Doppler

DIFFERENTIAL DETECTION OF lt/4-SfllFTED-DQPSK FOR DIGITAL CELLULAR RADIO

Sandeep Chennakeshu General Electric Co. Corporate R&D SchenectadyNY 12301

ABS1RACf

A ~igh capaci ty digital cellular system is being developed in the U.S. ThIS system will use filtered It/4-shifted-DQPSK modulation ac~ving a spectral efficiency of 1.62 bits/Hz. In this paper we hav~ studi~ the BER perform~ce of this modulation using differential detection, A f:li'1gent type differential detector with an integrated sample and camer frequency error correction algorithm is presented. Theoretical and simulation BER results are presented for static and lIat fading channels. Additional results are provided on the BER sensitivity to doppler, lime delay spread, carrier frequency errors and DC offsets.

I. IN1RODUCfJON

The need for an ino:~ in capacity in the U.S. cellular system has led to the use of digital technology, which upon adoption is ex~~ to provide ~ 3. fold increase in capacity. A comprehensive~puon . of the mam link level elements of this system is containedm [1]. This new system will employ TDMA as a channel access method and a digital modulation scheme. In this system 3 to 6 users (dala channels) will share a common 30 KHz RF channel each transmitting data in an assigned time slot which is part of a' larger frame. The gross bit rate to be transmitted over the channel is 48.6 kbps. The modulation scheme will be It/4-shifted-DQPSK. To restrict the adjacent channel interference (ACI) the It/4-shifted-DQPSK signal is filtered at the transmitter by a square root raised cosine filter with an excess .bandwi?th of 35.% (or roll-off of 0.35). A corresponding square root raised cosme filter IS to be used at the receiver.

Transmission of a 48.6 kbps signal within a 30 KHz channel requires a modulation with a spectral efficiency of 1.62 bits/Hz. In addition it is required that the ACI not exceed -26 dB. These requirements can be met by conventional filtered four phase modulation sc~es such as. QP~K and. OQPSK. However, for mobile radio appli- canons S~mmetnc Differential Phase Exchange Keying [2], also known as 1tI4-shifted-QPSK, has some advantages in comparison with QPSK and OQPSK. Three important advantages cited in [3] are summarized here. The main advantage of It/4·shifted-QPSK is that it can be detected using a coherent detector, a differential detector or a discrimi-nator followed by a integrate and dump filter. Differential detection and discrimin~tor detection allow simpler receiver realizations. Coherent detection is more complex than either differential or discrimi-~ detection due ~ the carrier recovery process. Further, in fast fad- I~g coh~rent de~uon results in a higher irreducible BER than differential ~tecuon. and discriminator detection. From this view point OQPSK, which requires coherent detection, is inferior to It/4-shifted-QPSK. . ~ second advan~e is that discriminator detection implies compatibihty for demodu~b~g analog PM. This compatibility is important for a dual mode (digital-analog) receiver. The third advantage relates to the effect of th~ variation ~ signal envelope on the output spectrum and power efficiency of a hnear power amplifier. Since the~nvelo.IX: of a It/4-shifted-QPSK signal does not pass through the origin It exhibits less envelope variation than QPSK and has better output spectral characteristics, However, with a reasonably linear amplifier operated with a small amount of back-off the advantage over QPSK is negligible [II].

OJ. SaulnierECSE DepartmentRPI, TroyNY 12180

The U.S. digital cellular system will use It/4-shifted-DQPSK [12]. 1tI4-shifted-DQPSK is essentially It/4-shifted-QPSK with differential encoding of the symbol phases. The differential encoding mitigates against loss of data due to phase slips. However, differential encoding results in a loss of a pair of symbols when an error occurs. In a lIat Rayleigh fading channel this translates to approximately 3 dB loss in Eb/No relative to coherent 1tI4-shifted-QPSK. 1tI4-shifted- DQPSK can be demodulated using coherent detection, differential detection and discriminator detection. An open loop coherent detectionscheme for 1t/4-shifted-DQPSK has been presented in [4]. In a fast fad-ing channel coherent detection results in a higher irreducible error rate than discriminator or differential detection [3.41. The BER performance using a limiter-discriminator has been studied in [3,4,5]. It has been observed that the presence of the limiter makes this detector sensitive to the transmit filter roll-off factor. However, the detector can be made independent of the transmit filter roll-off factor by adding two additional slice levels [4] or equivalently by modifying the phase of the decoded signal [3], prior to making a decision. In this paper we study differential detection of It/4-shifted-DQPSK which may be viewed as amodification of digital discriminator detection.

Differential detection or delay detection may be implemented at IF [4,7] or at baseband [6,7]. The baseband implementation allows a convenient realization on a digital signal processor (DSP). The baseband implementations considered in [6,7] are based on Sine-Cosine detectors. In this paper we present a Tangent type differential detector with an integrated sample timing and carrier frequency error estimation algorithm. This detector is less sensitive to carrier frequency errors and to amplitude variations in the received signal, relative to the sine- cosine detectors of [6,7].

It is widely accepted that in the presence of lSI the performance of the above differential detectors will degrade rapidly and will not be able to meet the performance requirements for the U.S. digital cellular systems, under multipath conditions [15]. In such cases an equalizer is required. However, when the lSI is small the differential detection scheme, considered here, offers a simple and robust alternative to the more complex equa1izer. Further, the detector presented here is easily modified to serve as a discriminator for analog PM demodulation. In this context our motivation is to study the performance of the tangent type differential detector in the mobile channel using U.S digital cellular signaling specifications.

In this paper the BER performance of the tangent type differential detector is tested using the IS-54 specified TDMA frame structure [121, for base to mobile transmissions. Theoretical results, on the BER performance, are provided for static and flat fading channels. The sensitivity of the detector to doppler, delay spread, sample timing accuracy, frequency offsets and DC offsets is studied through simulations and corresponding results are reported.

II. MODULATION

A It/4-shifted-QPSK signal constellation comprises symbols corresponding to 8 phases. These 8 phase points can be considered to be formed by superposing two QPSK signal constellations offset by 45 degrees relative to each other. During each symbol period a phase angle from only one of the two QPSK constellations is transmitted. The two constellations are used alternately to transmit every pair of bits

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.r

(di-bu) and as a result, successive symbols have a relative phase difference that is one of four angles, namely, ± 1tI4 and ± 31t14. Fig- ure I illustrates the 1t/4-shifted-QPSK signal constellation.

When the phase angles of 1tI4-shifted-QPSK symbols are differentially encoded the resulting modulation is 1tI4-shifted-DQPSK. This can be done by either differentially encoding the source bits and mapping them onto absolute phase angles of a 1tI4-shifted-QPSK signalconstellation or alternately by directly mapping the pairs of input bits onto the relative phases (± 1tI4, ± 31t14), as described in the followingsection.

Ill. TRANSMITTER

In the U.S. digital cellular system data is transmitted in a TDMA frame. A complete definition of the frame/slot structure for base- mobile and mobile-base ttansmission can be found in [1,12]. Figure 2 illustrates the frame/slot structure used in our simulations.

Figure 3 is a block diagram of the transmission scheme used in the simulation study. Data 10 be transmitted is buffered and organized into the TDMA frame format as shown in Figure 2. Next, bits blk and~ are paired (di-bits) and mapped onto differentially encoded signalphases, ~~k using a Gray code as illustrated in Table I. The 1tI4-shifted-DQPSK symbols, represented as a pair (I,Q) are then generated using the following relationship:

The pulse shaped signal is then modulated oeto the carrier, amplified by a linear power amplifier and transmiued, The transmitted signal can be represented as:

s(t) = :E g(t - nT) cos(roct + ~n) (8)

where, roc is the angular carrier frequency.

IV. CHANNEL

In this paper we consider three types of channels. A static channel, a flat Rayleigh fading channel, and a discrete multipath channel. White Gaussian noise is assumed as additive interference in each channel. The discrete multipath channel is modeled as a two ray model with both rays Rayleigh faded with equal average power and shifted in frequency by a Doppler spread proportional 10 the vehicle speed. as described in (13). The delay interval or delay spread ('t) between the two rays is expressed in terms of symbol periods. The rms delay spread, for this two ray model, is one half the delay interval between the two rays.

V.DEMODULATOR

(1)

(2)

where, Ik and Qk are the in-phase and quadrature components of the1tI4-shifted-DQPSK signal corresponding 10 the kth symbol. Hence. if~ represents the absolute phase angle for the kth symbol. basic tri-gonometric identities can be used to express (I) and (2) as:

(4)

(5)

The symbols are then pulse shaped using a square root raisedcosine filter which has a frequency response of the form:

T ~I ns (I-a)2T

I G(OI = ~ t I - sin [ltf (I fl - ir)] (I;) :s;1fl s

(I;)

Figure 4 is a block diagram of the demodulator. In this system the received signal is at the IF frequency. This signal is converted 10

baseband through direct digital conversion by a Dash AID converter and a sorter circuit, as described in [6,8]. The result is two parallelstreams of samples containing the in-phase (Ij) and quadrature (Qj)samples of the baseband 1t/4-shifted-DQPSK signal. These samples are then selected in pairs, once per symbol period, and adjusted for any frequency offset by the Sample and Phase Adjust (SPA) block.

The sample timing and frequency offset estimation process is described in the following section. The frequency correction is applied by phase rotating the sampled signal by an amount proportional 10 the

estimate of the offset in a direction opposite 10 the original rotation. Alternately, since noise is circularly symmetric the frequency offset correction can be applied by adding a corresponding phase angle to theoutput of the differential detector.

An important addition to the differential detector is the modulo-21t correction logic which is applied as follows: If ~~ is the difference between ~ and ~-lo which are the phase angles of the kill and k-lth symbols respectively, then mod-21t correction is applied as:

IF ~~ > 180" THEN ~~ = 360" - ~~.

o I fl > (I+a)2T

(fi)

where a is the roll-off factor and T is the symbol period. Alternately, the square root raised cosine filter can be expressed in terms of its impulse response which can he shown 10 be:

This correction reduces the BER when successive angles wrap-around the positive real axis. The need for this correction is explained by the following example: Let ~ = 10", ~k-I = 340" Then, without the mod-21t correction, ~~ = -330°, when it should actually be

~~ = 30". Thus, the mod-Zx correction removes the wrap-arounderror about the positive real axis.

The corrected relative phase angle is decoded directly into a pair

g(t) =

l-a+45£ It

~[(1+1. )sin( ~ )+(1-1.)cos( ~)]It 4a It 4a

Sin[It(1-a)+ ]+4a+cos[It(l+a)+]

1t.l.[1-(4a.l. i]T T

t = 0

t=±l4a

for all other t

(7)

of bits (di-bits) using the following differential phase decoder. The decoding logic determines the quadrant containing the corrected relative phase angle and outputs the binary value (2 bits) corresponding to the quadrant number minus l. The quadrants are numbered in an anticlockwise direction, starting from the positive real axis, as 1-2-3-4. For a Gray coded ttansmitted bit stream the quadrants are numbered in an anticlockwise direction as 1-2-4-3.

If the sampling rate of the AID is increased and the differencing operation is done at the sampling rate rather than at the symbol rate, then the above structure can be used to demodulate an FM signal. In this case the phase decoder and timing/frequency correction algorithm

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~i"9J

are obviously not used. To decode 1t14-shifted-DQPSK with this discriminator an integrate and dwnp operation is used prior 10 the phase decoder. The sample timing and frequency estimation algorithm remains the same.

VI. SAMPLE TIMING AND FREQUENCY OFFSET ESTIMATION

VII. TIffiORETICAL PERFORMANCE

In this section we provide expressions for evaluating the BER of the differential detector in a static and flat Rayleigh fading channel. based on the method of analysis presented in [5]. For Gray encoded 1t/4- shifted-DQPSK with equally probable signals the BER. in a static and flat Rayleigh fading channel channel. can be expressed as:

Sample timing estimation involves chasing a sample point in each symbol interval which will minimize BER. Sample timing errors result in the inclusion of intersymbol interference components. Carrier frequency offset is the frequency error between the local oscillator at the receiver and the transmitted carrier. The carrier frequency offset

I< 'I',,+II.t+-SItI4

BER= J J-It 'l'2+1I.t+-1tI4

p(1jI11~I)P(1jI21~~d1jlld1jl2 (11)

results in a constant phase rotation per symbol in a specific direction. This is equivalent 10 a shift in the frequency response of one of the baseband square root raised cosine filters by an amount equal 10 the frequency offset, resulting in a mismatch between transmit and receive filters and hence BER degradation.

Two techniques that address sample timing and frequency correction estimation are described in [9.lOJ. The scheme described here is similar in concept 10 that of [9.IOJ. in the context of chosing sample timing and frequency offset correction based on optimizing a metric expressed in terms of the two parameters. However. in each of these schemes a different metric has been chosen for obtaining an estimate of sample timing and frequency error correction.

In the present problem. prior 10 establishing sample timing it is necessary 10 synchronize 10 a IDMA frame/slot. This can be done using a correlation with the preamble sequence contained within each slot. We will asswne that this timing can be established 10 be within±N 1 « N.) samples of the true location. where N. represents thenumber of samples per symbol. Now. the best sample timing location must be selected from:

Similarly. the average symbol error rate (SER). can be expressed as:

I< 'I',,+1I.t+-71t14

SER = J J P (1jI11~I) P (1jI21~~ d1jl1 d1jl2 (12)-I< 'l'2+1I.t+-1fI4

where. 1jfi' i=l,2 and 'i. i=I.2 are the received and true phase angles of two successive transmitted symbols. respectively. 4>1and 4>2can take any of the following angles. 4>i= mitiS. m=1.2 ... S under the con- straint that .i4> = 4>1..... 2 is 1tf4. Note that. for equally probable signals we need only consider only one of four differential phase angles. for the purpose of BER calculation. P (1jfil4>J. i=I.2 represents the proba- bility density function (pdf) of the detected phase angle given thecorrect phase angle.

Static Channel

For a static channel the pdf of 1jIi given 4>ican be shown 10 be:

P(1jfil4>i)= 2~ e-2r [ I+~ COS(4)i-1jIJ

t" = tr.ync ±

NnT.

(9)

where T is a symbol period. n=1.2 •... N. and tr.ync is the sample location corresponding 10 frame/slot sync.

l'(CO·'(+r-'I'v (1-+ erfc[V2Y COS(4)i-1jfJl]

(13)

In order 10 establish sample timing. as described by (9). and estimate carrier frequency offset we perform a 2-dimensional search. as in [9]. 10 find the sample time and phase rotation (corresponding to the frequency offset) that will optimize the following metric:

where.lj = sample instant in each symbol.~i = differential phase angle of i'" symbol of preamble relative 10 the (i-I)'" symbol.Sa = phase rotation per symbol period corresponding a quantized esti-mate of the frequency offset.

= differential phase angle of the i'" symbol corresponding 10

where. erfc[Xl = .1 I e-

dt

and Y is the SNR expressed as EtfNo.

It is noted that (12) is nothing but the pdf of the phase jitter due10 AWGN. which is given in [14]. It is further noted that expressions similar 10 (11) and (13) have been previously derived in the context of limiter-discriminator detection in [5). and hold for the differential detector.

Flat Rayleigh Fading

Assuming that the amplitude variations follow a Rayleigh pdf and thatthe channel induced phase remains constant over two symbol durations it can be shown that:

the ~ sample instant. prior 10 decoding.Np = number of symbols in the preamble.

P(1jfi I4>J = 1 + 2_ COS(4)i-1jIi) [ .!. (14)

27t(1+2y) 7r'( a3(4)i-1jfi) 2

If the magnitude of the phase jitter due 10 A WGN is less that1t12 radians and there is no lSI. then the metric given by (10) is a rough app-oximatioo 10 chosing the largest ML estimate of the snr, for each sample time and frequency offset. averaged over the preamble.

An interesting feature of this sample timing selection scheme is that it allows the AID sampling clock to be free running. Further. the carrier frequency error varies very slowly in comparison 10 the frame rate. and hence carrier frequency error estimation does not have to be done in every time slot. Only sample timing adjustment needs 10 be done in every time slot. This scheme is affected by fast fading since the optimization is done only over a short preamble sequence and accordingly in fast fading the scheme has to be modified suitably. par-ticularly for longer time slots.

where

- f.L(~i.1jIi)- + sin(2f.L(4>i.1jIi)]

_ -I [ -2cos( 4>i- 1jfi) ]f.L(4)i.1jIi)- tan a(~i.1jfi)

and Y denotes the average SNR or average EJNo·

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The expressions given by (11).(12) and (14) also hold forIimiter-discriminator detection.

VIII. SIMULATION

In the simulation study we have assumed the IS-54 signaling specification for base-mobile transmission. Each lDMA frame is 20 ms long. comprising 3 time slots with each user transmitting every third slot. Each user transmits data in a 6.67 ms slot at a data rate of 48.6 kbps, The transmitted symbols were sampled at 8 times the symbol rate. A square root raised cosine filter. with a roll-off factor of 0.35 and truncated to 10 symbols. was used as the transmit filter. The receive filter had a square root raised cosine response which is matched to the transmit filter.

The BER performance was determined using a Monte Carlo simulation procedure. Each simulation was conducted over 1000 frames of data and averaged over 3 independent runs.

. The frame/slot synchronization jitter was simulated by using a uniform random number generator to jitter the frame/slot timing within±~ samples about its true location. The jitter was added at the begin-nmg of each slot and subsequently. sample timing was established anddata decoded.

Frequency offset was added by rotating the received data samples by an amount equal to the slope of the frequency change between two successive samples. Carrier frequency offset correction was performed by estimating the corresponding phase rotation. using (10). and adding the correction to the differentially detected angle.

IX. PERFORMANCE RESULTS

Figure 5 illustrates theoretical and simulation results of BER versus Eb/No for a static and flat Rayleigh fading channel. It is ob~rved that fo~ Eb/No larger than 10 dB the BER in flat Rayleighfading IS approximately equal to O.5(Eb/Nort. Figure 5 also showssymbol error rate (SER). which is observed to be roughly twice the biterror rate. as is expected with Gray encoding.

Figure 6 illustrates BER versus Eb/No, plotted as a function of the maximum doppler frequency at 900 MHz. considering the effect of sample timing selection. The maximum doppler frequency is defined asfimax) = VI')..; where V is the vehicle speed and ').. is the carrierwavelength. It is observed that the sample timing algorithm of (10) results in a small Eb/No loss « I dB) relative to the case of ideal sampling. The degradation with higher vehicle speed is observed to be small.

Figure 7 illustrates that the BER degrades rapidly with delay spread co. for the two ray channel described in Section IV. From Fig-ure 7 it is seen that in order to obtain an uncoded BER of 3% at 17 dB Eb/No the delay spread must be less than an eighth of the symbol period (= 5 118). It is interesting to note that the timing algorithm of (10) shows a slower rate of degradation than if timing were held at the ideal sampling instant corresponding to no delay spread.

Figure 8 illustrates the BER degradation resulting from carrier frequency offset and the improvement using the scbeme of (10). It is observed that there is negligible BER degradation for offsets less than~pproximately 450 Hz and frequency offset correction is not required. In the context of detection. For larger frequency offsets the correction scheme improves the BER. It is observed that when sample timing is included with frequency offset correction there is some additional degradation over the case when ideal sample timing is assumed due to errors associated with sample timing estimation.

Degradation in BER due to DC offsets is shown in Figure 6. It is assumed that the peak to peak signal variation does not exceed the dynamic range of the NO converter. It is seen that there is significant degradation in the irreducible BER for DC offsets on the order of 5%-10% of the peak to peak peak signal amplitude (AnJ. DC offsets canbe eliminated by a simple pre-processing circuit as described in [8].

X. CONCLUSIONS

In this paper we have presented a tangent type differential detector with an integrated sample timing and carrier frequency error estimation algorithm. The performance of this detector for It/4-shifted- DQPSK has been studied for base-mobile transmission using IS-54 signaling specifications. The BER in static and flat fading channels com- pares well with limiter-discriminator detection [3.4.5]. It is observed that the detector is sensitive to sample timing errors and large carrier frequency offsets. For frequency offsets less than approximately 450Hz there is negligible degradation. indicating that correction is not required. The timing algorithm offers acceptable performance in fast fading even with a short preamble of 14 symbols. The uncertainty associated with the proposed sample timing and frequency offset estimation is due to the use of a sub-optimal metric and a short preamble and can be improved by using a longer averaging period. The detector is extremely sensitive to DC offsets and a correction circuit is essential. It was also observed that the detector is insensitive to the roll-off factor of the transmit and receive filters. Further. the detector can be readily modified to demodulate an PM signal. a useful feature for a dual-mode receiver.

Although this detector is simple. robust and offers acceptable performance in a flat Rayleigh fading channel. its performance degrades very rapidly in a multipath channel and hence does not meet the recommended minimum performance standards for U.S digital cellular mobile receivers [15].

XI. ACKNOWLEDGEMENTS

The authors would like to thank A. Hassan and L. Ozarow for the useful discussions and helpful suggestions.

REFERENCES

[I] C-E.W. Sundberg and N. Seshadri. "Digital Cellular Systems for North America". Proceedings of the Global Telecommunications Conference. Vol. 1. pp. 405.5.1-405.5.5. December 1990. San Diego. California.

[2] F.G. Jenks. P.O. Morgan and C.S. Warren. "Use of Four-Level Phase Modulation for Digital Mobile Radio". IEEE Transactions on Electromagnetic Compatibility. Vol. EMC-14. No.4. pp.113-128. November 1972.

[3] Y. Akaiwa and Y. Nagata. "Highly Efficient Digital Mobile Communications with a Linear Modulation Method". IEEE Jour- nal on Selected Areas in Communications. Vol. SAC-5. NO.5. pp. 890-895. June 1987.

[4] S.H. Goode. H.L. Kazecki and D.W. Dennis. "A Comparison of Limiter-Discriminator. Delay and Coherent Detection for It/4- QPSK". Proceedings of IEEE Vehicular Technology Conference. pp. 687-694. May 1990. Orlando. Florida.

[5] S. 000. N. Kondoh and Y. Shimazaki, "Digital Cellular System with Linear Modulation". Proceedings of the IEEE Vehicular Technology Conference. Vol. I. pp. 44-49. May 1989. San Fran- cisco. California.

[6] GJ. Saulnier and W1. Rafferty. "DSP-Based Non-Coherent Dual Detector Demodulator for Land Mobile Radio Channels"• Proceedings of IEEE International Conference on Communica- tions. pp. 32.2.1-32.2.5. 1986.

[7] C-L Liu and K. Feher. "Non-Coherent Detection of It/4-QPSK Systems in a CCI-AWGN Combined Interference Environment. Proceedings of the IEEE Vehicular Technology Conference. pp.83-94. May 1989. San Francisco. California.

[8] G.J. Saulnier. C.M. Puckette, R.C. Gauss. R.I. Dunki-Jacobs, T.E.Thiel. "A VLSI Demodulator for Digital RF Networ1cApplica-tions : Theory and Results". IEEE Journal on Selected Areas inCommunication. Vol. 8. No.8. pp. 1500-1511. October 1990.

[9] G. Ascheid, M. Oerder, J. Stahl and H. Meyer. "An All Digital Receiver Architecture for Bandwidth Efficient Transmission at High Data Rates". IEEE Transactions on Communications. Vol.37. No.8. pp. 804-813. August 1989.

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[10] N.R. Sollenberger and J.C-1. Chuang, "Low-Overhead Symbol Timing and Carrier Recovery for TDMA Portable Radio Sys- tems', IEEE Transactions on Communications, Vol. 38, No. 10, pp. 1886-1892, October 1990.

[11) S. Ariyavisitakul and T.P. Liu, "Characterizing the Effects of Nonlinear Amplifiers on Linear Modulation for Digital Portable Radio Communications", IEEE Transactions on Vehicular Tech- nology, Vol. 39, No.4, pp. 383-389, November 1990.

[12] Cellular System: Dual Mode Mobile Station-Base Station Compa- tibility Standard, EIAfIlA, Project Number 2398, Electronics Industries Association, Engineering Department, October 1990.

[13] W.C. Jakes, Microwave Mobile Communications, Wiley, NewYork,1974.

[14] J.G. Proakis, Digital Communications, McGraw Hill, New York,1989.

[IS] Cellular System: Recommended Minimum Performance Standards for BOO MHz Dual-Mode Mobile Stations (DRAFI), TR4S.3, Pro- ject Number 2216 October 1990.

FRAME FORMAT

20 IDS (972 bits)

TIME SLOT I TIME SLOT 2 TIME SLOT 3

,

Figure 1 : 1tI4-shifted-QPSK Constellation

21 12 130 12

IsYN+~ DATA lovcc I DATA

0000

BASE TO MOBn..E SLOT FORMAT

SACCH : Slow Associated Control ChannelSYNC : Sync and Equalizer Training Sequence (Preamble) DATA : Traffic ChannelDVCC : Coded Diptal Verification Color Code

o 0 RSVD : Reserved bill

o Figure 2 : IS-54 Base-Mobile Frame/Slot Format

Table 1 : Di-bits to Relative Phase Mapping

Figure 3 : Transmission Scheme Used in Simulation

opt. ~

'.t.l

(~)

Figure 4 : Block Diagram of DemodulatorlDetector

190

=

s

loo

10-1

~ fading

~'"~

~

10-1de offset = O.1Aw

de offset » O.OSAp.,

fd (max)=107Hz, 67Hz, 27Hz

.;:t... : ••. \ j~ ". ...0..

Flat Rayleigh Fading ... :::. -.~ • 0

LEGEND

- BER (Theory)• • BER (simulation)- - SER

10-40 5 10 15 20 2S 30 35

Eb/No (dB)

Figure S : Error Performance in Static and Flat Fading channels

100

t=3T/8

:":'1dea1 Slllllple timin. •••• '.. • - - -. -"+ willi SIIIIIple timin, II fd (max)= 27Hz ••~: ••• -_~ _• wiIh SIIIIIple limilllll fd (max.l- 67Hz ••••o willi SIIIIIple timina II fd (max)= 107Hz ~

10-'5l--1 ..0..-~15----.20---2S..---3 ..0..-.-..35----.4O':---:'45

Eb/No (dB)

Figure 6 : Effect of Doppler on Sample Timing and Effect of DC offset

10-1

LEGEND

t=T/4

t=T/S i 10-2

!:- Ideal sample timing

assuming no lSIno offset

=;:- offse ..... SOHz

- - with sample timing (t=O)

o with sample timing (t=T/S)• with sample timing (t=T/4)+ with sample timing (t=3T/S)

t=O .••.•

10-3 .• - offset-9OOHz-0- offse .. 22S0Hz- - offse .. 900 Hz. freq recovery. ideal liming-.00. offsec.900 Hz. freq IIId timin. reco-r• otrseta22S0 Hz. freq recovery. ideal IiminIo otr 22S0 Hz. freq and timiDc recovery

10" ,----,-----,,--,,"---,----,---. --,--- 10~'------"---'---...----.---_._--~--~5 10 15 20 25 30 35 40 45

Eb/No (dB)

Figure 7 : Effect of Delay Spread on SampleTiming

5 10 IS 20 2S 30 35 40

Eb/No (dB)

Figure 8 : Effect of Frequency Offset

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-- -_. --- -_ .. _------

Doppler

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