Intermodulation Distortion in Switched Multibeam Antennas for Cellular Radio Systems

Mattias Wennstrom,¨ Anders Rydberg and Tommy Ober¨ g Signals and Systems Group, Uppsala University, Box 528, SE-751 20 Uppsala, Sweden, Email:mw@signal.uu.se

ABSTRACT To meet the requirements in the mobile system specifica- tion of allowed spurious emission, linearisation of MCPA:s The performance of switched multibeam antennas for cel- is required. Although linearisation techniques significantly lular radio systems is investigated when the transmit am- reduces the intermodulation distortion in the output signal, plifier is of a multicarrier (MCPA) type. The MCPA non- some residual intermodulation distortion remains, and it linearity generates intermodulation distortion in the trans- is useful to know to what level the intermodulation has to mitted signal that is spatially filtered by the array radiation be suppressed by the lineariser, as a lower level implies pattern. Hence, the intermodulation distortion becomes a more expensive linearisation method. The problem ad- direction-dependent, and the direction of the generated in- dressed in this paper is how the linearity requirements on termodulation products of any order is derived. It is shown the transmit MCPA depends on the frequency reuse dis- by using Monte Carlo simulations how the downlink car- tance for a system using switched multibeam antennas at rier to interference ratio depends on the frequency reuse the BS. The linearity of the MCPA is defined by using the distance and on the MCPA linearity measured as its noise noise power ratio (NPR) measured from a standardized power ratio (NPR). For reuse factor one systems, which NPR test [3]. is made possible by use of multibeam antennas, the linear

A cellular system with a total of frequency channels co-channel interference dominates the interference. On

equally distributed over cells is assumed in this paper. the contrary, for a reuse factor seven system it is shown

The frequency channels in each cell are further di- that a weak nonlinearity directly gives a degradation in

vided in a sector-trunkpool scheme where each 120 sec- carrier to interference ratio (CIR) due to intermodulation

tor has a unique set of frequency channels assigned distortion. However the reuse factor seven system has a to it. The mobile stations (MS) in the sector will receive large CIR overhead due to the increase in CIR using a interference of two types. First, linear interference comes multibeam antenna, and the outage probability is thereby from BS in the (primarily) first tier of co-channel BS. only slightly affected. Secondly, intermodulation interference is generated in the MCPA in the same BS as the MS is connected to, and if 1. INTRODUCTION the set of frequency channels used in the sector are equally spaced, it can be shown that the generated intermodulation products falls onto the same set of frequencies. The deployment of switched multibeam antennas at base stations (BS) in cellular TDMA/FDMA systems has either Note that the intermodulation interference is emitted with shown to improve the capacity or to extend the radio cov- low power, but the MS is usually close to the BS, hence erage by increasing the carrier to interference ratio (CIR). the signal has a low path loss. Compare with the linear The reduced interference levels allows for a reduction in co-channel interference from first tier BS, which is trans- frequency reuse distance, thereby increasing the spectrum mitted at high power, but the larger BS to MS distance efficiency of the cellular system [1]. gives a high path loss. Hence, there is a point in the de- gree of MCPA linearity, where the major interference at One drawback with the use of array antennas at the BS the MS changes from being linear interference, from first sites is the increased amount of hardware compared to tier BS, to intermodulation interference, from “own” BS. a conventional BS. For each antenna and for each frequency channel a single carrier power amplifier is required One property of MCPA:s in conjunction with multibeam for the downlink transmission. Thus, to reduce size, cost antennas is that the radiated IMP will be spatially filtered and power consumption of the BS, multicarrier power am- by the beam-pattern of the antenna array [5],[6]. This im- plifiers (MCPA) have been suggested for use in multi- plies that in some directions the generated IMP will be antenna BS [2]. The co-amplification of several carriers suppressed by the side lobe level of the multibeam radia- on different frequencies in an MCPA generates intermod- tion pattern and in other directions, the IMP power will be ulation products (IMP) due to the nonlinearity and due to amplified by the antenna array gain by coherent addition

the non-constant envelope of the combined signal. Often of the IMP from all antennas. Hence, the carrier to inter- ¤£ the third order IMP are considered (of type 2 ¢¡ - and ference ratio at the MS in the system depends on the posi- ¥¡§¦¨ ©£ ), as they fall onto other frequency channels tion and beam allocation of the other users in the cell and that are used in the system and thereby, cannot be removed in neighboring cells. A Monte Carlo simulation is used by ﬁltering. to estimate the outage probability, which is the probability that the carrier to interference ratio (CIR) for a MS fall at the MS is a function of the array pattern, the nonlinear below some threshold. The outage probability is evaluated characteristics of the ampliﬁers and the spatial distribu- for different MCPA linearities and at different frequency tion of the MS [8]. In the remaining part of the paper, the

reuse distances. study is restricted to the third order intermodulation prod-

. ¡

ucts that falls “in band”, i.e. at the frequencies 2

. ¡ £

¦4 ¨ and . This is justiﬁed by the fact that these 2. CO-CHANNEL INTERFERENCE ON THE IMP terms contains most of the intermodulation energy. DOWNLINK Furthermore, assume that the frequency channels in Fig. 1 are equally spaced, that is, the center frequencies are The frequencies in a cluster are assumed to be planned related as

according to a ﬁxed channel allocation scheme as seen in

¤£ 56¦87:9;

Fig. 1. Furthermore, each sector is equipped with an el- (2)

£ 7

where is the center frequency of frequency channel ,

9; is the frequency channel separation and is a refer- 8,20,32,... ence frequency.

7,19,31,... In each sector, the center frequencies of the used frequency

£=<> £

¦ 9? channels are related as where is 9,21,33,.... 11,23,35,... the cluster size. It is easy to verify that with this frequency 10,22,34,... planning, the generated third order IMP falls onto other frequencies used in the downlink in the same sector. For

5,17,29,... 12,24,36,... example frequency channel 13 and 25 generates IMP on

>A@ >

4 CB D

channel 1 ( 2 ) which is also used in that 4,16,28,.. sector, see Fig. 1. 6,18,30,.... 2,14,26,... B. Calculating the MCPA Output Signal 1,13,25,... If the complex gain of an MCPA as a function of the in- 3,15,27,... put power of a single carrier is measured, the AM/AM and AM/PM conversion characteristics of the amplifier is obtained. These are commonly used to describe the non- Figure 1: Assignment of frequency channels to sectors in linearity. When simulating MCPA:s in conjunction with a fixed channel allocation scheme with cluster size K=4 array antennas, each of the IMP in each of the MCPA:s cells. output signal must be separately calculated, because their relative phases and amplitudes will affect the radiation ement antenna array, hence fixed beams can be formed pattern of each IMP. A commonly used method uses the in each sector and thus beams in each cell. In the BS fast Fourier transform (FFT) to yield the output power transmit path, each antenna is preceded by an MCPA with at arbitrarily frequencies from a nonlinear device with a maximum and minimum output power per carrier of 43 multi-tone input. With more than one IMP on the same and 13 dBm respectively. The power regulation per trans- frequency in the output signal, the FFT method fail to dis- mitted carrier is performed in 2 dB steps and is based on tinguish between them, as it gives only the sum of the to- the received signal strength of the uplink signal averaged tal IMP on that frequency. Instead, Shimbo [9] proposed over the fast multipath fading. Path loss compensation is a method by fitting the AM/AM and AM/PM characteris- done for half of the loss, following the ideas in [7]: tics to a Bessel series expansion. With this method it is

! #"%$ possible to ﬁnd an analytical expression for the amplitude *+-, /.10£ '&)( (1) and phase of the desired signals and each of the IMP:s in

the output of a nonlinear ampliﬁer with a multi-tone input.

1.10£ , Here, is the MS-BS link gain, that is, the quotient Hence, this method suits our needs. Shimbo’s method is between the received power at the BS and the transmitted

$ described below.

power from the MS, which is assumed known and is L¤FIHKJ constant that has to be adjusted for optimal performance If EGFIHKJ and are the AM/AM and AM/PM character- of the system, see [7]. After the power regulation (1), the istics of the amplifier, find the coefficients M6N OQP in a Bessel

power is adjusted to be in the interval between minimum series expansion by solving

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and maximum output power. (U(U(

MSNTO N N OQV!W

Bzy {

g h¤i i

¡ mn\o!p

i i

A. Intermodulation Interference >

E!FjHKJlk XZY\[ Otsvu FIMCwxHJ i

arg i (3)

]:^ _a`T^cbcbcbd^ _de

i i |

Pdr i Consider a BS with transmit MCPA’s operating in it’s non- i

linear region, close to saturation to maximize the power for all amplitudes H in the input amplitude interval. Here > efﬁciency of the ampliﬁer. The power of the received IMP u is the 1st order Bessel function and note that the coef-

£=0 9 £ 9 £

O ¯ F® J ¯ ¯

ﬁcients P are complex. Assume that the input consists of property [5], where is the phase

}

phase modulated ( ~ZFlJ ) carriers with amplitude gradient over the antennas in the array for signal . The

9 £

¯ ° and write the input as phase gradient belongs to a set V , of different

phase gradients, unique for each beam the beamforming

¡Qn/ ©<¥§n/pp q

" network can generate.

.\0

k FlJ HKKk

(4) ´

"½¼

2¾ °»V

± (10)

À¿

r where is the center frequency of frequency channel . The output signal of the MCPA can be written as

The ﬁnite set °»V is a closed group under multiplication

¡t n1 <¥ n/ppUG

" }

and addition, following modulo- algebra. These prop-

FjlJ FI6J¥k kt (5) erties implies that the main-lobe direction of the desired signals are also main-lobe directions for the IMD (if no

where is the set AM/PM ampliﬁer conversion is assumed).

Using the FFT beamforming, (9) is simpliﬁed to

q q

R-

" " "

> £ £

B (-(U(

N N N W? N N ¢¢

B Á

¥T!

" }

Y\[ FIÃÂ:F JlJ

£ > £ >¢¡ ¡

r r

s s

FI J Fj Jt°F J

« (11)

¡ ¡

FÂ:F JlJ (6) Y1[ where

to restrict the output to the “in band” ﬁrst and third IMP.

q ©s

Now, deﬁne the set as

« «

£ £

9 (

J F ¯ ¾ Y1[¥F JlJ

Â:F (12)

£ >

" "

> £ £

B (U(-(

s s

¤£ N N N W¥ ¢

(7)

£ >

For example, the direction of the maximum radiated IMP

r ¥¡Ä ¤£

for a 2 product can be found as

to consider the output in the frequency channel with center

9 ¡Ä 39 £

"ÈÇÉ Ê 2 ¯ ¯

(

Á s

frequency only. Using the coefﬁcients from the least ^ »Å=Æ

Y\[ÃË (13)

square ﬁt in equation (3), the complex voltage gain for the ¾

¦ ¢¡© :th component in the output at frequency s and can be It is easily veriﬁed that (13) maximizes (11) for the 2

written as [9] ¤£ product.

§ q

} "

OQP u FIM¨vH J J Fj (8)

> 3. SIMULATION SETUP

£ >

Pdr

where u is the Bessel function of order . Note that the The purpose of the simulation is to calculate the cumula-

output amplitude of the desired carrier at frequency s is tive distribution function of the CIR at the MS in the fully

} "

(U(-( & & (-(U(

ÎÍ NtÏ)N=Ð

s s

Fj J N N N N W

loaded system. We simulate with a cluster size given by with jª . sx© and a ﬁrst tier of interfering BS. Each cell shape is assumed to be hexagonal and the MS are uniformly area dis-

C. The Far Field Radiation Pattern tributed within a cell. We assume that a four element an-

" Ï

tenna array are employed in each sector ( ). The an-

ÊQÑ

F J

Now consider the received power at the MS in direction tenna elements have a radiation pattern with ÒÓ

« ¬

from broadside of the array and on a distance from sensitivity (the front to back ratio is Ô dB). G2

the BS. Assume an element, -spaced linear array, The power received at the MS from the BS transmitting at ! where is the wavelength of the carrier frequency in the power is, after averaging over the fast multipath center frequency channel. Furthermore we assume a sim- fading,

ple ﬁxed beamformer, which can be implemented as the

fast Fourier transform (FFT), or if implemented in hard- Õ "%T!

ware, a Butler matrix. The phase of the beamformer “weight” Ë (14)

Ì×ÖSØ

£=0

7 ¯

applied to signal at antenna ® is denoted . The far

« Ù

where ¬ is the BS to MS distance, is the path loss ex- s ﬁeld radiated power in the direction of the :th signal component can then be calculated as ponent (set to 4) and is a lognormal distributed random

variable with mean 0 Ø dB and standard deviation 4 dB.

C¥T! "

B for the CIR estimation is picked from the center cell, to

i i

U²vl³´ ´

¡ n/ n10 >Apjµ¢¶· ¸nº¹tpjp

" }

` i

i avoid edge effects. The beam with the highest received

Fj Jl°F J¨± k i

i (9)

0 > i

i signal strength (RSSI) on the uplink for one particular user

r i

i is chosen as the beam for the downlink transmission and

« J where °F is the individual antenna element gain in di- the power is regulated according to (1). The users can be rection « . Using the FFT or the Butler matrix, we have the separated by using e.g. a training sequence method. A. The Transmit MCPA low CIR. This implies that the linear interference from the BS in the ﬁrst tier is the dominating interference. When The BS is assumed to be equipped with MCPA:s capable NPR is decreased, the ampliﬁer is working closer to the of amplifying a maximum of eight simultaneous carriers. saturation point and the interference becomes more dom-

The number of used frequency channels per cell is 12,21 inated by intermodulation distortion. Fig. 5 shows a

" ÐvNtÏ)N and 24 in the cases respectively. As a measure of the linearity of the MCPA, the noise power ratio (NPR) is deﬁned as the ratio between the linear output power den- 1 sity to the spectrum density within a pre-located notch[3]. When the number of co-ampliﬁed carriers is small (e.g. 0.95 four), we use the intermodulation distortion ratio (IMR) }

T 0.9 as a linearity measure instead, due to the large errors in- Γ voked when removing one carrier in the NPR measure- NPR=28 dB Pr{SIR> 0.85 ment. IMR is defined as the ratio between linear output NPR=38 dB NPR=48 dB power per tone to the highest intermodulation distortion Ideal MCPA power, assuming that all input carriers are of equal ampli- 0.8 tude but with independent phases. The AM/PM distortion is neglected in this study, it is of- 0.75 0 5 10 15 20 25 30 35 ten is small in a linearized amplifier, but the amplifier Γ [dB] T

AM/AM is modeled according to Cann’s model [10]

" Ú

H Figure 2: Area-averaged probability for different MCPA `

EGFIHKJ (15)

!ÞU

¢Û

ß linearities measured as NPR. The curves shows the down-

¦ ÜSÝ link with 4-element antenna arrays in each sector and clus-

ter size K=7. Ú

where is the small signal ampliﬁcation, àÅ is the output

Ô â

saturation level as the input amplitude H and ¡»á controls the knee sharpness, or the transition¡ smoothness NPR=24 dB NPR=33 dB

between the linear and nonlinear region. In the simula- 1 "ã

"ã NPR=42 dB

Å N tions, the values â are used. The input Ideal MCPA backoff, deﬁned as the average input power compared to 0.95 the input saturation point, is adjusted to give the desired } T

NPR. Γ 0.9 Pr{SIR> B. Performance Criteria 0.85

To evaluate the performance of the switched beam antenna 0.8 system, the area averaged probability of a received CIR at

a MS exceeding a target value äå . The outage probability 0.75 0 5 10 15 20 25 30 as the probability that CIR is below a pre-deﬁned power Γ [dB] T protection ratio. A power protection ratio of 15 dB were used in the simulations. Figure 3: Area-averaged probability for different MCPA linearities measured as NPR. The curves shows the down- 4. SIMULATION RESULTS link with 4-element antenna arrays in each sector and clus-

ter size K=4.

" Ð Fig. 2 and Fig. 3 shows the performance of the and

" comparison of the outage probabilities for the three cluster

system respectively for different NPR. Four carri- " Ï sizes considered. We see that the system is slightly

ers are co-ampliﬁed in each MCPA. The degradation due "

" Ð

more sensitive to intermodulation than the system, Ï to the intermodulation distortion is similar in the cluster size, although we have a degradation in CIR com- due to the reduced reuse distance, hence when NPR is de-

" creased, a MS can be interfered by intermodulation from Ð pared to due to the reduced reuse distance and BS in the first tier. Note that the asymptotic value of the hence increased interference levels, as can be seen as a "½ shift of the curves to the left in Fig. 3. The interference in outage probability for the case is 0.79 when NPR these cases are linear co-channel interference transmitted goes to infinity, hence the system is interference limited by the BS in the first tier and intermodulation distortion due to the short reuse distance, even with ideal MCPA:s. from the BS in the same sector as the MS is connected to. We see that when NPR is decreased, the interference 5. CONCLUSION

is dominated by intermodulation distortion. "æ

When the reuse distance is reduced to , see Fig. 4, The performance of a switched multibeam antenna system the NPR=41 dB coincide with the ideal MCPA curve for using transmit MCPA:s in a cellular FDMA network has that particular frequency channel. 1

0.95 REFERENCES }

T 0.9 Γ [1] M.D.Austin M.J.Ho, G.L.Stuber, “Performance of switched-beam smart antenna systems,” IEEE

Pr{SIR> 0.85 NPR=22 dB NPR=33 dB Transactions on Vehicular Technology, vol. 47, pp. NPR=41 dB Ideal MCPA 10–19, 1998. 0.8 [2] J.McGeehan G.Tsoulos, M.Beach, “Space division 0.75 multiple acess (SDMA) ﬁeld trials. Part 2: Calibra- 0 5 10 15 tion and linearity issues,” IEE Proc. - Radar, Sonar Γ [dB] T and Navigation, vol. 145, pp. 79–84, 1998. Figure 4: Area-averaged probability for different MCPA [3] N.Borges de Carvalho J.Pedro, “On the use of multi- linearities measured as NPR. The curves shows the down- tone techniques for assessing RF components’ inter- link with 4-element antenna arrays in each sector and clus- modulation distortion,” IEEE Transactions on Mi- ter size K=1. crowave Theory and Techniques, vol. 47, pp. 2393– 2402, 1999. 1 [4] T.S.Rappaport P.Cardieri, “Combined effects of nar- 0.9 rowbeam antennas and fractional loading factor in forward link cellular communication systems,” in Asymptote for K=1 0.8 Proceedings of Vehicular Technology Conference, Piscataway, USA, 1999, pp. 1074–1078. 0.7 K=7 [5] M.Wennstrom,¨ “Smart antenna implementation

Pr{SIR>15 dB} K=4 0.6 K=1 issues for wireless communications,”, Techni- cal report, Signals and Systems Group, Uppsala 0.5 University, Sweden, 1999, Technical Licenti- ate Thesis, http://www.signal.uu.se/Publications/ ab- 0.4 stracts/l991.html. 20 25 30 35 40 45 50 55 60 NPR [dBc]

[6] W.A. Sandrin, “Spatial distribution of intermodula- R-çè

Figure 5: 1-Pr A¨EvkW for different cluster sizes as a tion products in active phased array antennas,” IEEE function of MCPA linearity. Transactions on Antennas and Propagation, vol. 22, pp. 864–868, 1973. been studied by simulations on the downlink channel. The [7] M.Ljungberg C.Carneheim, S-O Jonsson, “FH- IMP will be spatially ﬁltered by the array radiation pattern GSM frequency hopping GSM,” in Proceedings of and is often radiated in another direction than the direction Vehicular Technology Conference, Stockholm, Swe- where the two, or the three signals that generate the IMP den, 1994, pp. 1155–1159. are directed. [8] S.Sowelam K.J. Maalouf, R.C.Gaus, “Error rate es-

The multibeam antenna makes the system more robust to timation in a multi-channel active phased array,” in

" nonlinearities, for Ð , the CIR is severely reduced IEEE International Conference on Communications, when the nonlinearity is present, by intermodulation dis- New York, USA, 1998, pp. 402–406. tortion from the own BS. However, the multibeam antenna

has increased the CIR to such an extent that the outage [9] O.Shimbo, “Effects of intermodulation, AM-PM

*í conversion, and additive noise in multicarrier TWT

éêìë W probability ¬ is only slightly affected. "æ systems,” Proceedings of the IEEE, vol. 59, no. 2, For systems the linear interference situation is se- vere and every dB degradation in MS CIR is expensive, pp. 230–239, 1971. hence the outage probability will be largely affected when [10] A.J.Cann, “Nonlinearity model with variable knee the NPR is decreased. sharpness,” IEEE Trans. on Aerospace and Elec-

Hence, it was demonstrated that by using a multibeam an- tronic Systems, vol. 16, pp. 874–878, 1980.

" Ð tenna in frequency planned network, we can use the generated CIR overhead to use a less complex or less expensive linearisation method. To reduce the intermodulation distortion at the MS, it is possible allocate new mo- biles to frequencies so that the generated intermodulation main beam points in directions where no mobile exists on