16 nd International Conferene on Mehanial, Eletroni and Information Tehnology Engineering (ICMITE 16) ISBN: 978-1-6595-34-3 A Study on The Performane of Multiple-beam Antenna Satellite Reeiving System Dezhi Li, Bo Zeng, Qun Wu* Communiation Researh Center, Harbin Institute of Tehnology, Harbin, China, 151 *qwu@hit.edu.n Keywords: Performane, Multiple-beam antenna, Channel mismath, BER, Satellite ommuniation system. Abstrat. High quality, high apability and wide overlay are desired in modern satellite ommuniation. Many new tehnologies have been used in ommuniation satellite, and multiple-beam antenna was one of them. Disussing the amplitude and phase inonsisteny of the RF multiple-reeiver is the most important part for the multiple-beam antenna in pratial appliation. The influene of the hannel mismath on the satellite multiple-beam antenna system has been disussed and simulated in this paper. We have given the signal to noise ratio (SNR) to bit error rate (BER) urves at last. And the disussion results have a ertain pratial appliation value for designing the satellite system. 1 Introdution Satellite ommuniation tehnology has attrated wide attention sine the birth of it beause of the advantages that wide overage, large ommuniation apaity, flexible networking, good mobility, not limited by geographial environment and so on. With the inreasing demand for satellite ommuniations, and the redution of the ost of ommuniation satellite users, the designers of the ommuniation satellite have taken many measures to meet these requirements. Multiple-beam antenna, as an important part of the satellite ommuniation system, has been widely onerned in the field of engineering and aademia. Multiple-hannel reeiver is an important part of multiple-beam antenna system [1]. It makes the satellite multiple-beam system to inrease the potential soure of nonlinear signal. So the study and orretion of the error of multiple hannels is one of the key tehniques of the multiple-beam antenna used in satellites. In order to ahieve reliable transmission of information, system designers must suffiiently know the possible interferene in detail in the ommuniation link and adjust the system margin and take the orresponding orretion tehnique in the planning stage, in the ase of whih the information transmission system an be designed to be reliable and superior performane []. Therefore, it is highly signifiant for the study and design of the satellite ommuniation system to have a researh on the nonlinear signal of the satellite multiple-beam antenna. For satellite multiple-beam ommuniation system, hannel mismath is an important fator whih restrits the transmission power and transmission effiieny [3]. James proposed the influene of hannel mismath on the multiple beam antenna in 1984. The influene of the amplitude and phase error of the signal to the main performane index of the array antenna is qualitatively disussed through theoretial analysis [4]. In fat, there are many kinds of distribution of the amplitude and phase error of the multiple-hannel reeiver for different hannel environments in the satellite ommuniation system, suh as Rayleigh distribution, normal distribution, et [5]. And different distribution has different effets on the system, whereas most of the present studies assume that the amplitude of the phase error is uniformly distributed, whih leads to the onlusion that the range of appliation is limited. There is no relevant researh to quantitatively analyze the range of amplitude and phase errors that an be tolerated by a ertain environment when appliable for designing the satellite ommuniation link. This paper mainly studies the performane of the multiple-beam 64
antenna satellite reeiving system at the ondition of the hannel mismath, in whih ase a onlusion has been drawn to show the effet of the hannel mismath on the system. The priniple and harateristis of the satellite multiple-beam antenna are analyzed in the next setion. Basi Priniple of Satellite Multiple-beam Antenna System Multiple-beam antenna is one that uses the same aperture to produe a number of different diretional beams [6] [7]. At present, multiple-beam antenna onfigured on the satellite has beome a key tehnology to improve the performane of the satellite ommuniation and redue the ost of the system. The effet of the amplitude and phase errors of the hannels on the performane of the satellite system is the big problem to be onsidered when multiple-beam antenna is used in the pratial appliation [8]. The priniple and the statistial harateristis of the satellite multiple-beam antenna are analyzed in detail in this setion. And we further study the effet of amplitude and phase errors on the antenna system. The satellite multiple-beam reeiving antenna as shown in the Fig. 1 omprises array reeiving antennas, multiple-hannel parallel reeivers, A/D onverters, digital down onverters, beamforming units and beamforming ontrollers [9]. The front antenna array is omposed of two-dimensional array whih ontains many antenna elements. The super-heterodyne method is generally applied in the reeiver. And the reeiver an realize down-onversion proessing, filtering and amplifying the array signal. O Figure 1. Struture of multiple-beam reeiving antenna system. Figure. Planar array of M N grid and its spae alloating relation. The antenna reeives the RF signal and transmits it into the reeiving hannel. And then the signal beomes the IF signal or the baseband signal. After AD sampling, the analog signal is onverted into digital signal whih is sent to the digital beam forming devie for proessing then. Finally the baseband digital beam signal is output by the system [1]. Planar array an be used to ontrol the beam in two-dimensional spae. A basi planar array of M N is showed in Fig.. The planar array onsisting of a total of M N elements is in the XOY plane. The array element spaing is d x and d y respetively and is the working wavelength. The diretion of the target is desribed with (, ). If the elements in the array are non-diretional, the lobe pattern of the array antenna without errors an be given by the equation (1) below [11]. E ( u, v) M1N1 jiu ( kv) aike (1) i k Where a ik is the weighted oeffiient of the array amplitude, determined by the distribution of the lobed shape namely by the required referene urrent u kd (sin os sin os ) and vkd (sin sin sin sin ). And k / y B B and that, B B x B B represents main lobe diretion. In general, there are errors in both the amplitude and phase of the array antenna. In the multiple-beam antenna system, the amplitude and phase errors have a great impat on the antenna 65
gain. If the amplitude error and phase error are independent random variables, lobe pattern with errors an be written as below. im1kn1 jiu ( kv ) ik ae ik () i k ik Euv (, ) (1 ) Where is the amplitude error and is the phase error between the two array elements, and that they both follow the normal random distribution with the mean value of zero. Main performane index of multiple-beam system are antenna gain, average of the beamwidth and so on. And the antenna gain is mainly disussed in this paper. In the ideal ase, the diretional gain of the antenna an be expressed as below [1]. G 4 P(,)/ P( u, v)sindd The antenna gain with errors an be approximately desribed as (3) 4 (,)/ (, )sin /(1 A ) (4) G P P u v d d G Where is the variane of the amplitude error and that A is the variane of the phase error. From the formula (4), it an be onluded that the amplitude and phase errors have a great impat on the antenna gain. In the next setion we will analyze the influene of the hannel mismath on the satellite ommuniation system. 3 Analysis on The Influene of The Channel Mismath on The Satellite Communiation System Effet of the hannel mismath on the satellite ommuniation system will be disussed below in detail. If the probability of eah symbol is equal, we set the symbol that the signal soure sends is un ( ) under the DQPSK modulation mode. Then un ( ) an be desribed as the following expression. un ( ) [ a, a1, a, a3] (5) Where n, T, T,..., i,1,,3 and 1/T is the Signal rate. And we an obtain that Pun [ ( )] a i.5. The output ( ) u n a n, b n with a two-bit form, un of DQPSK signal is expressed as where an and k,1,,. With a hypothesis that b n satisfy the following formula that E[ a( n) a( nk)] E[ b( n) b( nk)], P T a retangular funtion (unit pulse), the output of modulation an be expressed as the formula (6). (6) n n G t osw t is the St () A anpt ( ) ( nt)os wta bnpt ( ) ( nt)sinwt w is the arrier frequeny and A is the gain fator. Supposing that Where impulse response of the transmitting-end bandlimited filter and g( t ) is the impulse response of the orresponding low pass filter, the output of the filter in the N-th signal time interval an be desribed as below. Su( t) Aanht ( ) ( nt)os wt Abnhn ( ) ( nt)sinwt A aiht () ( it)os wt A btht () ( it)sinwt in Where the previous two items are the signals, the latter two items are inter-symbol interferene and ht gt pt. Due to the noise interferene with zero mean and variane in the uplink, the expression of the reeived signal is desribed as the equation below. S ( t) S ( t) n ( t)os w t n ( t)sin w t r( t)os[ w t 1 ( t)] (8) u u u us in (7) 66
Where nn1 r( t) r t n t r t n t 1/ {[ ( ) u( )] [ s ( ) us ( )] }, N 1 rs ( t) nus ( t) A bnht ( ) ( nt) and 1( t) tan. And Where u r ( t) n ( t) u r t A a n h t nt, rs () t N ( ) ( ) ( ) nn1 n t and n us t are in-phase and quadrature omponents of the noise in the uplink. N 1 and N are both the memory moments of send filter. Assuming that signal and noise are not related, the ovariane matrix of the reeived signal is * expressed as R ESwS [ ( ) ( w)] R n I. The atual array antenna system inluding the high frequeny amplifier, the mixer, demodulation and other analog iruits has a ertain bandwidth performane. Using the horizontal filter to simulate the frequeny response of the hannel, the L jwmt transfer funtion of the N-th hannel an be expressed as h ( w) a e, Where T is delay time of the tap. am anm( m,1,..., L)( n 1,,...,M) when the frequeny harateristis of the M hannels are onsistent [13]. Then we an obtain that hw ( ) h1 ( w)... hm ( w). In order to desribe the frequeny harateristis of the atual system hannel, we add the random disturbane and of the amplitude and phase to filter oeffiient a nm. The transfer funtion of the N-th hannel filter an be obtained as the equation (9) at the ondition of the hannel mismath. n m L j nm jwmt h n( w) anm(1 nm) e (9) m Assuming that the signal that eah hannel reeives keeps independent from eah other and the mean value is zero, and that the amplitude and phase perturbation of different hannels and the positions of different delay line on the same hannel is independent, the output signal of the array is ~ ~ desribed as the equation S ( w) S( w) H ( w). The vetor expression of the filter transfer funtion under the ondition of hannel mismath is showed as below. H ~ w h ~ w h ~ w h ~ ( w)] T ( ) [ 1( ), ( ),..., M (1) With the assumption that R is the ovariane of the output signal of the array when the hannels are mathed, the statistial desription of the effet of hannel mismath on ovariane matrix is showed as the equation (11). R ESwS [ ( ) ( w)] (1 ) R ( ) I (11) nm * e n Where is the variane of the amplitude perturbations and e is the variane of the phase perturbations. By solving the harateristi equation in the perturbation ase it an be proved that in the statistial sense, the hannel mismath does not hange the noise spae, but only hanges both the value of the eigenvalues and the model of the feature vetor instead, whih thus results in the distortion of the amplitude and phase of the reeived signal. Then the signals through demodulation will produe bit error. The degree of bit error is hanging with the variation of hannel mismath. 4 Numeral Results and Disussions In this setion, the performane of the array antenna maximum gain is simulated both in the perfet ondition and under the ondition of hannel mismath based on the disussion of setion 3. In this paper, a half wavelength dipole antenna of 8 elements uniform linear array is used for the simulation. The spaing between array adjaent ells is half of a wavelength and all array elements are under the ondition of onstant amplitude and in-phase. The maximum gain mean of array without oupling is hanging with the hange of hannel mismath as shown in Fig. 3. 67
Figure 3. The influene of hannel mismath on the mean of the array maximum gain without oupling. Figure 4. The influene of hannel mismath on the variane of the array maximum gain without oupling. From the Fig. 3, it an be onluded that the mean value of the maximum gain of the array is dereasing with the inrease of phase shift. However, there is a slight inrease in the variane of the maximum gain of the array with the phase shift rising as shown in the Fig. 4. In addition, the variane of the maximum gain is signifiantly inreasing with the rise of mismath-hannel amplitude variety. Based on the above simulations, the variane of maximum gain is less than 1dB for the ideal array without oupling in the ondition that the phase shift is less than 35 and the amplitude variety is less than db. And then the mean value of the maximum gain is more than 17dB. In the antenna array, the mutual oupling effet, whih an have a great influene on the amplitude and phase of the array, between the array elements is aused by that the array element spaing is too small. The mean and the variane of array maximum gain with oupling are hanging with the hange of hannel mismath as shown in Fig. 5 and Fig. 6. 33.5 33 Amplitude variety=3db Amplitude variety=db Amplitude variety=1db 3.5 Amplitude variety=3db Amplitude variety=db Amplitude variety=1db Mean of the maximum gain (db) 3.5 3 31.5 31 Mean of the maximum gain (db) 1.5 1 3.5.5 3 1 3 4 5 6 7 8 9 1 Phase shift ( o ) Figure 5. The influene of hannel mismath on the mean of the array maximum gain. 1 3 4 5 6 7 8 9 1 Phase shift ( o ) Figure 6. The influene of hannel mismath on the variane of the array maximum gain. From the Fig. 5, it an be seen that the mean of the array maximum gain is dereasing with the inrease of the phase shift when there is oupling between the array elements. the mean hanging range of the maximum gain is also inreasing with the rise of mismath-hannel amplitude variety. And the influene of hannel mismath on the variane of the array maximum gain for the array of oupling is the just same as the arrays without oupling as shown in the Fig. 6. Based on the above simulations, the variane of maximum gain is less than 1dB for the array with oupling when the phase shift is less than 3 and the amplitude variety is less than db, and then the mean value of the maximum gain is more than 33dB. Based on the analysis above, it an be onluded that for both the ideal array and the array of oupling the greater the degree of hannel mismath is, the bigger the error of the maximum gain is. 68
The mean of the gain dereases with the inrease of the phase error, with whih the variane of the gain rises whereas. The influene of hannel mismath is greater on the array of oupling than on the ideal array. 1 1-1 BER 1-1 -3 A=dB,P= o A=.4dB,P=6 o A=.8dB,P=1 o A=1.dB,P=18 o A=1.6dB,P=4 o A=.dB,P=3 o 1-4 3 4 5 6 7 8 9 1 11 1 SNR(dB) Figure 7. The urves of SNR to BER under different degrees of the hannel mismath. At last, this paper has measured the bit error rate (BER) performane with the Monte-Carlo method based on the ADS simulation platform. And we have established the whole ommuniation system on ADS platform model. Based on the results above, model parameters of hannel mismath is set to be that amplitude variety A ranges from to db and phase shift $P$ ranges from to 3. The relationship between signal to noise ratio (SNR) and BER at the ondition of different degrees of the hannel mismath is shown in the Fig. 7. It an be onluded that the SNR is lose to 1dB when the BER is 1 3 and that the demodulation threshold of the system is also rising with the degree of the hannel mismath inreasing. In the ase of hannel mismath, the SNR of the system is inreased by db in order to guarantee that the system BER is in the speified range. Hene we an see that there are real effets of the hannel mismath on the demodulation threshold in the system. 5 Conlusions This paper has introdued some basi priniple of satellite multiple-beam antenna system and analyzed the statistial desription of the ovariane of the ombined signal in the ondition of hannel mismath, where the modulation is DQPSK. Based on the analysis, the influene of the hannel mismath on the satellite multiple-beam antenna system has been disussed and simulated. What's more, the BER to SNR urves have been given to evaluate the system threshold. From the simulation results, it an be onluded that the variane of maximum gain is less than 1dB when the phase shift is less than 3 and the amplitude variety is less than db, in whih ase the SNR of the system is inreased by db in order to guarantee the BER performane. Finally, the data and urves obtained from this paper an provide a referene for designing the satellite system and also have a ertain pratial appliation value in engineering. Aknowledgment The authors would like to thank the National Natural Siene Foundation of China (611115) for the support. 69
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