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S. A. Ageyev, K. K. Vasiliev OPTIMIZATION OF THE METHOD OF ADAPTIVE DECORRELATION OF RANDOM SEQUENCES



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S. A. Ageyev, K. K. Vasiliev OPTIMIZATION OF THE METHOD OF ADAPTIVE DECORRELATION OF RANDOM SEQUENCES

Many problems in which digital signal processing on the background of noise is used, have the simplest solutions when interference has the nature of white noise. If interference has time-space correlation properties different from the properties of white noise, pre-decorrelation of input observations is frequently used. The method of a whitening filter was suggested in the papers by V. A. Kotelnikov. Other approaches to the solution of this problem are based on using an inverted correlation matrix of observations. However, the known methods presuppose stationary nature of observations, and involve considerable computational costs. At the same time, in many applications such as radar and sonar, image processing, composite objects management, etc., there arises a problem of creation of relatively simple and effective real-time procedures of adaptive decorrelation of non-steady processes.

In this paper, this problem is solved on the basis of pseudo-gradient adaptation methods. As an application of the results obtained, the task of signal detection on the background of noise with an unknown correlation function is considered.

The research conducted has shown that the suggested adaptive decorrelation and detection algorithms have the efficiency, comparable with the potentially reachable one, and can be implemented in real time on the existing component base. The results obtained correspond to the conclusions shown in [1], where it is stated that the procedure of signal detection on the background of weakly correlated interference can be implemented without taking into account correlation links of interference.


References


  1. V. I. Tikhonov, N. K. Kulman. Non-Linear Filtration and Quasi-Coherent Signal Reception, Moscow, “Sovetskoye Radio” Publishers, 1975, 704 pages.


B. Huseynov, Kh. Babazadeh OPTIMIZATION PROBLEMS OF MOBILE CELLULAR COMMUNICATIONS

Fast development of mobile communications during last years brought all companies involved in this sphere of telecommunications to a problem of the most optimum mobile network construction. In this scope several problems arose before us.

Subscriber of a usual fixed telephone communication has to reach a network element wheras mobile subscriber is followed by the network. So in a given area we need to put network elements which are connected to a switching centre and all mobile subscribers in the area. These elements will be further reffered as base stations.

Base station disposition implicates the following:

Link to switching centre

Effect area (coverage)

Channel capacity

Each item supposes certain expenditures and thus requires solving an optimization problem. In the paper only base station capacity problems are considered. Items 1 and 3 are tasks not only for mobile networks but can be associated with any other network. However combining with item 2 we get exactly mobile communication task.

The general task was divided into subtasks and solved gradually. Initial steps were setting and solving of the following problems.

Let us be given n stations A i , i{1,…,n}. Let each station be provided ki channels, i{1,…,n} ki{p1,…,pq}.

Channel will be called free at the given moment of time if it is not associated at this moment with any subscriber. Otherwise it is busy.

Definition 1: Load L of a channel during period of time t is ratio of the time t1 during that the channel was busy to the whole time t

Definition 2: Load of channels during time is

w
here ti – busy time of i-th channel.

Definition 3: Load of a station during time t is the load of all channels at the station.

L is load during time T*)of station A i , i{1,…,n}. li is average load of one channel of the station A i, that is li =Li /ki , i{1,…,n}.

Definition 4: If all channels of the station A I are busy when a subscriber requests a channel then we will say that subscriber was rejected.

Let Ri be number of rejects on a station A i , i{1,…,n}

ri is average number of rejects on one channel of a station A i that is ri =Ri /ki , i{1,…,n}.

Task 1: K=ki channels should be distributed between A i stations so that


 li ljmin , i{1,…,n}.

Task 2: m additional channels are given. K+ m channels should be distributed between A i stations so that li = lj , i,j{1,…,n}.

Task 3: Now let also coordinates (xi, yi ) of A i station be given. A station should be added and the channels should be redistributed so that li = lj , i,j{1,…,n}.

Common channel number is considered K+ m. Define coordinates (xn+1, yn+1 ) of the station A n+1

Remark: it is necessary for all tasks that li max , ri min .



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