Ililili TRANSACTIONS ON COMMUNICATIONS. VOL. COM-27, NO. 12, DECEMBER 1979
`
`16 QAM Modulation for High Capacity
`
`Digital’Radio System
`
`PHILIPPE DUPUIS. MICHEL JOINDOT. ALAIN LECLERT. AND DOMINIQUE SOUFFLET
`
`Abstract—A computational method allowing the calculation of bit error
`rate in the presence of filtering and some other impairments is described for
`16 QAM modulation; 3 breadboard working at a bit rate of 140 Mbits/s has
`been implemented and experimental results are compared with calculated
`values. The possible use of this modulation type for a high capacity digital
`radio-relay system is considered. Some parameters are introduced for this
`purpose. especially the net fade margin parameter. In the case of the 140
`Mbit/s system in the 10.7-11.7 GHZ frequency band. 4 PSK and 8 PSK
`modulation types are compared with 16 QAM. System gain, frequency
`arrangement. nodal capacity and outage performances are evaluated.
`
`be obtained and compared with the computed values. One of
`these results is reported concerning group delay distortions.
`
`11—16 QAM MODULATION
`
`A—Description 0f the Modulation
`
`l6 QAM belongs to the general class of multiple amplitude
`and phase shift keying (MAPSK) modulations and the modu-
`lated signal can be represented by the following equation: [2]
`
`0090-6778/79/1ZOO-177150075 ©1979 IEEE
`
`Vis a scaling factor.
`We assume that ak and bk are two independent random
`variables which can take on four values (*3, *1, l, 3) with the
`same probability; furthermore we assume that ah and a1, bk
`and bl'are independent Vk i].
`I
`‘
`Each value of :1; (tbsp. bk) is associated with a state of the
`dibit (A1, Bl) (resp. (A2, 82)) where Al, Bl, A2, 32 are
`binary data to be transmitted. We assume that the encoding
`rule is of the Gray type so that the two binary dibits associ-
`ated with two consecutive values of 0,3 (resp. bk) differ only
`by one bit.
`1 diagram shows the sixteen amplitude and phase
`The fig.
`levels of the modulated signal u(t) with the corresponding
`four bit words (A l , Bl , A2, 32).
`V
`Communication theory gives the structure of the optimal
`receiver and the error probability when the signal is observed
`in the presence of an additive white Gaussian noise (AWGN)
`with tWO-sided spectral density No/Z which represents quite
`well
`the thermal noise of the radio link receiver. Figure 2
`shows
`the scheme of the optimum receiver. MP.
`is
`the
`matched filter with impulse response X0). It is followed by a
`sampler and a threshold circuit for the decision. As we are
`primarily interested in the error probability on each of the
`data streams A 1, Bl, A2, B2, we will express the error proba-
`bility Pei” (respPeBl) defined by:
`
`If INTRO DUCTION
`
`HE development of high capacity digital radio relay sys-
`tems leads to the use of high level modulation schemes:
`8 PSK is currently used and 16 QAM (quadrature amplitude
`modulation) is now being investigated.
`At first this paper presents the general features of 16 QAM
`modulation; a computer procedure which is briefly described
`allows the calculation of bit-error probability taking into ac-
`count intersymbol interference and eventually some other im-
`pairments.
`In particular
`the influence of group delay and
`amplitude distortions was computed and the results were com-
`pared with measured values. Another computer simulation- was
`carried on to take into account non-linear distortions—AM-AM
`
`and AM-PM conversion— and experimental and theoretical
`data are displayed.
`After that, system parametersiin particular gross margin
`and net marginware introduced to be used in the design of a
`radio link. They allow the computation probability of the
`outage when fading occurs.
`These considerations are applied at a bit rate of 140 Mbits/s
`and in the 10.7-11.7 GHz frequency band which is assigned in
`France to digital systems [1]. Using the method which has
`been previously developed,
`the optimal frequency arrange-
`ment is determined for 4 PSK, 8 PSK and 16 QAM modula-
`tions. But it must be noted that these results can be extended
`to other bit rates and other frequency bands such as 6 GHz
`radio band.
`'
`
`A 16' QAM modem working at a bit rate of 140 Mbits/s and
`including a carrier
`recovery circuit
`(by the remodulation
`method) has been implemented in the CNET laboratories in
`Lannion. Experimental results (concerning the influence of
`filtering: distortions, sampling time errors, interferences) could
`
`Manuscript received January 16. 1979.
`P. Dupuis, M. Joindm. and A. Leclert are with the Centre National
`d'Etudes des Télécommunications, Lannion. Cedex, Franco.
`D. Sout‘flet was with the Centre National d'Etudes des Télécommu-
`nicutions. Lannion. Cedex, France. He is now with ECA-Automation.
`chncs. France.
`
`U(t) = V2 akX(t — k_T) cos wot—bkxo—kr) sin wot.
`l?
`
`(1)
`
`related to the carrier frequency f0 by the relation
`mo is
`mo = 27rf0. X(t) is the elementary impulse shape defined by
`
`X(t) = 1
`
`ift€[O,T],X(t)=0
`
`ift§E[Q,T]
`
`(2)
`
`Pam =P(/iial=Ai) PeBi=P(Bi¢B,)
`
`(3)
`
`where Ai is the output of the decision circuit.
`
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`

`

`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM—27, NO. 12, DECEMBER 1979
`
`quart/rub” 0x13
`
`“Irina/cl
`
`Iran/uh]
`
`~div/u
`
`grain/rm!../lw‘cc
`
`FIG. 3
`
`Simplified scheme of the radio link
`
`Introducing the average power Pm and the peak power PC
`of the signal u(t) we can write:
`
`PEAl =Pe‘“2 =—}4erfc
`‘
`
`Pm
`10002 _
`
`=fierfc
`'
`
`PC .
`18002
`
`v2
`
`v2
`
`i
`
`(6)
`
`As “signal to noise” ratios are usually expressed in dB we
`will introduce CNRO defined as:
`'
`
`Pm
`CNRO = 10 loglo —2.
`00
`
`'
`
`(7)
`'
`
`B~ Transmission of I 6 QAM Modulation of a
`Radio—Link Channel
`‘
`The transmission channel
`including transmitting and re-
`ceiving equipments can be represented by figure 3.
`Besides the. unavoidable degradation due to filtering, other
`transmission impairments occur, mainly due to:
`
`~thermal noise appearing in the resistive parts of the
`receiving chain
`'
`—radio-frequency interference
`—various imperfections (decision threshold shifts, error on
`sampling time).
`
`these impairments are listed in table 1. At first, non
`All
`linear distortions will not be taken into account.
`The system of figure 3 can be represented by using the
`low-pass equivalent channel as shown in Figure 4. Let us define
`the complex envelope U(t) by the relationship:
`
`u(t) = Re [U(t) exp [wot].
`
`(8)
`
`FIG. 1 Constellation of the 16 QAM modulation
`
`FIG. 2 Optimum receiver for 16 QAM signal
`
`At the output of the matched filter, the signal can take on
`four values at
`the sampling time:
`iVT, i3VT. The noise is
`Gaussian and its variance is 002 : NOT—1. With the assump-
`tion that WTNo‘l is sufficiently large—and it is valid in our
`case—the bit error probability can be expressed by the fol-
`lowing relationship:
`'
`
`PeAl =22“ = gpefll 2%1’932 =-};erfc(_>
`
`i
`
`.
`
`V2T V2
`
`2No
`
`(4)
`
`CNRO is the ratio (expressed in decibel) of the average
`power of the carrier to the noise power contained in the
`Nyquist bandwidth. The error probability can be plotted
`versus CNRO:
`the curve obtained in these conditions will be
`referred to as “theoretical curve” in further computations and
`used as a reference in the presence of impairments. The excess
`amount of CNRO to be provided will be called “CNRO degra-
`dation”. It depends obviously on the error probability.
`
`k
`
`erfc X is the complementary error function defined by the
`following formula
`
`2
`erfc X = —— /
`-
`x/F
`x
`
`+°°
`
`exp — t2 dt.
`
`(5)
`
`(8) gives immediately:
`
`V2 T(2N0)#1 can beregarded as the ratio of V2/2 to the noise
`power contained in the Nyquist frequency band [f0 — (2T)‘1,
`f0 + (Zn—1]. Starting from (4) we can write two slightly
`different expressions ofPeAi.
`
`Um = V201,; + mom—kn
`h
`
`= V 2 ckX(t—kT) 2 ckX(t—kT).
`k
`
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`

`DUPUIS et al.: 16 QAM MODULATION FOR DIGITAL RADIO SYSTEM
`
`TABLEI
`
`1
`
`Cowl"
`source
`
`_ Equivalent degradation
`Impairment
`i
` .
`(error rate : 10'4 )
`CNR
`eye-aperture.
`BN
`RF. X
`Filtering.
`1.6 dB
`16 %
`RF.RX 2.03
`(Butterworth
`IF.RX 1.28
`5th order)
`
`
`Residual_distortion0.7 ns
`Groupidelay
`0.6 dB
`Amplitude
`Phase errors
`Modulator
`1°
`2°
`Demodulator
`
`Regenerator : decision
`level drift
`0.5 dB
`
`Timing phase error
`1
`,.
`
`1
`
`
`
`
`
`= E2 '3} erfc
`
`TNT non-linearities :8dB
`Backoff (average power)
`Local
`interference
`carrier
`Clil = 30 dB
`Overall eye-aperture
`degradation
`
`Overall CNR degradation
`
`5.5.
`
`dB
`
`“h
`
`Now we use the very classical result: if v(t) is the response
`of a linear filter (complex gain G0» to the input signal u(t),
`then the complex envelope V(t) of v(t) is the response of the
`so-called low-pass equivalent filter (complex gain Gem) to
`the complex envelope U(t) of u(t).
`HTU) is the transfer function of a filter which is the low-
`pass equivalent of the cascade of I.F.
`transmitting filters,
`branching filters, and eventually other linear filtering effects
`like selective fading. HRQ‘) is the transfer function of the
`low-pass equivalent of the LP. receiving filter, and baseband
`filters before decision.
`
`The noise is a complex white Gaussian one. The complex
`decision device)complex representation of the demodula-
`tion—determines 5k (that is to say dk and Zak) as a function of
`the region where the observation is located.
`The observation at the input of the decision device, at the
`sampling time [2, can be written:
`
`Zoe) = V 2 came e k7) + iQ(te — ko]
`k
`
`+ nc(te) + z'né(te).
`
`(10)
`
`P(r) + 10(1) is the response of the global transmission filter
`(complex gain HTU) - HBO» to the fundamental impulse
`X(t) - HUGE) and ns(te) are Gaussian random variables un-
`correlated, with a variance 02:
`
`02=N/
`
`lHR(f)l2df=NOBR-
`
`(11)
`
`AWfiN.
`
`FIG. 4
`
`Low—pass equivalent model of the transmission system
`
`BR is the noise-bandwidth of the receiving filter.
`By dividing Z(te) in its real and imaginary parts X and Y,
`writing Pk, Qh, n0.
`115
`instead of P08 — kT). Q09 — k7),
`r1602), r1809) and considering the decision relative to ad and
`[)0 (this choice is unrestrictive because of stationarity) (10)
`becomes:
`
`X:Viglopci—ono+
`
`2 (11th *kakii + lie
`
`k #=0
`
`Y:
`
`+aoQ0 + 2 (kak +aka)] + "3-
`
`k=# 0
`
`(l2) can be rewritten in a more condensed form by intro-
`ducing the random variables 20 and 25 defined by:
`
`2c = - ono + Z (:1th — kak),
`k 7&0
`
`zs =aoQo + 2 (bigot +atQk).
`kit)
`
`(13)
`
`If we assume that the decision boundaries for X and Yob-
`
`Servations are defined by X (resp. Y) equal to 0 or iZPo V, if
`we assume furthermore that the ratio P0 Va—1 is sufficiently
`large so that the probability of overcrossing more than one
`decision boundary can be neglected, then the bit error proba-
`bilities defined by (3) can be expressed in the following form:
`
`PeA1|zc=i~P<lZcftvcl>PO>
`
`n
`
`:: if 1,2111 I 20
`
`(143)
`
`PeAzlzs
`
`M
`
`1P<|25+Vf1>n> =gPelezs
`
`(14b)
`
`where Pe I2 is the error probability conditionally to some
`given value of a random variable 2.
`(14a) and (14b) can be simplified by using the assumption
`about “a priori” distributions of ak and bk; thenzC and 28
`have the same probability density function which is even. As
`the Gaussian law of me and n5 is also even, then the following
`relation holds:
`
`P3141 =peA2=%peBi :_1Zpel32
`
`V(Po + 2)]
`
`a\/2—'
`
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`

`

`1774
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM—27, NO. 12, DECEMBER 1979
`
`2 is a random variable defined by
`
`Z ZEOQO "l’
`
`.kséO
`
`kak +dek
`
`(16)
`
`where ah ahd b'k are discrete random variables satisfying the
`“a priori” conditions defined in the beginning.
`.
`_
`.
`‘ The exact calculation of (15) is difficult: when Pk and Q),
`are non-zero terms only if k belongs to a finite set, 2 is a dis-
`crete random 'variable and (15) can be performed by the so-
`calléd exhaustive method. Even in this case however, a large
`amount of computer time is required.
`>
`It is the reason why we preferred to use a Gram Charlier
`expansion or (15) given by Ho and Yeh [2]. This method
`requires only the knowledge ’of the moments of the random
`variable z.‘ Since 2 is even, only the even-order moments M2,,
`are non-zero and (15) can be written:
`
`C—Descriptz‘on of th e Computational Procedure and
`Examples ofApplication
`
`Pk and Q are obtained by a Fast Fourier Transform from
`the frequency domain transfer function HTU) - HRCf).
`In
`most of the examples the filters were of Butterworth type
`with 3, 4 or 5 poles; but obviously any other choice remains
`possible and numerical values of amplitude and group-delay
`obtained from measurements could be introduced.
`The moments of 2 are obtained in reference [3] by a
`recurrence formula; unfortunately we found that in some cases
`when the intersymbol
`interference became too large,
`the
`method could not be used because some moments were nega-
`tive. So we had to use a classical method which requires much
`more time than the recurrence computation.
`
`Mare = 2'23”? 221‘)
`I
`
`(21)
`
`Pe" 1 = -§- erfc
`
`Pol/r;
`(Ix/f
`V1?
`
`- exp~
`
`Mzk
`1302172 4“
`2 2 ———2kH2k—1 _‘ -
`20 H (2k)!(2a)
`NE
`
`(17)
`
`Hn(x) is the nth 'order Hermite polynominal.
`It can be shown [3]
`that this series is absolutely cenver-
`gent.
`i only a finite number of terms must be kept for the practi-
`cal computational procedure.
`,
`The error probability given by (15) can be plotted versus
`CNRO; but
`it is alsoconvenient to introduce a slightly dif-
`ferent parameter called CNR defined by the formula:
`
`P ‘
`.
`' U
`.
`CNR=1010g10 ‘—"'
`
`The following relation between CNR and CNRO holds:
`
`c1~IR=cisR0 — 10101;10 312T.
`
`(18)
`
`(19)
`
`The CNRO and CNR degradations in the presence of an
`impairment will be respectively referred as DCNRO and
`DCNR.
`,
`.
`It is interesting to note that if we consider a filter satisfying
`Nyquist’s criteria shaped by the Fourier transform of X(t),
`2 becomes identically 0 and (15) becomes:
`
`
`P9141 -—PeA2 421281 —_ 1} P932 #Akerfc
`
`P,,“11 = E21[} erfc
`
`The sum is taken over all the possible values of the random
`variable 2 which is discretiz'ed by truncation of (16). Obviously
`in the case of “Hermitian symmetry” a lot of time can be
`saved because Qk is identically zero. This situation was en-
`countered in many numerical applications with Butterworth
`filters. The number of terms kept after trunbation of (16)
`can be chosen Versus the impulse response of the channel,
`carrier to noise ratio, and required accuracy.
`At first we looked at the influence of a single IF. filter,
`HTU) being assumed to be equal to unity. The DCNRO and
`DCNR degradations at Pa = 10f5 are plotted on fig. 5 versus
`the reduced 3 dB bandwidth, BT, of the IF. filter (5th order
`perfectly group delay equalized Butterworth filter). This type
`of IF. filter will be kept in the following example. A per-
`fectly group delay equalized Butterworth filter will be referred
`further as a PEB filter.
`Some other computations, detailed in [4] , were performed
`for different
`radio-frequency filtering arrangements. For
`instance, figure 6 represents DCNRO versus BT (defined in
`the same manner as in fig. 5) for four filtering arrangements.
`HT(]‘) is obtained by cascading two 5th order PEB filters, a
`receiving one with reduced bandwidth 2, and a transmitting
`one with various reduced bandwidths BtT.
`The influence of various group-delay or amplitude distor-
`tio’ns resulting from non'perfe'ct equalization was also investi-
`gated [3] using the computer procedure which has been just
`described.
`.
`As an example, let us assume a linear group-delay distortion
`in the filtering conditions of figure 6 with B,T = 2 and BT=
`1.15 (40 MHz for 140 Mbit/s bit rate). Measured and com-
`puted DCNRO (respectively dotted and solid line) are plotted
`on figure 7 versus peak to peak group delay distortion in 40
`MHz bandwidth.
`Let Us now consider the influence of interferences which
`is of primary importance in the analysis and design ofa radio
`link. All the interferers will be assumed to be sinusoidal.
`
`V N
`
`?
`
`— 4} erfc
`
`Pm V“
`
`.
`
`(20)
`
`The curve giving PEA1 versus CNR with Nyquist’s filtering
`is the same as with the optimum receiver; but the two curves
`versus CNRO are not identical because the noise bandwidth
`of shaped Nyquist’s filter exceeds the Nyquist’s bandwidth.
`
`The error probability can now be expressed by the rela-
`tionship
`
`V(Po +29]
`
`«vs/2—
`
`I
`
`(22)
`
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`

`

`DUPUIS et al.: 16 QAM MODULATION FOR DIGITAL RADIO SYSTEM
`
`
`
`<3
`
`«aGo‘4ash~l\‘uh.‘.
`
`BACK—(FF+DCNR
`
`IF REDUCED IAIDUIDTH
`
`.9
`
`
`
`
`
`
`
`
`
`J 1
`6‘ 7 o’ J 4
`OUTPUT BACK-OFF
`
`reduction factor (IRF) obtained from filtering. It is the ratio
`
`where Eecl is the equivalent eye aperture degradation (percent
`of the total aperture) due to one impairment.
`For example table 1 gives the degradation allocation for
`the 16 QAM modem implemented in our laboratory.
`The practical carrier to noise ratio CNR corresponding to
`the outage error rate (cg. 10—4)is referred to as CNR“ ' CNRb
`is related to the error rate (eg. 10‘”) during nominal un-
`faded signal conditions. Table 2 gives the values ofCNRa and
`CNRZ7 for three modulations.
`The third parameter is the adjacent channel interference
`
`FIG. 8 Degradation due to TWT amplifier non-linearities; solid line:
`calculated. A: experimental data. Note: M hop configuration in-
`cludes (M — 1) heterodyne repetitions
`
`is now clear that the computation procedure can be
`It
`generalized without any more difficulty if we can compute
`the moments of the new random variable 21. The computation
`is particularly simple with only one interferer and no inter-
`symbol interference (optimum receiver or Nyquist’s filtering),
`Then it can be shown classically that the same DCNRO is ob-
`tained with 16 QAM modulation for some CIR and with BPSK
`for CIR + 10 dB.
`
`In order to take into account the impairments due to non
`linearities, a computer simulation program has been used. The
`non linear amplifier is modeled by its AM-AM non linearity
`and AM-PM conversion. Plotted on fig. 8 is the sum of the
`power back-off and the degradation of CNR due to the ampli-
`fier versus the back-off. Experimental data are also given.
`Curves corresponding to an amplification without regenera-
`tion over two or three hops are displayed.
`
`III—PARAMETERS USED FOR THE DESIGN OF A
`DIGITAL RADIO SYSTEM
`
`A—Equz'pments
`
`CNRa and CNRb
`For any modulation scheme, as for 16 QAM modulation, a
`theoretical curve can be computed. If an error rate value is spec-
`ified, a value of CNRO is then specified too. Because of the var-
`ious impairments the CNR required to obtain the specified error-
`rate is CNRO plus some degradation DCNR. This degradation
`can be evaluated by an equivalent eye aperture method [5] :
`
`DCNR= — 20 log10 (1 — 2 Eeq)
`
`(24)
`
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`
`FIG. 5 Degradation of CNRO and CNR versus reduced bandwidth of
`the receiving IF filter
`
`
`
`
`
`
`
`
`0'
`
`IF RKDUCID IAIDIIUTM
`
`
`
`FIG. 6 Degradation of CNRO versus bandwidth of the IF receiving
`filter for different
`transmitting fil er reduced bandwidths: I: 1.4;
`o 1.6; V 1.8; A 2.0.
`
`
`
`
`
`
`
`
`
`1 l
`
`7 l J
`t 1 J l I r
`I
`J I
`l l A
`I
`PFAK-TO»PEAK GROUP DELAV DISTORTION
`
`FIG. 7 Degradation of CNRO with linear group-delay distortion versus
`peak to peak value in 40 MHz (hit rate: 140 Mbits/silF bandwidthi
`B = 40 MHZ); solid line—calculated curve; dashed line—experimental
`results.
`
`21 appears as the sum ofz (previously defined) and of the low-
`pass equivalent of the interferers taken at the sampling time. A
`new parameter called CIR (carrier to interference ratio) is
`defined by the formula:
`
`CIR:
`
`Pm
`'— .
`lOloglo PI
`
`(23)
`
`P, is the r.m.s. power of the interference.
`
`

`

`(26)
`
`T(f)—transfer function of the transmitting side filter
`R(f)—transfer function of the receiving side filter
`S(f)~—transmitted power spectrum from the modulator
`XS/2—frequency spacing between adjacent channels (Ml-lz).
`Fig. 9 shows the two forms of frequency arrangements
`(cochannel frequency reuse and interleaved channel arrange-
`ment).
`Plotted in fig. 10 are the values of IRF versus the frequency
`spacing between channels for two kinds of filters: Butterworth
`filters as in table 1 and raised-cosine filtering (roll-off factor
`0.5). The improvement brought by the latter is not so high
`for the close spacings.
`The [RF parameter only takes into account the power level
`of the interference. The statistical nature of the interference
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL COM-2‘7, NO. 12, DECEMBER 1979
`
`TABLE 2
`
`
`
`
`
`
`
`
`
`4 PSK
`14
`21
`
`CNRawml
`CNwaB)‘
`
`8 PSK
`20
`28
`
`l
`1
`
`
`24
`
`16 QAM
`
`34
`
`Interleaved arrangement
`
`FIG 9 Frequency arrangement.
`
`FIG 10 Adjacent channel interference reduction ‘factor (IRF) versus
`X/2 = X5/ 2S.
`Bandwidth
`
`1 Butterworth filtering
`5th order
`
`1.25
`RF-TX
`2.0S
`RF-RX
`1.2S
`lF-RX
`2 raised-cosine filtering (Roll-off factor: 015).
`
`
`
`I!
`
`I l
`
`0
`It
`
`between the interference power of one adjacent channel and
`the power of the desired channel.
`In the case of an interleaved channel arrangement, IRF is
`written thus:
`
`=
`
`loglo
`
`XS
`'
`2
`XS
`°°
`
`
`|R(f)12S<f—~—2>df
`/ IT re —2
`/ lTU)|2-|R0‘)12‘S(f)df
`
`(25)
`
`
`
`
`
`[0
`
`
`
`is however also of interest because the degradation is
`signal
`lower with a sine wave noise than with a Gaussian noise.
`Therefore we shall now introduce the AS parameters.
`AS: The curves of fig. 11 give the degradation of CNR
`versus the carrier to interference ratio CIR for 16 QAM modu-
`lation at 10—4 error rate. It appears clearly that 16 QAM modu-
`lation is more resistant
`to sinusoidal
`interference than to
`
`FIG. 11 Continuous line: sinusoidal interference (calculated)~Dashed
`line: Gaussian noise (calculated). A: sinusoidal interference (experi-
`mental data).
`
`Gaussian noise by AS dB. This parameter AS depends on
`modulation, bit error rate (BER) and CIR. For BER = 10‘4,
`the value AS,2 = 3 dB is quite reasonable in the CIR range of
`interest and is assumed to be the same for all the three modu—
`
`lations that have been considered. For BER :1 10'“), Ash =
`6 dB is obtained.
`SG:
`In order to take into account the transmitted power
`and the receiver sensitivity, the system gain SG is defined as
`the difference in decibel between transmitted and received
`powers at the error rate threshold.
`
`S6 = (Psat i190) e (—1 14 +1010g10 s +NF + CNR“).
`
`PMC Exhibit 2041
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`
`

`

`DUPUIS et al.: 16 QAM MODULATION FOR DIGITAL RADIO SYSTEM
`
`1777
`
`TABLE 3
`
`4 PSK
`MODULATION 16 QAM
`
`Requi red
`additional
`0
`.
`15
`(Psat " BO)dB
`
`
`
`
`: transmitted saturation power (dBm)
`: rms output amplifier back—off (dB)
`: modulation rate (Mbaud) (S = T’1)
`: receiver noise figure (dB).
`
`BiFade Margins
`MB: The value of the maximum allowed flat fading MB
`called “gross margin” (in French: “marge brute”) is easily
`calculated, from system gain, antenna gain and free space at-
`tenuation:
`
`MB = $6 +AGT +AGR — (145.5 + 20 loglo E10
`
`O
`
`+l
`
`* +Lf
`310 50
`
`.
`
`(27)
`
`ACT : transmitter antenna gain (dB), D: hop length (km)
`AGR : receiver antenna gain (dB), Lf: feeder loss (dB)
`f0
`: carrier frequency (Gl-lz).
`
`Using this MB parameter the outage probability can be cal-
`culated in the case of flat fading when remote radio interfer-
`ences are not taken into account.
`
`Poutage = P(BER 2 IO‘4) = P(A 2MB).
`
`(28)
`
`A is the fade attenuation (dB).
`In a practical case, however. radio interference (adjacent
`channels, adjacent hops,
`...) and propagation distortions de-
`crease significantly the outage time:
`
`P(BER 9 10‘4) >P(A 2MB).
`
`(29)
`
`MN; This parameter called “net margin" takes into account
`all impairments occuring only during fading [6] , [7] : distant
`radio interference, propagation distortion,
`intermodulation
`into a common microwave preamplifier and so on.
`
`The 16 QAM modulation exhibits comparatively higher
`values of CNRa and BO than PSK modulations. The resulting
`decrease of the system gain can only be compensated for by a
`higher transmitted power and/or a better receiver noise figure
`(see table 3).
`All the parameters defined until now were related to the
`equipment. Now let us consider parameters related to the
`propagation conditions, especially fading, and therefore intro-
`duce the fade margins.
`
`desired channel frequency. There is then some compensation.
`
`Two net fade margins must be distinguished according to
`the kind of outages. The short duration outages mainly due to
`multipath propagation affect the transmission quality. In this
`case the MNQ net fade margin of quality is introduced:
`
`P(A >MNQ) éP(BER> 10’4 l short duration outages).
`
`(30)
`
`The long duration outages due to rain affect the transmis-
`sion availability.
`In that case, the MND net fade margin of
`availability is used.
`
`P(A >MND) é P(BER > 10—4 I long duration outages).
`
`(31)
`
`IViPOINT TO POINT CAPACITY, OPTIMIZATION OF
`THE FREQUENCY ARRANGEMENT
`
`Let XPD (dB) be the cross polarization discrimination of
`the antenna. In the case of two adjacent channel interferences,
`the following formula holds:
`
`P(BER210-4)=P(A >Ma)+ /
`0
`
`p(A)P[XPD(A)
`
`MB
`
`+ lRF — 3 <a(A)]dA
`
`A—MB
`
`01(A) = —lOlog10(l — 10
`
`+ CNRO — A5,,
`
`(3 2)
`
`where p(A) is the probability density function of the fades.
`The limited amount of measured data does not allow for an
`estimation of the conditional probability ofXPD(A) (depend.
`ing on antennas) and the formula (32) must be simplified. We
`then obtain for XPD(A) < 25 dB:
`
`XPD(A) E XPD", (A) 3 XPDO — M
`
`(33)
`
`where XPD," (A) is the median value of XPD(A ).
`[9] with
`Measurements carried out at 7 and 13 Gl-lz [8]
`high decoupling antennas exhibited the following values:
`
`(3 = 0.7, XPD0 = 37 + AXPDO.
`
`(34)
`
`AXPDO : 0 dB for multipath caused fadings
`AXPDO = 7 dB for rain caused fadings.
`The corresponding curves are plotted on fig. 12. The net
`margin versus gross margin curves obtained from the simpli-
`fied way are displayed on fig. 13 b.
`In the case of multipath propagation the interference chan-
`nel can be less affected than the desired channel. lf. however,
`such a case occurs the polarization discrimination will be
`higher at
`the interference channel
`frequency than at
`the
`
`PMC Exhibit 2041
`Apple v. PMC
`IPR2016-00755
`Page 7
`
`

`

`
`
`
`
`
`+10’ 10
`
`35
`5.10’5 nos 10’5
`(b)
`(a)
`mm | unral-IBlll-Ml
`
`so
`
`A0
`
`45
`
`so
`
`10"
`
`
`
`
`
`
`
`
`
`
`
`
`
` *
`
`9
`
`10
`
`11
`
`12
`
`13
`
`I4
`
`15
`
`\6
`
`RF channel number
`
`FIG. 13
`
`(d)
`(a) Multipath outages (worst month). (in) Net margin versus
`gross margin (adjacent channel interference),
`—5 dB 0
`XI’DO + (IRF — 3) v (CNRa — Asa) =#10 dB A
`—15 dB V
`(c) Rain outages (per year). 1 MEDITERRANEAN, 2 SOUTHEAST,
`3 PARIS, 4 BRITTANY. (d) (IRF 7 3) 7 (CNRa \ Asa) versus RF
`channel number in 10.7-11.7 GHz band (ZS =1.0S, Y5 = 2.55).
`
`The choice of frequency arrangement depends on the net
`fade margin objectives. In France, the outage time objectives
`for 50 km link in the national network are:
`
`rain caused outage time < 2.10‘5 a year
`multipath caused outage time < 2.10’5 worst month.
`As far as the 10.7-11.7 GHz frequency band is concerned
`the statistical data give the following results (fig. 13 a and c).
`
`MNQ > 38 dB
`MND 2 42 dB (southeast region).
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-27, NO. 12, DECEMBER 1979
`
`a»z:
`
`ATTENUATIUN uo
`
`
`
`
`
`
`
`40
`
`15
`
`20
`
`25
`
`dB
`
`XPDrn
`
`FIG.
`
`12 Cross polarization discrimination (median value XI’Dm)
`versus attenuation.
`
`
`
`MNtdB) MND(dB)
`
`
`
`lo"
`
`
`
`are-5 10*5
`510-5
`(0)
`
`For MB = 45 dB it is therefore required:
`
`(IRF - 3) — (CNRa ~ 135“) 2 8 dB.
`
`(35)
`
`This parameter (IRF — 3) — (CNRa ~ Asa) is plotted on
`fig. 13 d versus the number of RF channels for the three
`modulations 4 PSK, 8 PSK and 16 QAM.
`Co-channel frequency reuse appears here as the borderline
`case of the interleaved arrangements. In this case we just have
`IRF — 3 = 0 dB. With the net margin objectives previously
`given,
`the maximum number of RF channels for the three
`forms of modulations is thus obtained:
`
`4 PSK
`
`6 channels
`
`8 PSK
`
`8 channels
`
`16 QAM 10 channels
`
`XS
`? = 69 MHZ
`XS
`? = 56 MHZ
`XS
`-- = 47 MHz
`2
`
`The curves given here are typical curves. It is possible to
`change one or other parameter and to obtain other frequency
`arrangements.
`
`V—NODAL INTERFERENCE
`
`The French microwave national network is a mesh network.
`The average length of the links is about 300 km. The number
`of radio links already reaches 6 or even more at the main nodal
`towers: Paris, Orleans, Dijon, Lyon.... Furthermore l or 2 hop
`regional links will be overlayed into the national network from
`the nodal towers. Thus, the improvement of the nodal capac-
`ity also matters to the system planner.
`
`A —Anterma Pattern
`
`In this paper we do not study the influence of various re-
`flections and antenna characteristics. We take into account
`the characteristics of a typical antenna:
`the parallel antenna
`decoupling DAP(6) and the orthogonal antenna decoupling
`DAX(6) (fig. 14). Equal
`transmitted power and equal hop
`lengths are assumed.
`‘
`Adjacent hop interference reduction due to antenna and
`filtering may be evaluated by the parameters IRA.
`IRAl -Interference from (1' + l) and (i — l) hops (fig. 15).
`
`7‘1 IRA1
`10 1"
`
`=10
`
`DAP(61)+IRF-—6
`1°
`
`DAX(9])—3
`1°
`
`+10
`
`(36)
`
`(lRF - 3 2 0 in the case of co-channel frequency reuse).
`IRA2 —Interference from (i + 2) and (i i 2).
`Interleaved-channel arrangement IRA2 = DAP(62) * 3.
`Co-channel frequency reuse IRA2—negligible.
`IRAioverall interference reduction.
`
`IRA
`10—
`
`10
`
`IRA1
`
`IRA2
`
`PMC Exhibit 2041
`Apple v. PMC
`IPR2016-00755
`Page 8
`
`

`

`DUPUIS et (21.: 16 QAM MODULATION FOR DIGITAL RADIO SYSTEM
`
`
`
`
`
`
`
`
`
`so
`
`so
`
`too
`
`deems
`AZIMUTM
`FIG. 14 Radiation pattern. 3 m antenna (1] GHz); DAP (6)—parallel
`decoupling; DAX(0)~orthogonal decoupling.
`
`I“)
`
`"UMARSH!
`
`
`
`
`
` I"
`
`,,,,_ .___ . a, .
`so
`GROSS HARGIN
`
`(dB)
`
`FIG. 16 Net fade margin versus gross fade margin (adjacent hop in
`tcrference).
`
`
`Ij.
`Nodal capacity
`
`
`(38)
`
`Adjacent hop interference matters when the desired path
`signal had faded to near the threshold:
`these interferences
`reduce the fade margin.
`_
`It may be assumed that the desired path and the interfering
`path do not fade simultaneously. These fadings are completely
`uncorrelated in the case of multipath and also in the case of
`the rain. if the rain intensity is hiin and the hops are long.
`With this assumption the curves of margin degradation are
`plotted on fig.
`l6. The required IRA must exceed ,MN +
`(CNRG — ASH). plus a few dB, depending on the objective of
`margin degradation. prescribed by the system designer.
`
`
`
`
`
`
`
`7
`
`[LAWN] ,1,”
`
`'
`
`'
`
`I2
`"if
`«F churn-I number
`
`ti
`fat
`MG. 15 Nodal interference
`
`FIG. 17
`
`IRA-(CNRa — AS“) parameter versus RF channel num her for
`different values of nodal capacity
`
`C—N0dal Capacity
`
`We define the nodal capacity for a given frequency band as
`the product of n, number of usable RF channels, by N,
`number of radio links.
`
`nodal capacity = YIJV
`
`where n is the number of usable RF channels, Nis the number
`of radial links.
`
`In this calculation only the main radio interferences are
`considered.
`
`Equal angular separation between adjacent paths is as-
`sumed.
`
`87 Fade Margin DBgr'ddatian
`
`Fig. 17 shows IRA — (CNRa‘ — ASa) versus N for different
`values of nodal capacity. Low level modulations require more
`bandwidth per channel, but permit closer juxtaposition of
`radial. paths. The tradeoff depends on the IRA —.(CNRG —
`ASH} objective (table 4).
`
`D—Intrddu‘ction of/l TC
`
`High-level modulations Such as 16 QAM appear very sensi-
`tive to interference. Their use is difficult if large nodal capac-
`ity is wanted.
`In order to improve this nodal capacity, the
`automatic transmission control ATC(A) may be introduced-
`and achieved by means of the supervisory line,
`
`Pt 2 (PSat —30) — ATC(A ).
`
`PMC Exhibit 2041
`Apple v. PMC
`IPR2016-00755
`Page 9
`
`

`

`TABLE4
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-27, NO. 12, DECEMBER 1979
`
`
`
`
`
`_
`30
`AttGULAR SEPARATION (Degrees)
`FIG. 18 Adjacent path protection with and without ATC.
`
`
`
`
`
`
`
`
`with a preamplifier, exhibiting a noise figure of 6 dB, and
`
`hr is gain and delay of the seCondary path relative to the
`primary pathhAwo'is notch offset.
`I
`,
`V The average value of delay depends on hop length and
`terrain conditions.
`_
`.
`.
`p
`‘
`Measurements Were achieved'over the 58 km hop Meudon-
`Bois. de Molle' [10]; near Paris, whichlmay be considered
`as an average hop in France, except for the length which
`is
`Iongergthan the average value of the French national
`nétWork (47 km). These measurements were carried out with
`4 DPSK modulation at thelbit rate of 216 M'bits/s in the
`11‘ GHZ frequency band. The measured‘median value of 7'
`Was 0.4 ns. The observed MNQ Was 20 dB for ME = 35 dB.
`An experimental IF tWo path simulator has been intro-
`duced in a 4 CPSK 140 Mbit/s modern. Taking into account
`the average value of T,
`the corresponding net
`fade margin
`versus gross fade margin-curve is drawn (in Fig, 19. ‘From
`computations, the performance curve of 16 QAM modulation
`has been found to be very close to that of 4 PSKmodulation
`(~2 dB additional margin degradation), This is because the
`
`
`
`
`
`
`
`#5
`
`30
`
`35'
`
`5O
`
`u-u.
`
`HEYFANJQIGIL
`
`Optimum