver’s correlator resources.2cos(2π×(fC + fS)×t)a(t − τˆ )sin(2π×(fC + fS)×t)2wSBOC(t)uBOC(t)2cos(2π×(fC – fS)×t)a(t − τˆ )sin(2π×(fC – fS)×t)2Figure 5-15, Single sideband search of BOC modulated signals94Receiver theoryThe result of a SSB search is a unambiguous PSK correlation peak as shown in Figure5-4.

If only one sideband is tracked, a 3dB or greater reduction in signal power isinevitable. It has been shown [Martin et al 2003] that the signal power loss can becompensated for by applying the single sideband technique to each side-lobe andcombining non-coherently. This technique can easily be implemented to BOC signalswhich are well separated from the centre frequency, but would require an extremelysharp filter roll-off (Nyquist filtering) for narrowly spaced signals, such as BOC(fC,fC). Therefore, the SSB technique is only suitable for BOC signals whose sub-carrierfrequency is greater than the code rate.The second approach to providing a single BOC search is to synthesise anunambiguous search function by using quadrature or orthogonal BOC correlations.This search technique first proposed by Ward in [Ward 2003] and subsequently hasbeen coined the ‘sub-carrier cancellation’ (SCC) technique [Heiries et al 2004].

Wedefine an orthogonal BOC subcarrier, ~s ( ) . If s( ) is a sine sub-carrier then ~s ( ) is acosine waveform. If s( ) is a cosine sub-carrier then ~s ( ) is a sine waveform. Figure5-16 shows the correlator structure required for using the SCC technique for BOCsearch.2~s (t − τˆ ) × a(t − τˆ )2uBOC(t)cos(2π×fC×t)wSBOC(t)b(t – τ)sin(2π×fC×t)2~s (t − τˆ ) × a(t − τˆ )2Figure 5-16, Sub-carrier cancellation BOC search technique95Receiver theoryThe correlations required for the SSC technique can be written as follows.Tw III()1= ∫ u BOC (t ) × cos ω 0 t + φˆ × b(t − τˆ )dtT 0(5-29)≈ A × cos φ − φˆ × trc(τˆ − τ ) × Λ(τˆ − τ ) × dTw IQI =()1u BOC (t ) × cos ω 0 t + φˆ × ~s (t − τˆ ) × a (t − τˆ )dt∫T 0()≈ A × cos φ − φˆ × trs(τˆ − τ ) × Λ (τˆ − τ ) × dTwQII =()1u BOC (t ) × sin ω 0 t + φˆ × s (t − τˆ ) × a (t − τˆ )dtT ∫0()≈ A × sin φ − φˆ × trc(τˆ − τ ) × Λ(τˆ − τ ) × dTwQQI =()1u BOC (t ) × sin ω 0 t + φˆ × ~s (t − τˆ ) × a (t − τˆ )dt∫T 0()≈ A × cos φ − φˆ × trs(τˆ − τ ) × Λ (τˆ − τ ) × dThe trs( ) function is a continuous triangular sine waveform where trs(τˆ − τ ) → 0 asτˆ → τ + n × TS , shown in Figure 5-17.trs(τˆ − τ )+1−2TS−TSTS2TS^τ-τFigure 5-17, Triangular sine functionThe first subscript denotes mixing with an in-phase (I) or quadrature (Q) carrierreplica, the second subscript denotes mixing with an in-phase (I) or quadrature (Q)sub-carrier replica and the third subscript denotes mixing with in-phase or quadrature96Receiver theory(orthogonal) code replica.

The BOC search correlation using the SCC technique canthen be written as follows.222wSBOC = wIII + wQII + wIQI + wQQI25-30The resulting SCC BOC search correlation is shown in Figure 5-18 for BOC(2×fC, fC)signal.1.2wIIIwIQIwSBOC1.003Correlation amplitude10.8ΛBF( R , 0)ΛBF2( R , 0)0.6ΛBF3( R , 0)0.40.204321−401R2344Code error (sub-chips)Figure 5-18, Magnitude envelopes of the wIII, wIQI and wSBOC correlations for a BOC(2×fC, fC)signalA comparison between the PSK search correlation and equivalent BOC searchcorrelation is shown in Figure 5-19.

The SCC technique creates a stepped correlationfunction which adequately approximates a single correlation peak. Including thequadrature carrier correlations wQII and wQQI removes the phase dependency of thesearch correlation, allowing location with only a coarse frequency lock. Extensiveanalysis and comparison of SSB and SCC search techniques is given via Monte-Carlosimulations in [Heiries et al 2004]. The SCC technique is shown to deliver equivalentperformance to SSB search across a range of carrier to noise densities (22 to 32 dBHz).97Receiver theory1.21.2wSPSKwSBOC143210.80.80.60.60.40.40.20.20123wSPSKwSBOC1410Code error (chips)a)50510Code error (chips)b)Figure 5-19, Comparison of PSK and BOC search correlations using the SCC search technique:a) BOC(2×fC, fC) b) BOC(6×fC, fC)The hardware requirements of the SSB and SCC techniques over conventional PSKarchitectures are shown in Table 5-4.

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