122

Un nouveau système servant à rejeter les interférences de gamme étroite en utilisant une communication bilatérale avec spectre étalé a été soumis (1). Ce système utilise la capacité propre à un canal de fréquence d'ondes réfléchies à 2 voix de rejeter les ondes réfléchies heurtées volontairement ou non par une interférence dans la gamme étroite. Après l'acquisition de synchronisation initiale, le système subit un processus (action-réaction) et une fois que ces tonalités d'interférence ont été décelées, on peut utiliser de simples codes convulutionnels sans interfoliage ou autres techniques de codage compliquées. Les marges d'erreur sont déterminées dans le cas d'une bande où la formation des signaux par modulation serait incohérente et ce pour un cas très grave de brouillage incluant le bruit blanc gaussien. Ces marges nous montrent combien la nouvelle technique est adéquate pour rejeter les interférences dans la banque de fréquence étroite à l'intérieur d'un canal à spectre étalé à 2 voix.

Introduction

Spread Spectrum communication systems are defined as those using a much wider bandwidth for transmission than that of the data information. These systems have been preferred by the military because of their inherent privacy, anti-jam and anti-intercept capabilities.2 3 They have also found many commercial applications in ranging, identification, selective calling and ran­dom access.4"6

However, these systems are hard to implement, and have in­creased probability of demodulation errors in the presence of nar­rowband interference, partial band interference, and jamming. This is caused by errors and results in correlation loss and syn­chronization loss. The recent advances in Surface Acoustic Wave devices (SAW7) and efficient synchronization circuitry8"10 should simplify the implementation and synchronization hardware. However, there remains the problem of more efficient encoding to reduce the demodulation errors in a Spread Spectrum (SS) channel with severe interference (or jamming).

Several authors 1 1 1 2 have applied convolutional codes to reduce demodulation errors in a worst case narrowband interference. The use of sophisticated convolutional codes and interleaving to ac­commodate severe interference gave very little improvement and using the very complicated sequential decoder only offered a 1 db improvement in bit probability of error over the simple feedback decoder.1 2 On the other hand, protection against burst interference by interleaving needs a lot of memory and control (2 1 6 symbols in reference 11). Also, a digital whitening technique has been recently suggested13 but this only applies to a Direct Sequence (DS) system.

This paper introduces a new two-way FH system which detects and cancels the narrowband interference tones. Once this is suc­cessfully done, a modest amount of coding will then be needed to improve the data error rate in the presence of only pure WGN. The main idea is to transmit a sequence of priori known bits following the initial acquisition of synchronization. By an averaging process, the second transmitter will then be able to detect those hops hit by tone interference and transmit their values to the first transreceiver. The first transreceiver will use this information to transmit only on clean channels (those with no tone interferences), and simple coding schemes can then be used since the transmission channels will be pure WGN channels.

In the following, the new system is discussed, the probability of error space scanned and error bounds are derived for a two-way noncoherent FH/FSK system. This paper only introduces the new system and presents analysis results for the proposed technique. No claim is made with respect to the performance of the actual system (yet to be implemented). However, this implementation, together with computer simulation, will follow in the near future in a separate paper. It is hoped that the presented analysis will clarify some of the advantages and disadvantages of the new technique.

Description and operation

Before any meaningful demodulation can be performed, both of the hopping waveforms used in transreceiver s No. 1 and No. 2 should be in exact time and frequency epoch. This is achieved dur­ing stage 1 shown in Figure 1, while the necessary synchronization circuitry is deleted for simplicity in Figures 2 and 3.

Following the acquisition stage, it is a straight forward approach to spend a few more milliseconds for the ultimate object of cancell­ing the narrowband interference. This goal is reached by the testing-telling processes (see Eqs. 2 and 3). During the testing stage (see Figures 1, 2, 5), one of the transreceivers, for example 71, transmits a long stream of test bits whose identity (0 or 1) is known apriori to the receiver R2. Each one of these test bits is transmitted using a distinct hopping frequency, chosen either pseudorandomly or selected from a stored list of hopping frequencies.

Figure 4 shows a testing preamble; it consists of a small odd number NN of frames and each frame is composed of MM test bits i.e. MM hopping frequencies, where MM is upper bounded by the total number of available hopping frequencies. The testing (or tell­ing, data, etc.) bits are used to biphase modulate, frequency shift or . . . , a low frequency sinusoidal waveform according to the current stage and the kind of modulation. However, all digital modulation techniques such as MFSK, DPSK, PSK . . . etc, are good can­didates for the new system.

This data carrying signal is then mixed with a high frequency hopping sinusoid, chosen and generated by the frequency syn­thesizer. This frequency synthesizer can be direct, phase locked loop or all digital synthesizer. The resulting spread spectrum FH signal is then up converted for further frequency spreading, if

Can. Elec. Eng. J., Vol. 10 No. 3, 1985

Interferences rejection by testing-telling spread spectrum systems

Rejet des interférences par action-réaction dans des systèmes à spectre étalé

By Dr. A.K. El hakeem, Department of Electrical Engineering, Concordia University, Montreal, Quebec.

A new system for narrowband interference rejection using a two-way Spread Spectrum (SS) communication has been presented.1 The system employs the inherent capability in a two-way Frequency Hopping (FH) channel to reject these hops hit by narrowband interference (intentional or unintentional). Following the initial acquisition of synchronization, the system undergoes a testing-telling process and, once these interference tones are detected, simple convolutional codes can be effectively used without interleaving or other sophisicated coding techniques. Error bounds are for­mulated for a noncoherent Frequency Shift Keying (FSK) channel under worst case jamming plus White Gausian noise. These bounds show the ade­quacy of the new technique for narrowband interference rejection in two-way SS channel.

ELHAKEEM: INTERFERENCES REJECTION 123

(1) (2) (3) (4) (5) (6)

1st Transreceiver H

Send Acquisition

Send Testing

Receive Telling

Pause-Resynchro-

nization

2nd Transreceiver r-

Send Receive Information Information

if

Receive Acquisition

Receive Testing

Send Telling

- ν -Pause Receive Send Resynchro- Information Information

nization

Figure 1: Time scheduling of the various processes in the proposed two-way system.

necessary, then amplified and transmitted. With a certain pro­bability p , narrowband unintentional inference and/or jammer tones will hit the hopping frequency of this signal, after which WGN will be added at the receiver R 2 . It is important to note that the demodulator of this receiver is turned on during the testing stage 2, while the demodulator at R x is turned OFF. This assumes that the proposed system is a half duplex, two-way communication system.

Once each SS signal carrying a test bit arrives at R 2 , affected by both WGN and possible narrowband interference, it will be suitably down converted in frequency, filtered, and then frequency despreaded by active correlation with the same hopping signal used at Tt. (Course and fine synchronization and accurate clocks are all assumed.) The subsequent digital data demodulator then gives the identity of the detected test bit, which is compared with the actual value known to the receiver R 2 and the decision made about the presence of narrowband interference in this specific hopping fre­quency. Each NN of these decisions are combined by a majority voting gate, the inference made about the presence of narrowband interference, and the value of any bad frequency hop is then stored for further uses.

Following the test process, the system switches to the telling mode and the transmitter T2 starts telling the receiver Ri about these hops hit by narrowband jamming. During the telling process, the same transmission format (see Figure 4) used previously for testing will be repeated for telling. Only, instead of transmitting apriori known data bits, 1 will be transmitted if the particular hop to be transmitted is hit by an interference tone (as indicated by the inference from the test stage). 0 will be transmitted if the test stage shows the absence of interference. At R l 9 the SS signals carrying these telling bits will be received in both narrowband interference and WGN, then down converted, filtered, frequency dehopped, and finally demodulated. Each NN telling bit decision will then be combined to give 1 or 0, and those frequency hops coresponding to 1 will be stored, and cancelled shortly during stage 4.

Following the telling stage, and during the pause-resynchronization stage 4, both transceivers will spend a very short period cancelling bad frequency hops and regaining syn­chronization. Synchronization is believed to be lost because of cancelling bad hops. Once both transreceiver s adjust their syn­thesizers at stage 5 or 6, (i.e. the actual information data transmis­sion from Tx to R 2 or from T2 to R x ) 9 starts immediately. Now, if the location of the interference tones changes within the whole SS bandwidth, the whole testing-telling procedure should be initiated again.

Channel interference model

The system assumed is a two-way, half duplex, noncoherent FH/FSK Spread Spectrum system. Unlike many models which ig­nore the WGN with respect to the narrowhead interference14 or

which consider WGN alone, 1 5 this analysis is more realistic in that it treats the simultaneous effects of the narrowband interference and the WGN. The tone interference model assumed is a worst case in which a jammer, which has a perfect knowledge of the system (ex­cept the hopping code), seeks an optimal distribution of its total power / over q separated tones. If this jammer tries to hit one of the hopping tones (the mark or the space frequencies in a FSK system), then the spacing between the jammer tones will be R C i and so the probability of hitting one symbol frequency will be given by

μ (B. W.) (D

where

R c is the bit data rate in bits/sec. B. W. is the total available SS bandwidth q is the number of jammer tones

For this and other jamming stretegies, reference 14 simply shows that the worst case occurs when the power in each jammer tone is equal to the signal power S 2 , i.e.

Q = S2 (2)

So from Eqs. (1 and (2),

= JR<

P ~ S*(B.W.)

which can be written as

P = - ^ - . ( K »

(3)

(SJR)db 10

(B. W.)

_ (SJR)âb 10

where

(SJR)db = lOlog,,, ( ^ — ) decibels

(4)

(5)

is the effective bit signal-to-jam ratio and, if some coding scheme is used, the encoded symbol signal-to-jam ratio becomes

(SJR)db = 101og,o [*±ψ]£ϊ . decibels (6)

124 ELHAKEEM: INTERFERENCES REJECTION

where R is the coding rate (112 or 113 or 2/3 . . . etc.) In Eq. (5), the ratio (B. W./Rc) is called the Spread Spectrum processing gain and it is absorbed throughout this paper in the definition of the (SJR). The final bit error rate during stages 5 and 6 depends on the possible outcomes of the compounded experiment, composed of the testing-telling and the information transmission stages. In the following, each stage is discussed separately.

where Ψ is the phase jump associated with the hopping of the syn­thesizer of #2 , assumed uniformly distributed between ο and 2ττ. Assuming ideal active correlation and subsequent low pass filter­ing, the signals appearing at the input to the demodulator cor­responding to M or 5 being transmitted are:

Sm ( 0 = Scos(«Mf + * 0 + n'(t) (10)

Test stage errors

Depending on the condition of interference, different cases app­ly. The first case is no tone interference in either M or S cells. Assuming M was transmitted, the signal appearing at the input of R2 after down conversion and filtering can be expressed as

5 M (0 = Scos(œht + ωΜί + φ) + n(t) (7)

while the signal corresponding to a transmitted space can be represented by,

5,(0 = Scos(œht + w,t + φ) + n(t)

where

(8a)

S 2 is the power of the signal, ωΛ is the high hopping frequency, ωΜ is the low mark frequency, ω, is the low space frequency, φΐ9 φ2 are two random variables uniformly distributed be­

tween ο and 2π, n(t) is the additive WGN whose single sides density is (N0/B. W.)t and

(SNR)db = 101og 1 0( · - ^ - ) (8b)

5/(0 = 5cos(a>,i + ¥ 3 ' ) + n'(f)

where

(11)

n'(t) is the effective WGN at the demodulator input, and Ϋ2' and Ϋ3' a r e a U(o, 2ir)

Now for noncoherent detection, either 5 m ( 0 or 5/(0 will be match­ed filtered, then envelope detected and sampled in two branches as in Figure 5. Since M or 5 are equally likely to be transmitted, it is assumed that M was transmitted, in which case, the envelopes of the signals at the output of the M and 5 matched filters are distributed as

_ , ^ v R\ P,+n(Ri) =-^re

-(Ri + 5 2) 27V' (12)

and

P ^ = W e - 2 W (13)

where N' is the single sided effective WGN power, and N' = noise density χ data bandwidth

Either 5 M (0 or 5,(0 will be correlated with the dehopping signal of the form

h(t) = cos(u>„i + *) (9)

T e s t Informat B i t s B i t s ? 9

i 4L J (A) (2) (5)

·*• **data — / r. rwr χ Λ l x c (B.W.) (B.w.y

where

Bdata is the bandwidth of the low pass filter

The probability of detection error is then well known as

Pti(error /no interference present) = P(RX < R2) = oo oo m

(14)

(15)

OFF other

ON (2).(5),(4)

Up-Converter )own-Converter and and

Amplifier Filtering

Digital Frequ Synthesize

ON (A)

C a n c e l Inter ferenci

Hops

OFF (2),(4),(5)

Store in­terference |hops corre-ponding tc

|a decision Of "1"

each NN Decision; at the

I (6)

Informat ion Bits

A second condition of interference involves either the Mor the 5 cells. Assuming, without losing any generality, that M was transmitted, (Mand 5 are equally likely), then the signals appearing at the outputs of the M and 5 filters become (if the interference hits the M cells),

5 M (0 = 5cos(aW + Φι) + Scos(œMt + φ2) + n'(t)

5,(0 = "'(0

The envelopes of these signals are distributed as6

-N'r2

Α ( Λ ) = Ri j rdrJ0(rR,)Jl(rS)e-

(16)

(17)

(18)

Figure 2: A simplified block diagram of the first transreceiver (acquisition and tracking circuitry deleted). and

ρ2(/ω = - τ τ - β R2 -RI Ν 2N'

So, the bit error in this case becomes:

ELHAKEEM: INTERFERENCES REJECTION

(19)

125

Information bits

Pi(Ri <Ri)= \ Pi(Ri)dRi \ P2(R2)dR2

P2 =

-N'r2

j R1 j dr rJ0(rRx)Jl(rS)e - j R2 -Rl 6 ~2N~

dR2

(20)

(21)

Performing the integration (w.r.t.)R2i (e R1^^') is obtained. Then, performing the integration (w.r.t.)Ru

j dRlRiJ0(rRl)e ο

Finally, P2 becomes

-R\/2N' XT, -N'r2/! = N' e

00 P2 = N' j dr. r.Jl(rS)e-N'i*

P2 = 2 2N* °\2N')

While if the interference tone hits the S cell,

SM(t) = Scos(a>„i + Φι) + Λ ' ( 0

S,(0 = Scos(a>,i + φ2) + rt'(r)

where

both φι and φ 2 are à U(o, 2τ)

In this case, the envelopes are distributed identically as

(22)

(23)

(24)

(25)

(26)

JL

L.O.

ψ

y . pp-Converter] and

Amplifier

Digital Frequency Synthesizer

ι OFF (3), (6)., (4)

Cancel Interference Frequencies

ON ( Test

2),(5)|

•N^otherwise pnterferena — * Frequencies

its Demodulator

OFF X^otherwise Store "1" or "o"

according to in­terference pre­sence or absence

Compari-|

Majority Vote Among

NN becisionsl

Figure 3: A simplified block diagram of the second transreceiver (acquisition and tracking circuitry deleted).

Pt2 = (probability of a test bit being in error/interference + WGN presence) = Σ all possible interferences in the M and S cells = Σ P(error bit/condition of interferences in M and 5) χ P(presence of interferences in M and S)

(30)

The probability of both M and S being in interference at the same time (p2) is excluded by the assumption of a certain interference model as stated earlier, and p, P2, P3 were defined earlier by Eqs. (4), (24), (29).

K { K , ) Ν 6 2Nf Io \ Ν )

Now since Ptl = (probability of a test bit being in error/only WGN present) was defined by Eq. (15), and since the comparison and majority logic will combine MV decisions at the same hopping

/ = 1 2 (21) frequency to decide whether this frequency has interference (see Figure 4),

and the detection error is:

00 00

P , ( / ? , < R2) = j P1(Ri)dR1 j P1(Ri)dR2

3 J N' IN' ' \ N' ) J N'

(28)

2N'

which can be written immediately as

Pa = 1 /2

Pt3 = Ρ (say one hop has interference + WGN/it really has in­terference + WGN)

NN

= j= (Ç) + 1 ( Λ

/

ν ) ( P , 2 Y d - Pt2YN'J (31) 2 J

where [x] is the smallest integer greater than or equal to x, while,

Pt4 = Ρ (say one hop has interference + WGN/it has only WGN)

NN

= y = (S) + 1 ( ν ^ ) ( ρ η ϊ ( ι - phyn-j (32)

(29)

since both i?i and /? 2 have exactly the same distribution and, conse­quently, they are equally likely.

Telling stage errors

Though the channel characteristics differ from bit to bit depend­ing on the presence or absence of narrowband interference, it is

Now considering all possible error situations due to the presence possible to treat them on an average basis. This means that the of interference during the test stage, channel is described by an average telling probability of error based

126 ELHAKEEM: INTERFERENCES REJECTION

- T o t a l Testing Period

1st Frame

hopping frequencies

To the majority vote

NNth Frame

£ 4 f 9 f 9 f 3 f 4 f 9

Figure 4: Testing (or telling) preamble transmitted. f4, f9, f3 · · · are hopping frequen­cies. MM can be up to the total number of hopping frequencies. The majority vote logic takes NN bit decisions at a time at the same hopping frequency.

Matched Filter 3 t

%

Envelope Detector

signal after

dehopping and low pass filtering

Matched Filter 3 t

%

Envelope Detector

signal after

dehopping and low pass filtering

signal after

dehopping and low pass filtering Matched

Filter at ω

s

Envelope Detector

Matched Filter at ω

s

Envelope Detector

Figure 5: A typical FSK non-coherent demodulator.

While the resulting bit information error during stages 5,6 is given by:

on all possible situations of interference and WGN. This is equal to:

Pttx = ]£) Ρ (bit error /a certain situation of Hltsmins* interference and WGN)

χ Ρ (occurence of this situation)

= p ( - ^ - y J ^ ) + ( l - p ) A 1 (33)

Now from Figure 4, it is clear that if a majority vote among NN bit decisions is performed, then the telling error will have a probability that [NN/2] + 1 or more (up to NN) bits are received in error. So, the probability of error in telling a bad frequency is:

Pt^ = Ρ (say/Λ is bad/good) = P(say/ A is good /bad) NN

= ' ·=(5 )+ΐ( ™ ) PK d - P*T* (34)

Pb - 2* aN compounded proabability products /. v. vu.xi leading to errors

= pP,3 Ptt21 Ph\B.W. + p(l - Pt3) (1 - PtÎ2) |Ph | b . w . +

{\-P)PUP^\PH\b.w. +

(\ - p)(\ - Pu)(\ - Pth)\Ptx\BW. (36)

Here, two differences exist between | PH \B.w. and PH (given by Eq. (15)). The first is that the calculation of Pti is based on the availability of the whole SS B. W. (during the telling mode), while IPHI b.w. is based on the effective reduced SS B. W. (during stages 5 and 6), where B W is related to B. W. by (35). The second difference is that IPH \B.w takes into account the coding process during stages 5 and 6.

Having cancelled almost all the interference hops, the channel can be approximated by a WGN channel and the bounds of Vertrbi [15] can be used, i.e.,

Bit information error rate

The bit error rate during information transmission stages 5, 6 depends on the outcome of the test and telling processes. For exam­ple, if the specific frequency hop has interference plus WGN noise, and the inference from the test process came the same; the decision will be to cancel this hop from the hopping list (during the stage pause—^synchronization 4), and 1 will employ this specific hop during the telling stage 3. Now, if Rx makes a demodulation error, 0 will be obtained instead, the particular hop will not be cancelled, and the information bit will be received in error with a probability \Ptx\B w. (similar to that in Eq. 15). This case is labeled/in Figure 6.

Another situation occurs if the test stage shows a bad hop and the telling stage is completed successfully. In this case, this specific hop will be cancelled from the list, implying a reduction in the available SS B. W. (see Case III, Figure 6). All possible outcomes of the pro­posed system compounded error space are shown in Figure 6. From this figure, it is clear that the reduced effective B.w. becomes:

b w = B.W. (1 - all compounded iiiivixx probability products leading to

frequency cancellation)

= B. W. [1 - [pPt3 (1 - Pth) + p(\ - Pt3)Pti2 +

(1 - P) P,4 d - P<H) + (1 - />) (1 - Pu) Pt(2]] (35)

The Telling

1 B.W.

Figure 6: Flow chart of the compounded error experiment. I, V, VII, XI lead to bit in­formation errors. Ill, IV, IX, Xlead to a reduction in theB. W. II, VI, VIII, Xllleadto no error, no B. W. reduction.

ELHAKEEM: INTERFERENCES REJECTION 127

TABLE 1

Bit error probability as a functional of (SNR)db, (SJR)db Κ = 3,R = 1/2, NN = 3

- 1 1

Note: This notation .28 Α -28 χ 10~n

(S//?)db -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

-4 .35 .35 .35 .35 .35 .35 .35 .35 .35 .35 .35 .35 .35 .35 .35 -3 .29 .29 .29 .29 .29 .29 .29 .29 .29 .29 .29 .29 .29 .29 .29 -2 .23 .229 .229 .228 .228 .228 .227 .227 .227 .227 .227 .226 .226 .226 .226 -1 .172 .17 .168 .167 .166 .165 .163 .163 .163 .162 .162 .161 .161 .161 .161 0

.12 .12 .11 .11 .11 .11 .1 .1 .1 .1 .1 .1 .1 .1 -1 .99

1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

1 .77 .73 .68 .65 .62 .60 .58 .56 .55 .54 .53 .53 .52 .52 .51 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

ζ .45 .41 .37 .33 .30 .28 .26 .25 .24 .23 .22 .21 .21 .21 .21

3 -1 -1 -1 -1 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2

3 .24 .21 .17 .14 .12 .11 .93 .84 .78 .73 .69 .66 .64 .62 .61

A -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2

4 .113 .90 .67 .50 .38 .30 .25 .21 .19 .17 .16 .15 .14 .13 .13

c -2 -2 -2 -2 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3

.46 .34 .22 .14 .93 .65 .49 .39 .32 .28 .24 .22 .21 .20 .19

/: -2 -2 -3 -3 -3 -3 -4 -4 -4 -4 -4 -4 -4 -4 -4

0 .15 .10 .57 .30 .17 .99 .66 .48 .37 .30 .26 .23 .21 .19 .18

7 -3 -3 -3 -4 -4 -4 -5 -5 -5 -5 -5 -5 -5 -5 -5

/

.14 .25 .11 .46 .20 .10 .59 .39 .28 .21 .17 .15 .13 .12 .11

ο -4 -4 -4 -5 -5 -6 -6 -6 -6 -7 -7 -7 -7 -7 -7

ο .83 .45 .15 .46 .16 .64 .31 .18 .12 .86 .67 .56 .48 .43 .40

Q -4 -5 -5 -6 -7 -7 -8 -8 -8 -8 -8 -9 -9 -9 -9

.12 .53 .13 .28 .69 .22 .87 .43 .25 .17 .12 .98 .82 .72 .65

10 -5

.10

-6

.38

-7

.62

-8

.87

-8

.15

-9

.33

-9

.10

-10

.42

-10

.21

-10

.13

-11

.87

-11

.66

-11

.53

-11

.45

-11

.40

r [2DS* / dS2 v dT(D, N) dN

N = \9D = e -S2

N' (37)

erfc V5 SP/N' (1 - 2e-s/2N) (39)

The relationship between the parameters S 2, Ν, BW. and the (SNR) db is clearly seen from Eqs. (8-b) and (14).

If the well-known characteristics of the specific coder is substituted in this equation,

d=5,K=3,R=U2,nD,N)= (38)

the bit error probability is

Error computation and conclusions

Finding an expression for the final bit error Pb as a function of the parameters (SNR)db, (SJR)db, NN, K, R is a straight forward algebraic substitution from Eqs. (8-b), (14), (15), (24), (29) into (30), (31), (32) to obtain P1%, P,3, Pu, then from Eqs. (4), (15), (24), (29) into Eqs. (33) and (34) to find PtÎ2, and so on until Eq. (36) is reached. However, since no meaningful insight into the resulting very bulky expression is possible, digital computation of Pb as a

\Ptl\s.w. <

128 ELHAKEEM: INTERFERENCES REJECTION

TABLE 2

Bit error probability as a function of (SNR)db and (SJR)ab for some of the codes in reference 11

(a) Κ = 7, R = 112, AWGN plus burst (narrowband) interference, CPSK production

(SNR)db 0 2 4 6 8 10 12

SJR = lOdb .45 .2 -2 -3 Not available from

.8 .2 reference 11

SJR = 6db .5 .4 .1 -1 -1 -2 -2

.2 0.1 .8 0.7

function of (5M?)db, (SJR)db, NN, K, R is a better and more typical alternative. Moreover, because the results came almost in­dependent of the level of (SJR)db, they were put into table form (see Table 1). It is interesting to see how the bit errors associated with the new system are invariant to a great extent with the level of (SJR)db. This is a direct consequence of the system's ability to re­ject the narrowband tones. However, the errors associated with the compounded decisions and finally the level of Pb depends largely on the (SNR)db.

For comparison, Table 2 shows some of the results from reference 11. There, low rate codes (112 and less) are used to com­bat the effects of tone interference (bursts), and the constraints length of the codes are larger than those in this paper. By using low rate coding, larger constraint length and a more efficient modula­tion technique (coherent phase shift keying), the system in reference 11 should yield better results. However, comparison of Tables 1 and 2 reveals the contrary.

The comparison becomes more clear if we recall that this analysis has considered worst case jamming, WGN and also phase cancella­tion in the mark cell (Eq. 24). Also, a modest amount of coding has been used; lower rate codes and/or higher constraint length codes should yield much better results in the pure WGN channel created by the new system. Extending the system to MFSK and DPSK together with using different simple coding schemes is currently be­ing investigated. Moreover, in a one-way SS system and/or multi-

tone hopping interferences, the system will cancel the interference on real time using two parallel demodulators. This is currently be­ing investigated by the author. Computer simulations of the new technique and hardware implementation will be described in a following paper.

References

1. A.K. Elhakeem and S.C. Gupta, "A New Technique for Narrowband In­terference Cancellation in Half Duplex Spread Spectrum Communications," NTC 79 Conf., Washington, D.C. pp. 15.1.1-15.1.7.

2. R.C. Dixon, Spread Spectrum Techniques IEEE Press, 1976. 3. L.A. Gerhardt and R.C. Dixon (Eds.), "Special Issue on Spread Spectrum Com­

munications," IEEE Trans, on Communications, Vol. COM-25, No. 8, August 1977.

4. C.R. Cahn, "Spread Spectrum Applications and State-of-the-Art Equipments," Magnavox Research Laboratories, MX-TM-3134-72, Nov. 1972.

5. MX. Schiff, "Proceedings of the 1973 Symposium on Spread Spectrum Com­munications," Naval Electronics Laboratory Center, San Diego, California 92152, 13-16 March 1973, Vol. I, Technical Document 271.

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