Efficient semi-blind estimation of multipath channel parameters via a delay decoupling optimization approach
Introduction
Multipath channel estimation is an issue of major importance in reliable wireless communications system design. Due to the multipath phenomenon in wireless applications, the introduced InterSymbol Interference (ISI) may cause a severe degradation in a system's performance. The problem is much more severe in high-rate applications, since, as the symbol rate becomes higher, the number of symbols spanned by a channel impulse response (CIR) with a certain delay spread is increased. Thus, an efficient and accurate estimation of the CIR is highly desirable, in order to mitigate interference and achieve reliable data detection.
In many high-speed wireless applications, the propagation channel can be modeled as a specular channel consisting of a relatively small number of dominant rays [1], with each one being characterized by its time delay and attenuation factor. Then, provided that the transmitter and receiver filters are known [2], the channel estimation task is reduced to that of estimating the parameters of the multipath channel components, i.e., the time delays and the attenuation factors. Two are the main advantages of using such a parametric approach. First, the number of required data is reduced, resulting in a significant saving in complexity, processing delay and, possibly, in bandwidth. Second, the mean square channel estimation error is expected to be lower since a more parsimonious parameterization of the channel is adopted, compared to conventional CIR estimation.
In a wireless communication channel, bandwidth is a precious resource, therefore the need for training sequence reduction is imperative. Thus, conventional training based channel estimation methods are inappropriate, especially when the channel span is large as in high rate applications. On the other hand, blind channel estimation methods require a high number of data and have very often limited performance. In such cases semi-blind estimation techniques may be employed [3], [4], [5], [6]. The main trait of a semi-blind scheme is that a purely blind criterion is suitably modified so as to incorporate information from a short training sequence [3]. The performance of a semi-blind method, if properly designed, can be significantly improved against the corresponding blind method.
The estimation of a multipath channel using a parametric modeling has gained considerable attention in recent years. Blind [7], [8], [9] as well as training based [10], [11], [12] channel parametric estimation methods have been recently proposed. These methods either rely on preliminary estimates of the CIR [8], [10], [12] or directly estimate the parameters of the multipath channel components [7], [9]. Recently, parametric channel modeling has also been applied to channel estimation in multicarrier (OFDM) [14] and multiuser (CDMA) [15], [16] system design. In a blind context, an important implication of parametric channel modeling is that the channel overmodeling problem, which is inherent in second-order statistics blind identification algorithms, can be overcome [9]. That is, channel parameterization with respect to delays and attenuation factors, leads to consistent channel estimates even if the channel order is overestimated. However, such an improvement is traded off with a need to perform a computationally costly multidimensional search, the order of which equals the number of multipath components.
In this paper, we propose a novel semi-blind technique, which exploits the specular channel structure by incorporating the knowledge of the pulse shaping filter. By applying the well-known sub-channel response matching (SRM) criterion [18] to the problem at hand and after incorporating limited input information, we end up with a least squares (LS) problem, which is separable with respect to the unknown parameter sets, i.e. time delays and attenuation factors. Specifically, it is shown that the optimization problem can be separated to two different subproblems. One subproblem which is non-linear with respect to the time delays and another subproblem which is linear with respect to the attenuation parameters. After revealing the special structure of the non-linear problem, a computationally efficient linear search method for the estimation of the unknown time delays is developed. In the sequel, the Gauss–Newton (G–N) algorithm may be applied in order to further improve the accuracy of the estimated values. Finally, the attenuation parameters are estimated by solving a low-order linear LS problem. The new method is very simple to implement and achieves a lower channel estimation error compared to other related methods, e.g. [3], at a reasonable computational cost. A basic feature of the proposed technique is that, due to the special form of the non-linear cost function, a highly inefficient multidimensional search is avoided and a small number of simple linear searches is executed instead. Moreover, the new method offers the possibility of trading off performance to complexity in an easy manner and yields good estimates even in cases of closely spaced time delays. The performance of the new method has been justified theoretically and tested through extensive simulations. Some preliminary results of this work have been presented in [17].
The paper is organized as follows. In Section 2 the multipath channel model is defined and the problem is formulated. In Section 3 the new method is derived and in Section 4 an efficient version of the proposed method is described. Performance issues of the new semi-blind technique are briefly discussed in Section 5 and simulation results are provided in Section 6. Concluding remarks are presented in Section 7.
Section snippets
Channel model
In general, the CIR encountered in wireless communication systems has a form which varies significantly depending on several factors, such as physical environment, transmission rate, mobility etc. However a common trait in most cases, particularly in high-speed applications, is that the multipath channel tends to be of a discrete form (i.e., it consists of a number of dominant multipath components). More specifically, if the CIR is assumed to be time invariant within a small-scale time
Derivation of the algorithm
In this section an efficient method for estimating the multipath channel parameters is described, by exploiting the special form of the non-linear cost function given in (12). In particular, the cost function is shown to possess the following two properties. First, the optimization problem can be split up into two subproblems in terms of the delay and attenuation parameters, respectively. Second, the delays are shown to be decoupled from each other, allowing for their efficient estimation.
An alternative version of the DECP method
In this section it is shown that by further exploiting the form of , an alternative equivalent procedure can be developed for estimating in an even more efficient manner the delay parameters. Let us first define the following quantities:That is, is the th column of matrix and stands for its sub-matrix formed by columns through .
Based on these definitions, matrix given in (19) can be written as
Computational complexity
It can be easily shown that the two versions of the new method presented in Tables 1 and 2 (i.e., DECP and DECPa, respectively) are completely equivalent, in terms of performance, by assuming a perfect decoupling of the delay parameters. However, even in practical cases, where decoupling is not perfect, the two algorithms perform in a very similar manner. This has been verified by extensive simulations, some of which are presented in Section 6.
To compare the two algorithms in terms of
Simulation results
In this section, we investigate the performance of the new parametric estimation method under various conditions. The two versions of the new method (i.e., DECP and DECPa) are compared with the semi-blind SRM-based method presented in [3], in which the CIR is estimated in a non-parametric manner, using a linear combination of a blind and a non-blind cost function. As a comparison measure we have used the root-mean-square-error between actual and estimated CIRs, i.e.
Conclusion
In this paper, we have proposed a new semi-blind estimation algorithm that exploits the specular channel structure and a-priori knowledge of the pulse shaping filter. The main contribution of this work is the observation that the optimized cost function is almost decoupled with respect to the time delays, a fact which allows for efficient estimation of the delay parameters. The new method is very simple to implement, it works well even for closely-spaced multipath components and is quite robust
References (21)
- et al.
Semi-blind channel identification for individual data bursts in GSM wireless systems
Signal Process.
(2000) Wireless Communications Principles and Practice
(1996)Multipath channel identification based on partial system information
IEEE Trans. Signal Process.
(January 1997)- et al.
Channel identification using a combination of blind and nonblind methods
SPIE
(1995) - A. Gorokhov, Ph. Loubaton, Semi-blind second order identification of convolutive channels, in: Proceedings of the...
- E. de Carvalho, D. Slock, Deterministic quadratic semi-blind FIR multichannel estimation: Algorithms and performance,...
- et al.
Blind estimation of multipath channel parametersA modal analysis approach
IEEE Trans. Comm.
(August 1999) - et al.
Improved blind channel identification using a parametric approach
IEEE Comm. Lett.
(August 1998) - L. Perros-Meilhac, E. Moulines, K. Abed-Meraim, P. Chevalier, P. Duhamel, Blind identification of multipath channels: a...
- et al.
Estimation of multipath channel parameters in wireless communications
IEEE Trans. Signal Process.
(March 1998)
Cited by (7)
On cluster-based channel identification
2012, Procedia EngineeringA robust parametric technique for multipath channel estimation in the uplink of a DS-CDMA system
2006, Eurasip Journal on Wireless Communications and NetworkingPerformance analysis of least mean square and recursive least square channel estimation techniques under multipath fading environmental conditions
2017, 2017 4th International Conference on Advanced Computing and Communication Systems, ICACCS 2017Performance analysis of subspace based downlink channel estimation for W-CDMA systems using chaotic codes
2013, Wireless Personal CommunicationsQuasi-convexity of the asymptotic channel MSE in regularized semi blind estimation
2011, IEEE Transactions on Information TheoryComparison of different channel estimation algorithms from ITS perspective
2011, Proceedings - 2011 Annual IEEE India Conference: Engineering Sustainable Solutions, INDICON-2011