Multi Dwell Architectures for DS-CDMA Code Acquisition ... - CiteSeerX

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Multi Dwell Architectures for DS-CDMA Code Acquisition in Fading Channels Carlo Caini, Giovanni E. Corazza, Alessandro Vanelli-Coralli Abstract—In this work the problem of code synchronization for CDMA cellular networks, such as IS-95 or cdma2000, is addressed. A multi-dwell testing procedure is adopted and optimized in multiple dimensions. The effects of correlated fading, inter-chip interference, frequency offset, multiple-access interference, and noise are taken into account in the determination of false alarm and detection probabilities. Numerical and simulation results, in terms of time for correct acquisition, confirm the accuracy of the proposed approach and show the definitive advantage of multi dwell architectures. Index Terms—CDMA, Code Acquisition, Fading, Spread Spectrum, IS-95, IMT-2000.

I. Introduction A theoretical framework for the evaluation of a spread spectrum code acquisition sub-system in the presence of arbitrary fading conditions was presented in [1]. This study referred to a multi-dwell architecture with a MAX/TC (Maximum/Threshold Crossing) criterion and a constant false alarm rate (CFAR) threshold design. The above framework can be applied to a great variety of actual synchronization sub-systems and scenarios, such as navigation/localization, military communications, and commercial wireless communications. However, aiming at being very general, it does not deliberately consider any aspect related to the specific implementation of the PN-receiver. On the contrary, this paper aims to investigate a specific architecture implementation, with reference to a CDMA cellular network, exploiting and complementing the general analysis presented in [1]. This study case applies to third generation mobile communication systems (3G) and beyond. In particular, the forward link of a terrestrial CDMA cellular system is considered. From a base station (BS) to the mobile terminals (MT’s), traffic and signalling channels are multiplexed together and transmitted according to a synchronous Code Division Multiplex (CDM) scheme. At the MT, code acquisition can be performed on the purposely transmitted pilot signal, which is not data modulated and has a significant power margin with respect to traffic and other signalling channels. On the contrary, multiplex signals coming from different base stations are asynchronous and with variable power levels. In the presence of such impairments, one could consider the application of multiuser synchronization techniques such as those described in [8], [9]. However, there are several issues here which should be taken into account: (i) the MT receiver complexity must be kept to a minimum; (ii) the low signalThe authors are with the Department of Electronic, Computer Science and Systems, University of Bologna, Bologna, Italy. E-mail: [email protected], [email protected], [email protected] This work was carried out under IST-SATIN project

to-noise ratio (SNR) and rapid fading conditions impair severely any estimation procedure; (iii) the interferers contain pilot signals themselves, which are all valid candidates for acquisition and locking on to the strongest one, which is favored by the near far effect, is perfectly acceptable. In essence, multi-user synchronization techniques are more useful in the reverse link, while for the forward link traditional searching procedures which treat interference as additional background thermal noise [3] continue to be the favored choice. In the analysis, which refers particularly to IS-95, or cdma2000 [10], the effects of correlated fading, inter-chip interference (ICI), frequency offset, noise, synchronous and asynchronous multiple-access interference (MAI), are taken into account. The architecture investigated for the PN-detector can be classified as non coherent, with active correlation and non-coherent post-detection integration. CFAR is achieved by means of an energy detector, working in parallel to the PN one, which provides an unbiased estimation of the background noise and interference in absence of cell synchronization. Analytical expressions for detection and false alarm probabilities at a given dwell, are derived in the paper. They represent the interface, as in [4], between a general analysis and the specific options of the PN-detector. Making use of them, we carried out an overall analysis of the system performance, after having optimized, by means of analytical tools, the multi-dwell system parameters, i.e. the dwell lengths and thresholds. The main results for the optimized structures are presented in the paper, for several kind of fading correlation. Analytical results are supported (and complemented when necessary) by simulation ones. II. System model The forward link of a CDMA cellular system, orthogonal Walsh-Hadamard (WH) sequences [10] of length H are customary used to discriminate amongst the H different channels potentially transmitted by a base station. The ith chip in the `th WH-sequence is indicated as wi` (WHchip), taking values ±1 and having duration Tc . The unmodulated pilot signal is conventionally assigned the WHindex 0, corresponding to the all ones sequence, wi0 = 1, i = 0, ...H −1. The chip rate and the data symbol duration are Rc = 1/Tc and Ts = HTc , respectively. Note that to the end of pilot epoch acquisition the presence of signalling and traffic channels may be considered as internal MAI. To protect the CDM signal from external MAI coming from other coverage cells (or antenna sectors), the signal is multiplied by two PN scrambling sequences api and aqi used for in-phase and quadrature spreading. They have the same

2

chip rate as for the WH-sequences but a greater length, L. ∆ ∆ Defining the operators |i|A = i mod A and bicB = b Bi c, where bxc stands for the largest integer less than x, the low pass equivalent CDM transmitted signal can be written as

s˜T (t) =

+∞ X q X

³

Ec` ap|i| + jaq|i|

i=−∞ `²A0

L

L

´

` b` g(t−iTc ) w|i| H bicH

(1) where A0 is the set of WH-indices corresponding to the active users in the antenna sector including the pilot signal, Ec` and b`i are respectively the transmitted energy per chip and the ith data symbol for the `th user, g(t) is the unitenergy impulse response of the pulse shaping filter. Denoting by ρ(t), θ, ωd , τ0 the overall fading envelope, the phase rotation, the Doppler radian frequency shift and the delay introduced by the radio channel, the baseband equivalent of the received signal can be expressed as s˜R (t) = ρ(t)ej[θ+ωd t] s˜T (t − τ0 ) + µ ˜e (t) + η˜(t)

account for frequency error by considering a power loss Ω with respect to the ideal case [3], setting ωd = ωa = 0. A. Overall detection results and PN-detector decision statistics Focusing on the post-detection sampled output, xd , d = p, q, let Rg (τ ) the transmitted pulse autocorrelation function, φ = θa −θ the carrier phase offset, ρ(k) = ρ[(k+∆)Tc ], τ = τ0 − ∆Tc , with τ ∈ [−∆Tc , (1 − ∆)Tc ), and αp = 0, oc the ratio between the power αq = − π2 . Denoting by IIor spectral densities of the interference coming from other cells and the CDM signal total power, it can be shown [2] that, in the H1 cells, the normalized mean and variance of the the post-detection sampled output are  d 1}  = µd1 (j) = E{x√(j)|H  Ior  q   0  = M Ec /Ior ρ(j)R (τ ) cos(φ + α ) g d Ω H1 : d = p, q Var{xd (j)|H1 } 2   σ1 (j) = =  Ihor n i o    = M ρ2 (j) F (τ, 0) + νR2 (τ )(1 − Ec0 ) + Ioc g

2

(2)

where µ ˜e (t) and η˜(t) are the low pass equivalent of the external MAI (coming from other coverage cells or antenna sectors), and of the wide-sense stationary, complex, zero-mean, additive white Gaussian noise (AWGN) process, with two-sided power spectral density (PSD) N0 . The delay τ0 can be decomposed as the sum of an integer multiple of Tc and of a residual fractional delay. In the subsequent analysis, only the fractional part is left in τ0 (i.e. τ0 ∈ [0, Tc )), while the integer part is assigned to the epoch offset of the locally generated PN sequence.

Ior

(3) where the ICI factor is defined as F (τ, m) =

+∞ X

Rg2 (nTc + τ )

(4)

n=−∞ n6=m

and having introduced the parameter ν to take into account the internal interference cancellation in the H1 cells [2], i.e. the loss of energy that occurs when the accumulator length M is a multiple of the WH sequences length H (ν=0 in presence of cancellation, ν = 1 otherwise). Considering H0 cells, we have

III. Signal detection The acquisition sub-system architecture is based on the Rake receiver structure used for data demodulation. For the purpose of code acquisition each finger of the Rake is composed of two I-Q PN-detectors, with interleaved sampling times 1/2 chip apart (on time and late correlation, respectively). This means that there are two synchronization cells per chip with a total number of cells equal to Nc = 2L. The schematic block diagram of the architecture of an I-Q PN-detector is shown in Fig. 1. Note that frequency downconversion adds a radian frequency offset ωa and a phase rotation θa . Downconversion is followed by despreading. Due to the very low SNR, phase tracking is not deemed practical, and non-coherent detection is used. Furthermore, as the overall frequency error prevents the coherent correlation length, M , from being sufficiently large, non-coherent post-detection integration of length L is also used. In an optimized multi-dwell test this length varies with the dwell order and is denoted by Li , i = 1, ..., N . Therefore the time spent in the ith dwell is given by ti = M Li Tc . Nyquist-rate sampling is enforced at time instant tk = (k + ∆)Tc , where ∆ is either 0 (on-time correlation) or 1/2 (late correlation), to account jointly for the two PN-detectors per finger. As customary, we separately

Ior

H0 :

 µd (j) = 0 σ02 (j) =

E{xd (j)|H0 } √ =0 Ior Var{xd (j)|H0 } =M Ior 2

h ρ2 (j)F (τ ) +

Ioc Ior

i d = p, q

(5) P+∞ 2 R (nT + τ ) is the augmented where F (τ ) = c n=−∞ g ICI-factor. The next step in the characterization of the PN-detector is to derive the statistical distribution of the post detection output, u. Assuming the fading constant during the postdetection integration, u results conditionally distributed as  2 2 in H0 σ0 χ2L (0) µ ¶ u∼ (6) Lλ σ12 χ22L in H1 given ρ 2 σ1 where χ2n (δ) is the standard chi-square distribution with n degrees of freedom and non-centrality parameter δ and λ = [µp1 ]2 + [µq1 ]2 . B. Energy detector and CFAR To achieve CFAR, we make use of an auxiliary energy detector [2] whose output σ ˆ 2 , distributed as σ ˆ2 ∼

4σ02 2 χ (0), M 2M L

(7)

MULTI DWELL ARCHITECTURES FOR DS-CDMA CODE ACQUISITION IN FADING CHANNELS

results to be a scaled, unbiased and asymptotically optimum estimate of the variance σ02 . Introducing the normalized test variable z = u/ˆ σ 2 , and substituting σ ˆ 2 with its mean value (simulation results showed the validity of this approximation), in the ith dwell we have  1  χ2 (0) in H0  8Li 2Li µ ¶ z∼ 1 σ12 2 Li λ   χ 8Li σ02 2Li σ12

Fz|H0 (Z) = 1 − e

(8) in H1 given ρ

LX i −1 k=0

Ãs Fz|H1 ,ρ (Z) = 1 − QLi

1 k (4Li Z) k!

C.2 Search mode (first dwell), H0 -sector

s Li λ , σ12

σ2 8Li Z 02 σ1

(9)

! (10)

C. Detection and false alarm probabilities under a multidwell MAX/TC criterion Let ξi , i = 1, ..., N , be the thresholds in the various dwells. The uncertainty region is divided into Ns sectors, with Ncs cells each, that are serially tested to find the sector that contains the H1 -cell, called H1 -sector (being the others the H0 -sectors). In the first dwell testing, we select cell C (j) if z (j) = max z (i) ≥ ξ1 , else we go to the next seci

tor. Once a candidate cell is selected, this synchronization hypothesis is verified performing multiple dwell tests with different thresholds. The analytical expressions for detection and false alarm probabilities at the different dwells can be derived from (9) and (10), exploiting the statistical independence of the test variables ensured by CFAR. They are schematically reported in the following. C.1 Search mode (first dwell), H1 -sector Correct detection: the H1 -cell test variable is above threshold and is the maximum inside the tested sector (Ncs cells), with probability Z∞ Ncs −1

fz|H1 ,ρ (z) [Fz |H0 (z)]

dz

(11)

ξ1

where fz|H1 ,ρ is the probability density function of the normalized test variable, conditioned on H1 and fading, obtained from (8). Missed detection: all of the test variables inside the sector are below threshold, with probability N cs −1

Pm,1 (ρ) = Fz|H1 ,ρ (ξ1 ) [Fz |H0 (ξ1 )]

N cs

Pf a,1 = 1 − [Fz |H0 (ξ1 )]

(13)

Correct rejection: all the tests variables are below threshold, with probability 1 − Pf a,1 . At the end of the search mode, the cell selected is then repeatedly tested in the subsequent N −1 dwells with either immediate or non-immediate rejection [1]. C.3 Verification mode (other dwells), H1 -cell

where QL (a, b) is the generalized Marcum Q-function of Lth order.

Pd,1 (ρ) =

Error : at least one test variable associated to an H0 -cell is above threshold and is greater than the H1 -cell test variable, with probability Pe,1 = 1 − Pd1 − Pm,1 .

False alarm: at least one test variable is above threshold, with probability

Note that in H0 the normalized test variable z does not have any dependence on fading, as requested by CFAR. The corresponding cumulative distribution functions (CDF) are [5] −4Li Z

3

(12)

Correct detection: the H1 -cell test variable is above threshold, with probability Pd,i (ρ) = P r [z > ξi | H1 , ρ] = 1 − Fz|H1 ,ρ (ξi )

(14)

Missed detection: the H1 -cell test variable is below threshold, with probability 1 − Pd,i . C.4 Verification mode (other dwells), H0 -cell False alarm: the H0 -cell test variable is above threshold, with probability Pf a,i = P r [z > ξi | H0 ] = 1 − Fz|H0 (ξi )

(15)

Correct rejection: the H0 -cell test variable is below threshold, with probability 1 − Pf a,i . IV. Numerical results The system parameters considered in the derivation of the numerical results presented in this section are reported in Table I. The fading envelope ρ(t) is modelled as a Rayleigh process and we make the assumption that fading on two consecutive H1 cell tests is independent. Further, on the basis of channel coherence time, we distinguish three cases: ”perfect correlation” (PC), when the fading is constant on a single multi-dwell test, ”uncorrelated” (UC), when the fading on two consecutive accumulator output is assumed independent, and ”intermediate correlation” (IC), which corresponds to a speed of about 150 km/h. The assumption of independence between H1 cell tests allows us to apply the general analytical results based on the flow graph approach, reported in [1] and in [7], obtaining the average acquisition time and its variance from the detection and false alarm probabilities derived here. Note that in the PC case numerical results can be obtained by analytical formulae, allowing us to perform in a very short time a full optimization of the multi-dwell architecture with respect to the vectors of post detection integration lengths, L = {L1 , ..., LN } and of thresholds, Ξ = {ξ1 , ..., ξN }, as described in the following. In accordance with the J-STD-018 standard [11] the channel conditions are specified in terms of Ec /Ior and

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Ioc /Ior . For the optimization phase the values Ec /Ior = −11.3 dB and Ioc /Ior = 1.8 dB have been chosen, considering up to 8 dwells. Dwell lengths, thresholds and average acquisition time achieved under the optimization conditions are summarized in Table II. Note that, as far as the average acquisition time is concerned, the advantages provided by the adoption of multi-dwell architectures are apparent. Standard deviation results, not reported here for brevity, do not differ sensibly from that of the corresponding average acquisition time, except for the single dwell architectures. A deeper insight on the impact of multi-dwell architectures on the system performance is given by the inspection of Fig. 2, where the average acquisition time versus the Ec /Ior ratio is reported for all the optimized architectures. The performance gain that can by achieved by increasing the number of dwells N (i.e. the complexity of the acquisition system) is not limited to the optimization point but quite general. Moreover, it can be seen that much of the gain is obtained passing from a single dwell to a double dwell architecture with a rapid saturation; in practice, with a 6 dwell architecture all of the potential gain is achieved. For this reason, we selected this architecture to investigate the dependence of the average acquisition time from both the Ec /Ior and the Ioc /Ior ratios in Fig. 3. We can observe the presence of a knee value for Ec /Ior , under which we have a quick performance worsening, while above it the slope of the curve tends to become rapidly flat, with short acquisition times. Increasing the background loading, Ioc /Ior , results in a gradual but evident performance degradation. The impact of fading correlation on system performance is investigated in Fig. 4, considering the 6 dwell system. By inspection of the figure, we can observe that different assumptions on fading characteristics lead to different performance, although the distance in terms of Ec /Ior for a given mean acquisition time is generally less than 1 dB. IC and UC results are obtained by simulation, while PC data are obtained both analytically (continuous line) and, for Ioc /Ior = 2 dB, also by simulation (markers). The substantial agreement validates the much faster analytical approach. Finally, in Fig. 5, the average acquisition time is compared with its median value (50% percentile) and other percentiles curves, such as the 70% and 90 %. (all percentile curves obtained by simulation). The 70% and 90% percentile curves are above the average, but the qualitative behavior is the same. Consequently, we can conclude that a comparative analysis can be safely limited to the evaluation of the mean acquisition time.

expression of the detection and false alarm probabilities, which, inserted in the general formulae for the acquisition time evaluation presented in literature, allow us an overall performance analysis. In the paper, analytical results are supported and complemented by simulation ones. Note that the analytical evaluation proved to be instrumental in carrying out the system optimization. Results show that multi-dwell systems offer a definitive advantage with respect to the single-dwell choice, while the impact of fading correlation on the system performance, when CFAR design is adopted, depends on the system characteristics, as well as on the actual signal to interference ratio.

V. Conclusions

TABLE I Parameters used in numerical evaluations

The performance of a CDMA multi-dwell code acquisition subsystem, designed under a CFAR criterion, is investigated. The effects of fading correlation, inter-chip interference, frequency offset, multiple-access interference, and noise are taken into account in the derivation of decision variable statistics. The aim is to obtain the analytical

References G.E. Corazza, C. Caini, A. Vanelli Coralli, A. Polydoros,”DSCDMA Code Acquisition in the Presence of Correlated FadingPart I: Theoretical Aspects”, submitted for publication on IEEE Trans. on Commun. [2] C. Caini, G.E. Corazza, A. Vanelli Coralli,”DS-CDMA Code Acquisition in the Presence of Correlated Fading-Part II: Theoretical Aspects”, submitted for publication on IEEE Trans. on Commun. [3] A.J. Viterbi, ”Principles of Spread Spectrum Communications”, Addison Wesley,1995. [4] S. Glisic, M.D. Katz, “Modeling of the Code Acquisition Process for Rake Receivers in CDMA Wireless Networks with Multipath and Transmitter Diversity”, IEEE Journal on Selected Areas in Commun., Vol. 19, n. 1, pp. 21-32, Jan. 2001. [5] J. Proakis, ”Digital Communications”, fourth edition, Mc Graw Hill International Editions, 2000. [6] G.E. Corazza, ”On the MAX/TC Criterion for Code Acquisition and its Application to DS-SSMA Systems”, IEEE Trans. on Commun., Vol. 44, No. 9, pp. 1173-1182, Sep. 1996. [7] G.E. Corazza and A. Polydoros, ”Code Acquisition in CDMA Cellular Mobile Networks Part I: Theory”, in Proc. IEEE ISSSTA’98, 1998, pp.454-458. [8] E.G. Strom, S. Parkvall, S.L. Miller, and B.E. Ottersten, ”Propagation Delay Estimation in Asynchronous Direct-sequence Code-division Multiple Access Systems” IEEE Trans. on Comm., Vol. 44 n. 1 , pp. 84 -93, Jan. 1996. [9] S.E. Bensley, and B. Aazhang, ”Subspace-based Channel Estimation for Code Division Multiple Access Communication Systems” IEEE Trans. on Comm., Vol. 44 n. 8 , pp. 1009 -1020, Aug. 1996. [10] V. K. Garg, ”IS-95 CDMA and cdma2000 Cellular/PCS Systems Implementation”, Prentice Hall, Communications Engineering and Emerging Technologies Series, NY, 2000. [11] ”Recommended Minimum Performance Standard for 1.8 to 2.0 GHz Code Division Multiple Access Personal Station”, TIA/EIA/J.STD-018 Interim Standard, July 1997. [1]

Code length, L Chip rate, Rc Number of fingers Number of correlators Walsh Hadamard lenght, H Search mode Freq. offset, ωa Normalized fractional delay, τ0 /Tc Correlation lag, ∆? Number of cell per sector Ncs Coherent correlation lenght, M

32768 chips 1.2288 Mchip/s 4 2 64 serial 5550.0 Hz 0.24 0.5 1 64

MULTI DWELL ARCHITECTURES FOR DS-CDMA CODE ACQUISITION IN FADING CHANNELS

5

10 L {16} {4, 32} {1, 8, 32} {1, 2, 8, 32} {1, 2, 4, 16, 64} {1, 2, 4, 8, 16, 64} {1, 2, 4, 8, 16, 32, 128} {1, 1, 2, 4, 8, 16, 32, 128}

Ξ {0.45} {0.45, 0.37} {0.45, 0.37, 0.37} {0.37, 0.32, 0.35, 0.35} {0.3, 0.3, 0.3, 0.32, 0.32} {0.35, 0.27, 0.27, 0.3, 0.3, 0.32} {0.35, 0.27, 0.27, 0.3, 0.3, 0.3, 0.3} {0.32, 0.17, 0.22, 0.27, 0.27, 0.3, 0.3, 0.3}

TA 16.2 7.3 4.9 4.0 3.7 3.6 3.5 3.4

TABLE II Optimization data (Ec /Ior = −11.3 dB and Ioc /Ior = 1.8 dB)

9 Mean acquisition time (s)

N 1 2 3 4 5 6 7 8

8 7 -4 -2

6

0

2

4

-12

-11

6

8

Ioc/Ior=10 dB

5 4 -6

3 -8

2

-10

1 0 -15

-14

-13

-10

-9

-8

-7

-6

-5

Ec/Ior (dB)

[ G ( f )]*

sp( t )

Fig. 3. Performance dependence on the channel conditions. Mean acquisition time vs. Ec /Ior (dB) with Ioc /Ior (dB) as a parameter; 6 dwell architecture, perfect correlation, analytical results.

νp ap aq

c o s[ ( ω0+ ωa)t + θa] sR( t )

+

yp

∑1

M

xp

( )2

+

( k + ∆)Tc

u

∑1

L

10

PC (f.a.) UC (Sim) IC 150 km/h (Sim) PC (Sim) PC (f.a.)

9

π/2

-ap sq( t )

(1 )

+

yq

∑1

M

xq

( )2

νq

[ G ( f )]* ( 2)

(3 )

(4 )

(5 )

(6 )

Mean acquisition time (s)

8

aq

Ioc/Ior=6 dB

7 6 Ioc/Ior=2 dB

5 4 3

Ioc/Ior=-2 dB

2 1

Fig. 1. PN-detector schematic block diagram. 1) Down-conversion. 2) Chip matched filtering, sampling. 3) I-Q Despreading. 4) Coherent correlation. 5) Square and sum. 6) Post-detection integration.

0 -15

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

Ec/Ior (dB)

Fig. 4. Fading correlation effects. 6 dwell architecture. Perfect correlation (PC), uncorrelation (UC), intermediate correlation (IC, 150 km/h). Analytical (A) and simulation (S) results. 20 Ioc/Ior=2 dB

10

16

PC average

9

N=1

14 12

N=2

10 8 N=8

6

PC50%

8 Acquisition time (s)

Mean acquisition time (s)

18

4

PC70%

A-6 Ioc/Ior=2 dB

7

PC90%

6 5 4 3

2 2

0 -15

-14

-13

-12

-11

-10 Eb/No dB

-9

-8

-7

-6

-5

1 0 -15

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

Ec/Ior (dB)

Fig. 2. Influence of the number of dwell on system performance. Mean acquisition time vs. Ec /Ior (dB), Ioc /Ior = 2 dB, perfect correlation, analytical results.

Fig. 5. Comparison among average acquisition time (analytical) and its percentiles values (simulation). 6 dwell architecture. Perfect correlation.