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:[email protected] 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 fre- quency 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 probabil- ity 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- . ¡ 3 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 , 5 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 CBD 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 M6NOQP in a Bessel power is adjusted to be in the interval between minimum series expansion by solving R " > and maximum output power. (U(U( MSNTO N NOQV!W Bzy { f V g h¤i i ¡mn\o!p q i i A.