A subspace-based online calibration algorithm for an asynchronous CDMA-based antenna array☆
Introduction
Space–time processing techniques employing multiple antennas are used to increase spectrum efficiency and capacity for future cellular communications. For the downlink beamforming, which is one of the most fundamental space–time processing techniques, accurate channel estimation such as direction of arrivals (DOAs) and time delays is essential. Most high-resolution DOA estimation algorithms, however, require perfect knowledge of the array manifold, which is not feasible in practice. The gain and phase responses of a channel (or an antenna) vary according to temperature and humidity changes from day to day [10], and therefore online calibration is preferable in wireless cellular communications. Various array calibration methods with or without known source directions have been proposed [4], [5], [8], [9]. In [5], the direction-independent array gain and phase are estimated by using knowledge of the true field covariance at the sensor locations. In [4], one first estimates the DOAs with the unknown sensor parameters being set at their nominal values. These estimated DOAs are then used to estimate the unknown sensor parameters with an optimization technique. This two-step process continues iteratively until a certain convergence criterion is met. The other methods for the case where the DOAs are known have been studied in [8], [9].
The methods in [4], [5], [8], [9], however, require that the number of signal sources should be less than the number of antennas and are not applicable to direct-sequence code-division multiple access (CDMA) communication systems. Furthermore, deploying known signals at a known location may not be acceptable since it would increase multiple access interference and decrease the channel capacity as well.
To cope with this problem, we extend the calibration algorithm in [4] to an asynchronous CDMA-based antenna array by adopting the model in [3], [2]. The algorithm is based on the two-step procedure, one for estimating channel and the other for estimating the unknown array gain and phase, as was done in [4]. Our algorithm utilizes the code sequence of an arbitrarily chosen reference user and is applicable to the situation where the total number of signals is less than M times N, where M is the number of antennas and N is the processing gain of the code sequence. The algorithm, which is applicable to a non-linear array, does not require a priori knowledge of the channel information such as multi-path delays and DOAs of the signals. The proposed algorithm estimates the channel and the unknown array (complex) gain constants by exploiting the eigenstructure of received spatial and temporal signals. To verify the performance of the algorithm, we use synthetic data as well as field data measured through a custom-built W-CDMA test bed.
Section snippets
Signal model
Assume M antenna elements and K users in a cell. Suppose that received continuous-time signals zm(t), (m=1,…,M) at the receiver front-end, are down-converted (by the IQ mixing at each antenna) to baseband and then converted to discrete-time signals by sampling the outputs of the integrator which integrates receiving signals over a subinterval Tq=Tc/Q where Tc is the chip duration and Q is the oversampling factor. The multipath channel and the receiver front-end are shown in Fig. 1.
An estimation algorithm for both channel and gain-phase parameters
The proposed algorithm is based on a two-step procedure. First, by minimizing a certain cost function J1 described below, we obtain the channel parameters such as DOAs and the impulse response . Next by using the obtained channel parameters, we find the calibration (complex gain) vector which minimizes a certain cost function J2, with respect to either one of the constraints belowwhere . The above two steps are iterated until the cost function J2 converges to
Computer simulation results
According to our simulation study, constraint (a) or constraint (b) in (1) gives a similar performance. Thus, we only present the result for the case of in this paper. We use a uniform circular array with six antennas separated by half a wavelength. We use random BPSK modulated data streams and the Gold codes with the processing gain of N=31. We assume that each of 15 users (K=15) produces two multi-path signals (Lk=2). For simplicity, we consider the azimuthal angle only. The DOAs of
Conclusions
We present an array calibration algorithm that can be used in an asynchronous CDMA system. The algorithm requires us to know the spreading code of an arbitrarily selected reference user only (which is already available at the base station). Computer simulation and experimental results with field data indicate that the proposed algorithm performs well even when a multiple access interference is present. At the cost of increased computational burden, the proposed algorithm estimates jointly the
References (10)
- et al.
Spatial signature estimation for uniform linear arrays with unknown receiver gains and phases
IEEE Trans. Signal Process.
(August 1999) - et al.
Subspace-based channel estimation for code division multiple access communication systems
IEEE Trans. Commun.
(August 1996) - M. Eric, S. Parkvall, M. Dukic, M. Obradovic, An algorithm for joint direction of arrival, time-delay and...
- B. Friedlander, A. Weiss, Eigenstructure methods for direction finding with sensor gain and phase uncertainties, Proc....
Estimation of sensor gain and phase
IEEE Trans. Signal Process.
(January 1994)
Cited by (0)
- ☆
This work was supported in part by the University Research Program of the Ministry of Information & Communication, by the Korea Science and Engineering Foundation managed through MICROS ERC, and by a contract from SK-Telecom.