Volume 15, no. 2Pages 118 - 124

Analysis of the Influence of the Lagrange Multiplier on the Operation of the Algorithm for Estimating the Signal Parameters Under a Priori Uncertainty

N.E. Poborchaya, E.M. Lobov
The paper considers a recurrent regularizing algorithm for joint estimation of distortions of a M-ary quadrature amplitude modulation (M-QAM) signal obtained in a direct conversion receiver path. The algorithm is synthesized using a modified least squares method in the form of Tikhonov's functional under conditions of a priori uncertainty about the laws of noise distribution. The resulting procedure can work both on the test sequence and on information symbols after the detection procedure. We analyze the influence of the Lagrange multiplier on the accuracy of the estimation procedure and on the complexity of the algorithm. It is shown that, with the same accuracy, the regularizing algorithm requires significantly fewer iterations than the procedure without the Lagrange multiplier, and therefore has a lower computational complexity.
Full text
regularizing algorithm; a priori uncertainty; modified least squares method; direct transform receiver.
1. Hsu C.-J., Cheng R., Sheen W.-H. Sheen Joint Least Squares Estimation of Frequency, DC Offset, I-Q Imbalance, and Channel in MIMO Receivers. IEEE Transactions on Vehicular Technology, 2009, vol. 58, no. 5, pp. 2201-2213. DOI: 10.1109/TVT.2008.2005989
2. Weikert O. Joint Estimation of Carrier and Sampling Frequency Offset, Phase Noise, IQ Offset and MIMO Channel for LTE Advanced UL MIMO. IEEE 14th Workshop on Signal Processing Advances in Wireless Communications, 2013, Darmstadt, pp. 520-524. DOI: 10.1109/SPAWC.2013.6612104.
3. Tikhonov A.N., Leonov A.S., Yagola A.G. Nelineynye nekorrektnye zadachi [Nonlinear Incorrect Tasks]. Moskva, Nauka Fizmatlit, 1995. (in Russian)
4. Bakushinskiy A.B., Kokurin M.Yu. [Iterative Stochastic Approximation Methods for Solving Irregular Nonlinear Operator Equations]. Computational Mathematics and Mathematical Physics, 2015, vol. 55, no. 10, pp. 1637-1645. (in Russian)
5. Golubev G.K. [Concentrations of Risks of Convex Combinations of Linear Estimates]. Problemy peredachi informatsii, 2016, vol. 52, no. 4, pp.31-48. (in Russian)
6. Poborchaya N.E. [Methods for Estimating the Parameters of a Random Signal in Conditions of a Priori Uncertainty]. Elektrosvyaz', 2010, no. 3, pp. 24-26. (in Russian)
7. Poborchaya N.E. Stationary Channel Factors and Signal Disturbances in a Direct Converter Receiver in a System with MIMO Joint Estimation Algorithm. Systems of Signal Synchronization, Generating and Processing in Telecommunications, Svetlogorsk, 2020. DOI: 10.1109/SYNCHROINFO49631.2020.9166068.