V. Zaharov, F. Casco, M. Gutierrez

Departamento de Ingenieria Electrica, Universidad Autonoma  Metropolitana - Iztapalapa,

Mexico D.F., MEXICO

Received February 05, 2001



Two different beamforming approaches in space division multiple access (SDMA) for mobile satellite communications: switched-beam antennas and adaptive array antenna systems  are considered. The algorithm that meets both the  low computational complexity and high convergence requirements in the adaptive array antenna system of SDMA are developed. The hardware implementation of adaptive algorithm is considered as well.




In the satellite communication systems , as a rule, many users are active in the same time. Since resources of the systems (the transmitting power, the bandwidth) are limited, it is advisable to use the channels with complete charge i.g. to create the multiple access to channel. This generates a problem of summation and separation of signals in the transmission and reception parts respectively. Deciding of this problem consists in the development of orthogonal channels of transmission in order to divide signals from various users unambiguously on reception part.  Currently the methods of multiple access widely use so as time division multiple access (TDMA), frequency division multiple access (FDMA) and code division multiple access (CDMA), as well as their combination [1,2,3].


The significant factor in the performance of multiple access in a satellite communications system is interference. It causes cross-talk, missed or dropped calls, and upsets customers. Most importantly, interference limits traffic-carrying capacity from the finite RF spectrum. Interference can come from another users, other cell sites operating on the same frequency, or out-of-band RF energy leaking into the allocated spectrum. The most usual types of interference are co-channel interference and adjacent channel interference. Co-channel interference is caused by transmissions from non-adjacent cells using the same set of frequencies, where there is minimal physical separation from neighboring cells using the same frequencies. Adjacent channel interference is caused by RF leakage on the subscriber's channel from a neighboring cell using an adjacent frequency. This can occur when the user's signal is much weaker than that of the adjacent channel user.  Signal to interference ratio (SIR) is an important indicator of call quality; it is a measure of the ratio between the mobile phone signal (the carrier signal) and an interfering signal. A higher SIR ratio means increasing overall system capacity.


Taking into account, what in the systems of satellite communications every user has own unique space position, this fact maybe used for the separation of channels in the space and as consequence to increase SIR ratio. Such method is named Space Division Multiple Access (SDMA) [3]. More perspective from the point of view the realizations of systems SDMA is applying of smart antenna array with different level of intelligence consisting from the antenna array and digital processor. Since, the frequency of transmission for satellite communications systems enough high (mostly 6 or 14 GHz), the dimensions of array placed on  orbit commensurable with dimensions parabolic antenna, what is necessary condition to put of such systems in orbit. Applying of systems SDMA the most perspective for satellite communications systems for low (till 1500 km) and middle orbits

(till 10000 km), when the signals of users achieve the satellite antenna under different angles (±22 degrees for the middle orbits). In this instance, ground level maybe split into the zones of service determined by beam pattern lobes in different directions, as shown on figure1.

There are two different beamforming approaches in SDMA for satellite communications: one (Switched-Beam Antennas) is to track each subscriber of a given cell with an individual beam pattern as the target subscriber moves within the cell, and the other (Adaptive Array Antenna Systems) is to select one beam pattern for each subscriber out of a number of preset fixed beam patterns depending on the location of the subscriber.


The work purpose is the description of the SDMA principles in satellite communication systems and development of effective adaptive algorithm with low cost implementation for digital processor.




It is possible, using array antennas, to create a group of overlapping beams that together result in omnidirectional coverage. It is the simplest technique, and comprises only a basic switching function between separate directive antennas or predefined beams of an array. Beam-switching algorithms and RF signal-processing software are incorporated in smart antenna designs. For each call, software algorithms determine the beams that maintain the highest quality signal and the system continuously updates beam selection, ensuring that customers get optimal quality for the duration of their call.  One might design overlapping beam patterns pointing in slightly different directions similar to the ones shown in figure 1.

Fig.1  The beam patterns for the cover of the earth surface


Every so often, the system scans the outputs of each beam and selects the beam with the largest output power. The black cells in figure1 reuse the frequencies currently assigned to the mobile, so they are potential sources of interference. The use of a narrow beam reduces the number of interfering sources 'seen' at the base station. As the mobile moves, the smart antenna system continuously monitors the signal quality to determine when a particular beam should be selected.


For  switched-beam antenna we shall consider two-dimensional antenna array with Nxelementsin plane x and Nyelements in plane y with distance betweenelements dx and dy accordingly. The expression for the multibeam antenna array we present in the form [4]




where ;  and  accordingly angle of elevation  and the azimuth of arriving signal which are limited by values  ; ,  are some constants determining phase shifts in planes x and y, are the patterns of linear adaptive arrays in corresponding planes.


The necessary condition of the signals which coming from various directions to be orthogonal is

 . In this case , , , ,  and we obtain orthogonal spread pattern with   beams in the plane x è  beams in the plane  y  in which maximum each of beam coincides with zeroes other. Hereinafter without loss of generality accept . The resulting pattern of multibeam antenna array we present in the form                           


,        (2)

where for the middle orbits 


Thus  the satellite communication system SDMA which using switched-beam antenna  present in the form of the orthogonal beamforming scheme.  When the signal ui(t) from i-th users with direction of and  is arrived of antenna array input,  the output signal of the beamforming we present as


                                    .                        (3)


In the case when L users are active in the same time the eq.(3) we rewrite  in the matrix form


                                                                   ,                                                              (4)

where  is resulting multibeam pattern,


, ,  is an output signal of beamforming, Xi is N dimensional column vector, Ò is transpose symbol.


The high quality signal (HQS) for the switching beam technique can be determined as follows




Switched-beam antennas are normally used only for reception of signals since there can be ambiguity in the system’s perception of the location of the received signal. Switched-beam antennas gives the best performance, usually in terms of received power, but also suppress interference arriving from directions away from the active beam’s center, because of the higher directivity compared to a conventional antenna, some gain is achieved. In high-interference areas, switched-beam antennas are further limited since their pattern is fixed  and they lack the ability to adaptively reject interference. Such an antenna will be easier to implement in existing cell structures than the more sophisticated adaptive arrays, but it gives a limited improvement.




Adaptive array antenna systems continually monitor their coverage areas, attempting to adapt to their changing radio environment, which consists of (often mobile) users and interferers. In the simplest scenario - that of a single user and no interferers - the system adapts to the user’s motion

by providing an effective antenna pattern that follows the user, always providing maximum gain in the user’s direction. The principle of SDMA with adaptive antenna application is quite different from the beam-forming approaches described above (figure 2


Fig.2  The principle of SDMA with adaptive antenna application


The processing of events occurs in SDMA adaptive array antenna systems could be presented as a  following sequence:

·        "Snapshot", or sample, is taken of the signals coming from all of the antenna elements, converted into digital form, and stored in memory.

·        The SDMA digital processor analyzes the sample to estimate of the radio environment, identifying users and interferers and their locations.

·        The processor calculates the combining strategy for the antenna signals that optimally recovers the users signals.  With this strategy, each user’s signal is received with as much gain as possible and with the other users’ and interferers’ signals rejected as much as possible.

·        An analogous calculation is done to allow spatially selective transmission from the array. Each user’s signal is now effectively delivered through a separate spatial communications channel.

·        The system now has the ability to both transmit and receive information on each of the spatial channels making them two-way channels.


As result, the SDMA adaptive array antenna system can create a number of two-way spatial channels on a single conventional channel, be it frequency, time, or code. Each of these spatial channels enjoys the full gain and interference rejection capabilities of the array. In theory, an array with m elements can support m spatial channels per conventional channel. In practice, the number is somewhat less because take place the received multipath signals which can be combined to direct received signals. In addition, by using special algorithms and space diversity techniques, the radiation pattern can be adapted to receive multipath signals which can be combined. These techniques will maximize the signal to interference ratio (SIR) (or signal to interference and noise ratio (SINR)).


The more detailed benefits of an SDMA system include the following:

  • The number of cells required to cover a given area can be substantially reduced.
  • Interference from other systems and from users in other cells is significantly reduced.
  • The destructive effects of multipath signals – copies of the desired signal that have arrived at the antenna after bouncing from objects between the signal source and the antenna — can often be mitigated.
  • Channel reuse patterns of the systems can be significantly tighter because the average interference resulting from co-channel signals in other cells is markedly reduced .
  • Separate spatial channels can be created in each cell on the same conventional channel. In other words, intra-cell reuse of conventional channels is possible.
  • SDMA station radiates much less total power than a conventional station. One result is a reduction in network-wide RF pollution. Another is a reduction in power amplifier size.
  • The direction of each spatial channel is known and can be used to accurately establish the position of the signal source.
  • SDMA is compatible with almost any modulation method, bandwidth, or frequency band including  GSM, PHP, DECT, IS-54, IS-95, and other formats. SDMA can be implemented with a broad range of array geometry and antenna types.


Without loosing of generality we will consider only one dimension array but obtained results can be easy spread on two dimension case  using technique presented in [5]. The main parts of smart antenna base station with interchannel signal processing are show in figure3.      


                       Fig 3.  Block diagram of  interchannel  processing in smart antenna  base station


 It consists  L elements array,  Direction of Arrival (DOA) matrixes, tracking unit (R-1) and weighting matrix (W).  We present the matrix of DOA as N row of the steering vectors


                                                             ,                                        (6)


where , , is i-th reference angle.

are element space and wave length respectively, T is symbol of transpose.

When in input of array are affected  signals from M users then the signal at the input of L antenna elements  is given by

                                                                                               ,                                                    (7)


where is signal from i-th  user which satisfy the "narrowband assumption",  ,  is angle of i-th user arrival signal, n(t) is zero-mean thermal noise present in the receiver, Pi  is the power of the i-th user signal.

The output signal after DOA’s matrix  when  is


                                                  ,                                                   (8)


where  ,

~  is conjugate and transpose symbol.


We will consider the effectiveness of the adaptive system using criteria of signal interference ration maximization (MSIR) by suppressing the signal from interference sources. In case of SIR maximization is to be used, the optimum weight vector W  is given by


                                                                 ,                                                               (9)


where  is N´N correlation matrix of the total received signal, .

From eq.(9) follows that weigh vector of i-th user which maximize SIR relation  in i-th  channel of adaptive version in comparison with no adaptive



can be obtained as

                                                 .                                                    (11)


From (11) follows that


                                                                   ,                                                            (12)


where P only scale factor for each channel and can be omitted .

The output vector from N channels


                                                               ,                                                    (13)


where ,  and  x is input vector after DOA matrix




The output signal at  the i-th user channel is given by


                                                                     .                                                            (15)




When one use k sample size  for estimation of weight vector then formula (12) can be rewritten as



where  is maximum likelihood estimation of matrix R.

In many of real scenario the input data are nonstationary. We can present this data as a sliding windows with k vectors, each for N elements and denote these data as a matrix X


where       , i = 1,2,...,k is column vector of i-th sample ("snapshot").

Presentation of data as shown in eq.(17) permits apply recursive adaptive algorithm for weight vector modification.  Consider RLS algorithm given by one rank matrix modification formula. For this purpose the matrix Rk  in (16) we  write as follows





where  is forgetting factor,  ,

We can rewrite (18) as



Introducing  of matrix of  coefficients C




we can rewrite  the  matrix X as a weighted matrix by matrix C


.     (21)


It is well known [6],[7] that  is computed without matrix division using the matrix inversion lemma.                                      





Even with the powerful signal processor available today it is a very challenging task to perform  eq.(22) in real time because the computational complexity of this operation O(N2). The base operation of this algorithm is matrix for vector multiplication, that sufficiently large for real time processing.




Evidently that adaptive algorithm must be implemented with number of  contradictory demands. This is, first of all, high convergence to optimum solution, since in low convergence will be seen the high level of interference at the beginning part of connection with subscriber. In the second place, the adaptive algorithm preferably must to have low hardware implementation, since adaptive processor  have to put in satellite. The first demand dictates applying of the direct matrix inverse algorithms of adaptation, and second recursive implementation of such algorithms.

The convergence of recursive direct matrix inverse algorithms of adaptation in detail is investigated in [4], [6].


We present recursive least square (RLS) vector operations efficient algorithms for real time weights optimizing and signal tracking that apply eq.(22) with computational complexity  O(N).   Applying of this algorithm for tracking allows decrease its complexity of hardware implementation.


For i = 1,2,...,k the output vector can be obtain as following




where i = 1,2,...,k  is output of channels in i-th moment of time .

Making substitution                                   


eq.(23) can be rewrite  as


where  is scalar.

Inverse of matrix then we present as



Then taking into account eq.(26) we rewrite  eq.(24)






The algorithm of output signal obtaining Yi in the i-th moment of time we present in the next stage

1.      Initialization

        ,    .

2.    for i = 1,2,...,k-1              (i is currently sample number )

(training part)  

                  (processing part)


3.    for  i = k ,k+1, k+2,...

(training part)

              (processing part)

          for j = 2,...,k

                     (shift in memory that memorize vectors z )


In the stage 1 is being put constant  and nulling the memory that stores the vectors z.

Then in stage 2 is being filled out  the memory  by no zero elements. The stage 3 is processing  of the data in real time. At that, the new vector  obtained after processing part have to shift in the place of , the vectorin the place of and so on.




The architecture of processor has shown en figure 4. As follows from this figure the processor consist  k identical blocks that presented in figure 5 (k-1 blocks  for training procedure and 1 block for sample processing).  As follows from figures 4 and 5 it needs approximately 2Nk multipliers and adders to hardware implementation of processor.

Fig 4. Architecture of processor

Fig 5. Processor’s base block architecture





The sample scenario was created. The antenna array consists L=20 linearly arranged elements with spacing. Number of channels N=8. Number of users M=8. Each sources was simulated as Gaussian distributed with SNR and azimuth location that have shown in table 1. Algorithm was applied with forgetting factor . Convergence of algorithm was evaluated as number of samples when parameter Gi no worse then 3 db in comparison with optimum solution.  200 independent simulations have been averaged.


Table 1.





Convergence (number of samples)

Proposed algorithm

Conventional algorithm










































The table shown that convergence of proposed algorithm is no worse then 5 samples in comparison with conventional  algorithm, but how follows from part above proposed algorithm have advantage en computational complexity and hardware implementation.




Two approaches for SDMA satellite communication systems are presented: switch beam and adaptive technique. Tracking adaptive algorithm and its hardware implementation for computing the optimum weight vector in accordance with MSIR criterion for adaptive antenna station developed. The proposed algorithm has a linear complexity because one uses only vector operations and can be easy implemented in software and hardware.



1.      Sklar B. Digital Communications: Fundamentals and Applications.- Prentice Hall, New Jersey, 1988.

2.   Tomasi W. Electronic Communications Systems Fundamentals Through Advanced.- Prentice Hall, New Jersey, 1996.

3.   Liberti J.C., Rappaport T.S., Smart Antennas for Wireless Communications: IS-95 and Third-Generation CDMA Applications. Prentice Hall, NJ, 1999.

4.   MonzingoR.A., Miller W. Introduction to Adaptive Arrays. - John Wiley & Sons Inc, New York, 1980.

5.   Dudgeon D.E., Mensereau R.M. Multidimensional Digital signal processing.- Prentice Hall, Englewood Cliffs, 1984.

6.   Haykin S. "Adaptive Filter Theory", Prentice Hall, NJ, 1996.

7.   Golub G.H., Van Loan C. F. "Matrix Computations". 2nd edition, The Johns Hopkins University Press, North Oxford   Academic Publishing Co., Baltimore and London, 1989.

V. Zaharov, email: f_zvv@rambler.ru, F. Casco, M. Gutierrez
Departamento de Ingenieria Electrica, Universidad Autonoma  Metropolitana - Iztapalapa, Mexico D.F., MEXICO