HIGH BIT-RATE DIGITAL MOBILE RADIO TRANSMISSION WITH A DECISION FEEDBACK EQUALIZER

Hiroshi Suzuki, Takashi Ueda, Akihiro Higashi

NTT Electrical Communication Laboratories Room 908C, "IT, 1-2356 Take Yokosuka-shi, 238-03 Japan

ABSTRACT This paper discusses high bit-rate digital mobile radio transmission performance in a selective fading environment. Analysis and computer simulation show the amount of performance improvement by utilizing a preset-type decision feedback equalizer. The equalizer adopts RLS algorithm for tap coefficient determination. The performance is approximately analyzed by using zero- forcing criteria. This criteria is separately applied to the minimum and non-minimum phase conditions of two-wave selective fading model. The improved performance is almost equivalent to that of two-branch selection diversity reception. Finally, hardware implementations of a dynamic selective fading simulator and a decision feedback equalizer are demonstrated.

INTRODUCTION

High bit-rate transmission over 64 kb/s in mobile radio channels suffers severe transmission performance de- gradation caused by selective fading in the radio propagation. The fading occurs due to mult ipath propagation in the channels, which results in l inear waveform distortion of the received signal. Furthermore, the distortion changes dynamically. One promising technique to improve the performance in dispersive channels is the adaptive equalizer technique [l].

Several papers have shown tha t applications of Decision Feedback Equalizers (DFE) and Maximum Likelihood Receivers (MLR) are effective for improving the transmission performance [2]-[41. In order to successfully apply the equalizer, detailed experiments under dynamic selective fading conditions are necessary [5].

This paper discusses DFE performance for QPSK transmission in the selective fading environment . Furthermore, experimental hardware operations focusing on a selective f ad ing s i m u l a t o r and a DFE a r e demonstrated.

PROPAGATION CHARACTERISTICS

The QPSK signal s(t) with a transmission bit rate 1/T is given by the following complex representation:

where E&) is a complex envelope representing the QPSK whose symbol rate is 1/22', wc is the angular carr ier frequency, and Re[%] is the real part of x . Received signal r(t) a t the predetection band pass filter (BPF) output is a sum of several multipath delayed components:

dt) = Re IE,(t) exp (jw, t 11 (1)

dt) = Re [Er(t) exp (jwct)l (2)

(4)

i = l where N, is the number of components, A&) represents an amplitude fluctuating due to fading, Ck is delay time and N(t) is an additive complex Gaussian noise of power N. Intersymbol interference a t the BPF is assumed to be negligibly small. The component A&) consists of Nk waves Aki whose delay time spread is negligibly small compared to symbol duration 2T. The i-th component of A&) has a carrier frequency offset fo cost&, where f , =wd2n is the maximum Doppler frequency, and 8i is the incident angle. For 1 GHz band carrier frequency, f' becomes 92 Hz a t 100 km/h vehicle speed. The standard deviation of z, is from 2 to 4 ps in urban areas. Dispersion of q larger than 2T frequently occurs for signal transmission with a bit-rate more than 64 kbk, and results in severe signal distortion. This is observed in actual propagation, as shown in Fig. 1 (a) with flat fading and (b) with selective fading.

RECEIVER WITH A DFE

A. Receiver configuration A receiver configuration is shown in Fig. 2. The mixer circuit with a frequency synthesizer converts the received signal into an intermediate frequency(1F) signal. An automatic gain control ( A N ) amplifier amplifies the IF signal to an appropriate level for detection. A quasi- coherent detector, whose reference signal frequency is adjusted by an automatic frequency control (AFC) circuit, converts lhe amplified signal frequency to baseband.

Fig. 1 Received signal spectrum (a) with flat fading (b) with selective fading

6.1.1. CH2655-9/89/0000-0171 $1 .OO 0 1989 IEEE 01 71

f R F v 0 I W

SYNCHRO-

CoNTRoL RESPECWE

- CIRCUITS B+

Fig. 2 Receiver coilfiguration

The received signal is severely distorted due to the selective fading. Two A/Ds, therefore, sample the waveform of in-phase and quadrature components in baseband with a sample rate over 1/2T. A correlator extracts frame timing. A frame synchronization circuit adopting Recursive Least-Squares (RLS) algorithm can estimate the frame frequency with accuracy lo-' in the dynamic dispersive channels 161. A clock synchronization circuit generates the optimum clock phase for the equalizer. A memory circuit temporarily stores the received burst signal, and outputs the stored signal to the equalizer a t a slow rate.

B. Performance The configuration of a decision feedback equalizer is shown in Fig.3. In a fast fading environment, conventional methods such as the steepest descent method cannot determine the tap coefficients. The equalizer includes an exponentially weighted RLS processor which adjusts the tap coefficients by using training sequence. The RLS algorithm is the deterministic counterpart of the Kalman filter theory. Derived coefficients are optimum in the sense of least-square error. An amount of error, on the condition that the tap number is infinite large and noise power spectrum density is small compared to that of signal, is almost equal to that of zero intersymbol interference constraint, i.e., Zero Forcing (ZF) condition. The DFE performance is approximately analyzed using a simplified model, i.e., ZF for two-wave reception. This ZF application in the fading environment results in transmission perform- ance almost equivalent to that of selection diversity reception, as described below: 1) ZF for two-wave reception The following discussion adopts a two-wave model with delay time 2T for simplicity. Received signal Ri sampled a t the rate 1/22' is

R = (woSi + w ,S - 1)A (5)

where wo=Ak(ti)/A is a n received amplitude of the direct signal Si=E,( t i ) , and w1= A& Iti)exp(-jo$?T)/A for delayed signal Si-1 = E , ( t i - n . Variable A represents local standard deviation of the received amplitude. Complex variables WO and w1 are two-dimensional Gaussian processes whose averages are zero and deviations are one. Equalizer combiner output Yi becomes

NF NB Y i = F,R,,,/A- 1 BkSi-& (6)

k= 0 k = l

TAP COEFFICENT DATA INPUT OUTPUT

FEED-FORWARD FILTER 1 1 FEEDBACK FILTER

I

' L - - - - + 4 - - ' PROCESSOR RLS

Pig. 3 Decision feedback equalizer

where Fk is lhe tap coefficient of the feed-forward filter and Bk is that of the feedback filter. It is assumed that the input signal to the equalizer is amplified by the AGC amplifier to RilA and that the input signal for the feedback filter is correct. There are two optimum ZF solutions for coefficient values according to the minimum and non- minimum phase conditions: 1 -a) Minimum phase condition For the minimum phase condition: lwol? Iwll, the ZF algorithm results in a very simple solution:

I71 l/wo fork=O

"F

(8) wl/wo f o r k = l B = [

0 for & = 2 , 3 ; . . , N ,

The equalizer combiner output becomes Yi=Si under noise free condition. This solution allows obtaining the signal from only the feed-forward tap of k = O which contains Si and Si-1 components. The equalizer extracts the Si component and eliminates the Si- 1 component.

I n s t a n t a n e o u s i n p u t c a r r i e r level C a t t h e predetection BPF output i s

where it isassumed that <SiSi-l> =Oand lSil=lSi-1l=l. Therefore, the instantaneous carrier to noise ratio ye is

(10) C A' N N

rc= -= - (Iwd2+Iw,12).

On the other hand, the combiner output complex signal to noise ratio (SNR) rs is

(11)

Equation (11) shows that the equalizer selects the direct component WO. Therefore, the value of rs is about 3 dB less than 7c when Iwllwol is nearly equal to one. 1 -b) Non-minimum phase condition For the non-minimum phase condition, lwol<Iwll, the ZF condition results in another solution:

F =B,/wl (12) 0 ( UJLJ)&-~ l-(WdW1)B1

F = _ - for 1 4 k S N F (13) w1

6.1.2.

.

W >

b- w

4 w N

l w o l 1w1 I

t T

l w o l ' Iw,I

0

-10 -5 0 5 i n

P i i n i i v i irvrl ~ l ~ l ~ ~ ~ o ~ 7 ( A D )

Relative error versus relative level Fig. 4

B,=O for 2 5 k 5 N B (14)

where B1 is an arbitrary complex number. This solution satisfies the Z F condition if FN,-*O or equivalently Iwdw11241. The value of B1 is determined by minimizing noise power at the combiner output.

2(NF+1)

2NF

1 -IwdwJ E = > 1

The noise Nout in (15) is minimum when 1 -IwdwJ

where * denotes a complex conjugate. Therefore, SNR rs and CNR rC are related as

IS;I2 70

The approximatioi of the right hand side is satisfied if NF is large or Iw1IwOl261. The equalizer combiner output becomes Y,=Si under noise free conditions when the tap coefficients are adjusted to (12)-(14). This solution allows obtaining the signal Si from the feed-forward taps of K = 0 and 1, and the other components from Si-1 through S ~ + N , are eliminated. Equation (18) shows that the equalizer selects the delay component w1.

If the feed-forward filter taps are not sufficiently long, the value of IFN,I~ is not small enough to satisfy the ZF condition. Therefore, the w&+N, component is not small

6.1.3.

-*---)-.---* - - --. - --a- - w i t h o u t DFE

:, , ....................................... .- .....................

t w i t h D F E ' : R A Y L E I G H 4

: F A D I N G , .............. ........... .....

5 10 20 20

AVERAGE EdNo(dB)

Pig. 5 Average BER performance versus average EdN,

enough. This component causes intersymbol interference, and becomes residual error &,.2

(19) The combiner output signal ratio to error including the residual error cr2 is

7 , re =

(20) 1 +IwdwJ2 + lwdwd 2NF ( 1 - E l w d w J 2 )

E 7 c The dependence of rS and re normalized by rC with

respect to lwl/wo12 is shown in Fig. 4 for re equal 20 dB. The parameter value NB is 2, --, 8 and 03. The curve of rs given by (11) is derived for the minimum phase condition: lw1/wolSl, however, the curve is extended to Iwl/wol>l in the figure. The curves of rs and re are symmetric when NF +CO, and when NFis finite, re decreases from the value of symmetric curve. As NF increases, the penalty of re decreases. However, when N&6, the amount of the penalty decrease becomes small. In the figure, results of tap coefficient determination of RLS algorithm for N F = ~ is shown by black dots. These almost agree with the derived curves. 2) BER performance of selection diversity reception In the single-wave case, average bit error rate (BER) P, of the above described equalizer output for QPSK with matched filtering and channel identification is equivalent to that of antipodal detection. The BER performance is shown for the static and Rayleigh fading conditions in Fig. 5 where Eb is average energy per bit, and No is noise power spectrum density.

In the two-wave selective fading case, coherent QPSK detection with matched filtering and with the above ideal DFE's operation is almost equivalent to the selection diversity reception. This is because the propagation

01 73

-

condition changes dynamically between minimum phase and non-minimum phase conditions, and the DFE extracts the larger component and el iminates the smaller component. The BER performance of two branch diversity with r / 2 is approximately given by

pe = 3ir2 (21)

The BER performance given by (21) is shown in Fig. 5 by a solid line.

In this figure, results of computer simulations a re shown by the black dots. The simulation results agree well with the theoretical ones. The DFE used in the simulation consists of a seven-tap feed-forward filter and a one-tap feedback filter. It is assumed that the dynamic behavior for a short burst period is negligible. Fig. 5 shows that the ideal DFE is effective in the selective fading environment.

C. Adaptive Algorithm The previously described RLS processor determines the init ial t ap coefficient values. In the f a s t fading environment, adaptive process by the RLS processor is necessary. Performance of the RLS algorithm greatly depends upon its averaging time constant, or forgetting factor. Long term average reduces a error due to noise, whereas the long average increases another error due to time-varying amplitude. The former error results i n increase of noise in the BER performance. On the other hand, the latter error results in a lower limit of BER performance.

EXPERIMENTS

A. Selective Fading Simulator In order to verify the t ransmission performance experimentally, a hardware fading simulator is effective [71-191. A new simulator which can simulate selective fading environment in which delay time, amplitude and phase of a received signal fluctuate dynamically was constructed. The simulator configuration is shown in Fig.6. The simulator utilizes sixteen transversal filter LSIs, and generates the fluctuations described below.

The simulator adopts digital signal processing to simulate the complex envelope of received signal b,y baseband digital signal processing, and it can be applied to any part of the receiver through the following three in terraces. (i) Digital interface to the equalizer, and timing processor. (ii) Analog interface to the AIDS. (iii) Carrier interface to the radio receiver. Furthermore, the delay profile data recorded in the actual propagation experiment can be interpolated and loaded in the simulator. The simulator specifications are shown in the Table.

The microprocessor units with a high-level language program supporting parallel processing can generate various statistical fluctuations according to propagation models. For example, the variables in (2)-(4) are approximately characterized by the following probability distribution functions under the long-term stationary processes.

IAkil : Log-normal IAK(t)l : Rayleigh si : Modified Bernoulli OD : Vehicle speed distribution Oi : Uniform

6.

DATA \\GENE , INPUT

w . I I .. .

Fig. 6 Fading simulator

Table Fading Simulator Specifications

Maximum Sampling Rate 5M samples/s Minimum Delay Time 2ODns Maximum Delay Time 25.6~5 Maximum Number of Delayed Waves Quantization 8bits Maximum Doppler Frequency 300HZ

128 waves

lMHz

1 c)

IMHz

(f)

Fig. 7 Fading simulator output: 1MbIs-QPSK, Roll-off 0.5. (a)-(c)directwave(A=l, @=120°), (d)-(e) with a delay wave (A= 1, @= 120")

Top: Signal space diagram Middle:Eye pattern Bottom:Modulated spectrum

The simulator output signals are shown in Fig. 7. This figure shows signal space diagrams, eye patterns at the analog interface, and spectra of the carrier interface, (a) without a delay wave, and (b) with a 2T-delay wave whose amplitude level is equal to the direct wave and whose relative phase is 120 degrees. I t is shown that the hardware operates well for transmission bit-rate up to 1 M bls .

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B . DFE A decision feedback equalizer, and framing and timing recovery circuits are under construction. The results on the decision feedback equalizer are described below; the others will be reported elsewhere.

A static signal space diagram of the received signal sampled at the A/D converters is shown in Fig. 8 (a). A 22'-delay wave (amplitude: 1 and phase: 120 degrees) is added to the direct wave (amplitude: 1 and phase: 0 degree). Noise of CNR 21 dB is added to the signal by the fading simulator. When the estimation of the above components and timing are complete, the equalized signal is shown in Fig. 8 (b).

Under dynamic fading conditions, the amplitudes and phases fluctuate. For example, with 0.5 ms burst signal transmission in a 100 Hz maximum Doppler frequency environment, the received signal components rotate by an angle of 8=rr/lO radian maximum. This situation is demonstrated in Fig. 11 (e) and (d), where conditions are (c) direct wave: + 8, delay wave: - 8, and (d) direct wave: + 8, delay wave: + 8. Conditions similar to (c) usually occur. However, in order to use more noisy or a faster fading environment, it is necessary to adopt an the adaptive process after the training sequence.

CONCLUSIONS

Performance of high b i t - ra te digital mobile radio transmission in a selective fading environment was discussed. The performance was improved by utilizing a preset-type decision feedback equalizer. The equalizer adopts the RLS algorithm for tap coefficient determination. Approximate theoretical consideration showed t h a t improved performance is almost equivalent to that of selection diversity reception with a 3 dB penalty. Computer simulations using a DFE with a seven-tap feed- forward filter and a one-tap feedback filter verified the results. Finally, hardware implementations of a dynamic selective fading simulator and a decision feedback equalizer were demonstrated. Although the analysis based on the two-wave model is too simple in the ac tua l propagation, th i s model is effective for hardware performance verification and comparison in laboratories.

ACKNOWLEDGEMENT

The authors wish to acknowledge to Mr. Hiroaki Fuketa, Dr. Masaaki Shinji, and Dr. Kenkichi Hirade for their encouragement,and Dr. Takeshi Hattori for his guidance and helpful suggestions.

REFERENCES

[11

[Z]

S. U. H. Qureshi, "Adaptive equalization," Proc. IEEE, vol. 73, pp. 1349-1387, Sep. 1985. J.-E. Stjernvall, B. Hedberg, K. Raith, T. Backstrom and R. Lofdahl, "Radio test performance of a narrowband TDMA system DMSSO," Internation. Conf. Digtal Land Mobile Radio Commun. Venice, pp. 310-318, June 1987.

Fig.

141

151

VI

181

[91

(C) (d)

8 Equalizer output (a) Distorted equalizer input, CNR 21 dB (b) Equalized output, static conditions (c) Equalized output, dynamic conditions:

(d) Equalized output, dynamic conditions: Direct wave: + 8, Delay wave: - 0

Direct wave: + 8, Delay wave: + 8

G. D'Aria and V. Zingarelli, "Results on fast-Kalman and Viterbi adaptive equalizers for mobile radio with CEPT/GSM system characterist ics," Proc . of Globecom '88,26.3.1-26.3.5,1988. H. Suzuki, "GMSK maximum likelihood receiver for mobile radio transmission," Tech. Report of IEICE of Japan, CS 88-2, May 1988. R. W. Lorenz, "Impact of frequency-selective fading on digital land mobile radio communication at transmission rate of several hundred kbiffs." IEEE Trans. on V T , vol.VT-35, pp. 122-128, Aug. 1987. K. Fukawa and H. Suzuki, "Configuration and performance of clock recovery circuit for high speed digital mobile transmission system," Tech. Report of IElCE of Japan, RCS 88-57, Feb. 1988 B-473 (in Japanese). K. Hirade, T. Hattori, F. Adachi," Fading simulator for land mobile radio communication," Tram. IEZCE of Japan (B), J58-B, pp. 449-456, September 1975 . H. W. Arnold and W. F. Bodtmann, "A hybrid multichannel hardware simulator for frequency selective mobile radio path," IEEE Trans. on Commun., COM-31,3, pp. 370-377, March 1983. R. W. Lorenz, "Modelling of the time and frequency variation of the mobile radio channel," Proc. Digital Land Mobile Radiocommunication Workshop, Pontecchio Marconi, pp. 63-72,1985.

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