Compensation of co- and adjacent-channel interference in FM receivers

SIGNAL

PROCESSING Signal Processing 36 (1994) 201-208

ELSEVIER

Compensation of co- and adjacent-channel interference in FM receivers Armin Schlereth Institute of Communication Theory, University of Erlangen-Nfirnberg, D-91058 Erlangen, Cauerstrafle 7, Germany

Received 16 April 1993; revised 8 July 1993

Abstract The problem of co-channel and adjacent-channel interference in EM receivers is considered. Three new digital algorithms are presented, which have the capability to suppress interference noise at the output of a conventional digital FM demodulator. For this, the information of the envelope of the input signal is used.

Zusammenfassuag Es wird die Problematik der Gleich- und Nachbarkanalst6rung in FM-Empffingern behandelt. Drei neuartige digitale Algorithmen werden vorgestellt, die die Eigenschaft besitzen, das Interferenzger/iusch am Ausgang eines konventionellen digitalen FM-Demodulators durch Kompensation zu reduzieren. Hierzu wird die Information der Einhiillenden des Eingangssignals genutzt.

R6sum6 Le probl6me de l'interf6rence entre canaux communs et canaux adjacents dans les r6cepteurs FM est consid6r6. Les trois nouveaux algorithmes digitaux pr6sent6s ont la capacit6 de supprimer le bruit d'interf6rence ~ la sortie d'un d6modulateur FM conventionnel et digital. Pour cela, l'information d'enveloppe du signal est utilis6e. Key words: Adjacent-channel interference; Co-channel interference; Compensation; Estimation; FM receiver

I. Introduction

with

In this paper the d e m o d u l a t i o n of F M signals in the presence of one co-channel or adjacent-channel interferer is discussed. In order to realize the digital F M d e m o d u l a t o r at the m i n i m u m sampling rate of a b o u t fA = 6 0 0 k H z , a B a s e b a n d - D P L L (BBD P L L ) is used [5]. The input signal is g ( t ) = ~ a(t)e j6°"~ J + ~ b(t)e j~(') , Y desired signal

(1)

Y interferer

0165-1684/94/$7.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 1 6 5 - 1 6 8 4 ( 9 3 1 E 0 0 8 6 - Z

4'°(0 --- 2~ A fo

~)b(t) = 2 ~ A F b

v.(r) dr,

f

v~(r)dr + 2~"

Afvs Y carrier

"t,

offset

AF.,b are the frequency deviations of the two received F M signals. In the case of a co-channel interferer, the carrier offset AfTs is zero.

202

A. Schlereth / Signal Processing 36 (1994) 201 208

Rearranging Eq. (1) yields

L_ p(t) 9(0 = a(t)e j*°{'l 1 + ~

after demodulation. This leads to better signalto-noise ratios (SNR)o at the output, if the conventional demodulator locks onto the desired signal.

" ~b(t) e j{*,{0- ~°~,)1

2. Compensation of co-channel interference

=~a ()t r ()t e j(~°(t} + ~b.,(t)},

(2)

with

p(t) sin ~,(t) 1 + p(t)cosO(t)J'

(3)

r(t) = x/1 + pZ(t) + 2p(t)cos ~b(t).

(4)

~ba~(t) = arctan

Assuming p(t)<< 1 the following assumptions are made: q~a~(t) ~ p(t)sin 0(t),

(5)

r(t) ~ 1 + p(t)cos O(t),

(6)

r(t) is the envelope normalized to the amplitude a of the desired signal. Fig. 1 shows the phasor diagram of the input signal relative to the desired signal. In [6] digital algorithms are proposed, which compensate an adjacent-channel interferer by estimating the phasor of the interferer and subtracting it from the input signal. In this paper the information of the normalized envelope r is used for compensation of co- and adjacent-channel interference

In [3, 4], a new algorithm is presented, which improves the signal-to-noise ratio (SNR)o at the output of a PLL FM demodulator using a combination of the envelope and the demodulated signal as follows:

[2r(t)-_ 1] ,[4~a(t) +,. ~.~(t)], y,(t) = l_

r(t)

(7)

o.,p., signal of the FM-demodulator

Here an ideal FM demodulator is assumed, which provides the instantaneous frequency Ca + ~a~" An important constraint is that the amplitude a of the desired signal has to be known in order to use the information of the envelope a(t)r(t) of the input signal in (2) for the evaluation of r(t). Substituting Eq. (6) in (7) yields

F 1 + 2p(t)cos~(t) 1 y,(t) ~ L -1 + p-~-c--os-s~ j [q~.(t) + ~.~(t)].

(8)

If p(t) << 1, then

y,(t) ~ [1 + 2p( 0 cos O(t)] [1 - p(t) cos 0(t)]

,°l

x [~.(t) + q~a~(t)].

(9)

Neglecting higher-order terms, we get

~

d*b'**}

0,

Fig. 1. Phasor diagram of the normalized input signal.

yl(t) ~ [-1 + p(t)cos ~k(t)] [q~,(t) + q~,~(t)].

(10)

Substituting (6) in (10) leads to

yl(t) .~ r(t)[dp.(t) + ~,,(t)] ~ y2(t).

(11)

Further on, Yl (t) in (7) is called version I of compensation, which is as a first approximation nothing but the multiplication of the normalized envelope r(t) with the output signal of the FM demodulator. The compensation according to Eq. (11) with the output signal y2(t) is called version II.

A. Schlereth / Signal Processing 36 (1994) 201-208

case of co-channel interference on condition that

In order to understand the compensation in (11), use Eq. (5) to get the derivative

~a~(t) ~ IS(t)sin ~b(t) + p(t)(b(t) cos ~O(t).

203

~b(t) << Cka(t).

(12)

3. Compensation of adjacent-channel interferer

Thus,

y2(t) = ~,(t) + p(t)~p(t)cos ~(t)

+ p(t)~p,(t) cos ~(t)

In Eqs. (5) and (6), there are components p sin and p cos ~. If

+ h(t) sin ~(t) [1 + p(t) cos ~(t)]

p(t)e j*(° = p(t) cos ~b(t) + jp(t)sin ~(t)

is an analytical signal, which means that its spectrum is zero for f < 0, then the imaginary part is the Hilbert transform of the real part [2]. In the case of a positive carrier offset AfTs this is nearly fulfilled. Taking into account the sign of AfTs we get for

= ~pa(t)+ p(t)dpb(t)COS #/(t) + h(t)sin~(t)[1 + p(t)cos~(t)].

(13)

Assuming constant amplitudes of the desired signal and the interferer, we get y2(t) ,-~ t~(t) + p~b(t)cos ~b(t).

(14)

AfTs >0:

Using Eq. (12), the output signal of the ideal FM demodulator is

and for

yo(t) = ~,(t) + ~,,(t)

AfTs < 0:

$,(t) + p[$b(t)

-

-

Ca(t)] COS~(t).

p(t)sin~(t)~{p(t)cos~(t)},

(17)

p(t)sin~(t) ,~ -:gC{p(t)cos~b(t)}. (18)

It should be noted that again the amplitude a of the desired signal has to be estimated in order to get the normalized envelope r(t), which is used for the calculation ofp cos ~ according to Eq. (6). As a second step, the Hilbert transform of +pcos~b is evaluated and the result is derivated and subtracted from the output signal of the FM demodulator.

(15)

Comparing Eqs. (15) and (14), the difference is obvious. The compensation eliminates the term p~(t) cos if(t) but not the term with the derivate of the interferer phase ~bb. So it is expected that both versions of compensations show advantage in the

ae jOc',,be jd)b

(16)

anglecalculation ,*x

A

: 0a÷0o~ .Yl

delaYofHHtime l

@ll'

,Y2

"" •

t

Fig. 2. Compensationstructure.

-~Y3

204

A. Schlereth / Signal Processing 36 (1994) 201-208

D P L L of order one is used with the Z-transform of the linearized system

Further on, this compensation algorithm is called version III.

'~(z) 4.

Simulation results

4'(z)

-

z

-1

(19)

So the phase estimate is just the input phase with a delay of TA.

Fig. 2 shows the compensation structure used in computer simulation. As F M demodulator, a BB-

a)

,,21 0

0.1

0.2

0.3

0./-,

0.5

0.6

0.7

0.8

0.9

O.B

0.9

1

t/ms

b)

,3t 0.1

0.2

0.3

0./.,

0.5

0.6

0.7

t/ms

Fig. 3. Output signals of the compensation structure: (a) co-channel interferer; (b) adjacent-channel interferer.

205

A. Schlereth / Signal Processing 36 (1994) 201-208

Then the envelope of the input signal is simply generated by multiplying with e-J(~° + ~°') and taking the real part of the result. The sampling rate is fA = 1/TA = 600 kHz. The input signal consists of the desired signal and one interferer according to (1). The amplitudes a and b are assumed to be constant.

a)

/ -fA/2

4.1. Sinusoidal modulation

In Fig. 3 there are some simulation results in the case of a sinusoidal signal va(t). The frequency deviation is 40 k H z and the m o d u l a t i o n frequency is 1 kHz. The interferer is not m o d u l a t e d and has a carrier offset of 0 or 50 kHz. The amplitude ratio

....

j

I

HH(f}

Jr,-1 [f.fg,H ,n] t fg,H

/

fA/2-lg,H

flg,H

-fA / 2'*fg,H

-fg,H

O.

fA/2

/

/

-,rl-2 J. fg,H

f

xl0 -~

AFef f = 2 0 k H z

tl.'

<3

j///

-.,,.o,

1.05

n:l

0.95, 8.9

t

t

I

•

0.85 0.8

5 ,

,

,

,

~

,

,

,

10

20

30

~0

50

60

70

B0

90

fg,H

Fig. 4. Design of the Hilbert transformer: (a) frequency response of the proposed Hilbert transformer; (b) error variance A as a function of n and fg,H (in kHz).

206

A. Schlereth / Signal Processing 36 (1994) 201-208

is b / a = x / ~ corresponding to (SNR)HF = (a/b) 2 = 10. The Hilbert transformation with the frequency response n n ( Q ) = - jsgn(~) for IO = 2~fTAt <~ X is done in the frequency domain by multiplying HH((2) with the discrete Fourier transform of its input signal, which is periodic. The real part of the inverse discrete Fourier transform of the result provides the desired output signal in the time domain. The peaks in the output signal of the BB-DPLL arise when the phasor (g/a)e -j4'a in Fig. 1 passes his minimum value. At an amplitude ratio of (b/a) = 1.0, the envelope ar even vanishes, if the angle (~bb-q~,)mod2n is n. So version I fails because a division with zero has to be avoided. In that case the output signal Yl is simply set to zero. So for ar = 0, versions I and II provide the same result. In the case of a co-channel interferer (AfTs = 0kHz) with b/a = x / / ~ the results of versions I and II in Fig. 3 look very similar. The improvement in the signal-to-noise ratio (SNR)0 at the output is about 7dB for versionI and about 13 dB for version II. It is pointed out that the output signals of the compensation structure were not band-limited before calculating the (SNR)o. Version III (assuming a positive carrier offset) shows advantage if the instantaneous frequency (q~b -- ~a) is positive. If (~b -- q~) < 0, then the amplitude of the interference noise is doubled, so the (SNR)o is 3 dB poorer compared to the BB-DPLL without compensation. In the case of an adjacent-channel interferer, the results are just the other way round. Versions I and II are only about 1 dB better than the BB-DPLL, whereas the gain in the (SNR)o for version III is nearly 17 dB.

Monte-Carlo method [1]: v,,b(t)

apsinc%t

= [UL(t) + UR(t)] + k

+ [UL(t) - - UR(t)]

Y pilot

sin(2covt)

(20)

with UL(R)(t ) ~ left (right) channel.

The effective frequency deviation A Feff corresponds to the rms of va,b(t) without pilot. If the amplitude h of the desired signal is known, the Hilbert transformer Ha remains to be designed. Fig. 5(a) shows the frequency response of the filter Hn which is proposed. The parameters n and fg, n are optimized by minimizing the error variance A = E{([p sin ~ - (p cos ~) * hH] * hD) 2 } (* denotes convolution).

(21)

of the non-analytical component of the signal pe jq' with a positive carrier offset AfTs- ha is the impulse response of the filter HH without delay time and ho is the impulse response of the linearized BB-DPLL describing the approximate differentiation of the input phase as follows: L

~b(k) = q~(k)- ~b(k - l ) = 4)(k)* hD(k).

(22)

The results in Fig. 4(b), which are calculated for identical effective frequency deviation of the desired signal and the interferer and for p = 1 show that the ideal Hilbert transformer with H n ( O ) = -jsgn(O) for It2[ ~< n is not the best choice. So in computer simulation (Fig. 5), a FIR filter according to Fourier design of the optimal Hilbert transformer with n = 3 and fg, H = 45 kHz is used. The frequency response of this filter is N

Hn(t2) = j 2 Y' eusin(/~t2)e -jNa, O=I

4.2. Monte-Carlo simulation As an application, the digital demodulation of FM signals in commercial broadcasting is considered. The modulated signals va(t) and vb(t) are both stereo-multiplex signals generated by the

with CO--

6 E1

2

/~ = I(1)N

3

sin (~g,H)-] ~t~g,. _l [ ( - 1)o _ 1],

(23)

A. Schlereth / Signal Processing 36 (1994) 201-208

o)

207

l,O

ARTS: 0kHz

~

~

30

20

o

10

n,.

z

0 •

t

[

;

O

-10 ..... I ............. :......................................... I

Version I

.....

Version II

........

Linearization

I I

-20

.4

BB-DPLL

____

.........................................................

Version

-30

.........................

III .....................

i

0

5

10

15

20

(SNRIHF

25

30

=

b) 60

T o

/-0

20

z

t"

o

/

-20

I - - I ............................................................. I :

-/.0

- .......

i

5

BB-DPLL Version I V e r s i o n I I ...................... Version

Ill

Linearization I

10

15

20

25

30

(SNRIHF

Fig. 5. Output SNR versus (SNR)H F = (a/b) 2 in dB (bandwidth of post-detection low-pass filter = 53 kHz (rectangular)): (a) co-channel interferer; (b) adjacent-channel interferer.

and f2 = 2 n f T A .

In Eq. (23) the delay time InTa equals NTA. The parameter N is set to 11, because this leads to

nearly the same result for the minimum value of A as shown in Fig. 4(b). Further on the amplitude a of the desired signal should be estimated. The simplest way to do this is to filter the envelope ar in the compensation

208

A . Sch lereth / Signal Processing 36 (1994) 201~08

structure in Fig. 2 by a low-pass filter. If the bandwidth of the filter is sufficiently small its output signal corresponds to the mean value ar

all

1 ( 2 ) 4 + higher-order terms 1 ,

up to 19.6 dB. Here the difference between linearization and computer simulation is again caused by the amplitude estimation, which is not considered in Eq. (21). At low values of the (SNR)HF, higherorder terms in the phase noise according to (3) decrease the gain of the (SNR)o compared to the conventional BB-DPLL.

(24) which is in the case of low values of p a good estimate of the amplitude a. In computer simulation (Fig. 5) the low-pass filter is a second-order recursive filter with equal ripple of 30 dB in the stopband and a stopband cutoff frequency of 10 kHz. Fig. 5(a) shows results in the case of an interferer with no carrier offset. The frequency deviation AFerr of the desired signal is 20 and 10 kHz in the case of the interferer. These are realistic values in F M broadcasting. In order to examine the simulation measurements the linearized noise terms in Eqs. (12) and (14) are used for calculating the (SNR)o for the B B - D P L L and versions I and II (dotted lines). There are two reasons for the difference between the linearization and the computer simulation in the case of versions I and II. First the amplitude estimation, which is not considered in Eqs. (12) and (14), causes a loss of about 1.5 dB. The second reason is that higher-order terms are neglected, which are important for low values of the (SNR)HF. This is especially significant for version II. For version III, Eq. (21) is evaluated, which corresponds very well with the simulation measurements. Fig. 5(b) shows results for an adjacent-channel interferer with Afrs = 100 kHz and AFerf = 20 kHz. The desired signal is the same as used in Fig. 5(a). Versions I and II provide very poor results and so they are not suitable for the compensation of adjacent-channel interference, whereas version III leads to an improvement of the (SNR)0 at high (SNR),F

5. Conclusion Three new digital algorithms are presented with the ability to suppress output noise in conventional digital F M demodulators caused by co-channel or adjacent-channel interference. They require an estimate of the amplitude a of the desired signal, in order to calculate the normalized envelope of the whole input signal of the demodulator. Using the information of the envelope for compensation after demodulation a gain in the signal-to-noise ratio has been achieved.

References [1] K.-D. Kammeyer,R. Mann and W. Tobertge, "Applications of constant modulus algorithms for adaptive equalization in time-varyingmultipath channels", in: Digital Signal Processing, 1987, pp. 421 425. [2] A.V.Oppenheim and R.W. Schafer, Digital Signal Processing, Prentice-Hall, Englewood Cliffs,NJ, 1975, Chapter 7.4, pp. 358-361. I-3] A.M. Pettigrew and T.J. Moir, "Reduction of FM threshold effectby inband noise cancelling", Electronics Lett., Vol. 27, No. 12, June 1991, pp. 1082 1084. I-4] A.M. Pettigrew and T.J. Moir, "Inband noise cancelling in FM systems: The white noise case", Electronics Lett., Vol. 28, No. 9, April 1992, pp. 814-815. [5] W. Rosenkranz, "Design and optimization of a digital FMreceiver using DPLL techniques", Proc. lnternat. Conf. Acoust., Speech Signal Process., Tampa, 1985, pp. 592-595. [61 A. Schlereth, "Digital algorithms for suppression of adjacent channel interference in FM-receivers", Proc. Internat. Conf. Acoust. Speech Signal Process., Minneapolis, 1993, Vol. III, pp. 5-8.