**1. Introduction**

254 Wireless Communications and Networks – Recent Advances

[14] John G. Proakis, "Digital Communications", McGraw-Hill Companies, Inc and publishing house of electronics industry, China. ,fourth edition, pp.766 , 2001. [15] Guosong Li, "Research on channel estimation in wireless OFDM systems", Ph.D thesis,

University of Electronic Science and Technology of China, 2005.

[17] MAXIM Integrated Products, Datasheet of MAX2828/2829, 19-3455, rev0, Oct. 2004 [18] F. M. Gardner, "Interpolation in digital modems – Part I: Fundamentals," IEEE Trans.

[19] F. M. Gardner, "Interpolation in digital modems – Part II: Implementation and performance," IEEE Trans. Commun., vol. COM-41, pp. 998-1008, Jun. 1993. [20] F. M. Gardner, "A BPSK/QPSK timing-error detector for detector for sampled receivers," IEEE Trans. Commun., vol. COM-34, pp. 423-429, May. 1986.

[16] IEEE P802.11n/D1.0, March 2006.

Commun., vol. 41, pp. 501-507, Mar. 1993.

The combination of multiple-input multiple-output (MIMO) antennas and orthogonal frequency-division multiplexing (OFDM) can achieve a lower error rate and/or enable highcapacity wireless communication systems by flexibly exploiting diversity gain and/or the spatial multiplexing gains. Such systems, however, rely upon the knowledge of propagation channels. In many mobile communication systems, transmission is impaired by both delay and Doppler spreads [1]-[7]. In such cases, explicit incorporation of the time-varying characteristics of mobile wireless channel is called for.

The coefficients of a linearly time-varying (LTV) channel can be usually modeled as uncorrelated stationary random processes which are assumed to be low-pass, Gaussian, with zero mean (Rayleigh fading) or non-zero mean (Rician fading) depending on whether line-of-sight propagation is absent or present [1][6]. Recently, the basis expansion models, i.e. the truncated discrete Fourier basis (DFT) models, polynomial models and discrete prolate Spheroidal sequence models, have gained special attentions, especially for the situation that channel is caused by a few strong reflectors and path delays exhibit variations due to the kinematics of the mobiles [1]-[2] [5]-[6] [16] [25]-[28].

In conventional pilot-aided channel estimation approaches, MIMO channels can be effectively estimated by utilizing the time-division multiplexed (TDM) and (or) frequencydivision multiplexed (FDM) training sequences [5]-[7] [20]-[23] [25]. Although the channel estimates are in general reliable, extra bandwidth or time slot is required for transmitting known pilots. In recent years, an alternative approach, referred to as superimposed training (ST), has been extensively studied in [8]-[19] [26]-[28]. In the idea of ST, additional periodic training sequences are arithmetically added to information sequence in time- or frequencydomain. The advantage of the scheme is that there is no loss in information rate, and thus enables higher bandwidth efficiency. However, some useful power must inevitably be allocated to the pilots, and thus resulting in information signal-to-noise ratio (SNR) reduction. Meanwhile, the information sequences are viewed as interference to channel estimation since pilot symbols are superimposed at a low power to the information sequences at the transmitter. The existing ST-based channel estimations are mainly restricted to the case where the channel is linearly time-invariant (LTI), where the channel transfer function can be estimated by using first-order statistics [8]-[13] [17]-[18]. In the latest contributions, J. K. Tugnait [16] extended the conventional ST to time-varying environment where the LTV channels are modeled by complex exponential bases. For the issue of training power allocation, the optimal pilot power has been investigated by [24] for different taps of low-pass filter, and then, the optimization of ST power allocation for LTI channel is mathematically analyzed based on equalizer design [15] [19].

In this paper, a new ST-based channel estimator is proposed for OFDM/MIMO systems over LTV multipath fading channels. The main contributions are twofold. First, the LTV channel coefficients modeled by the truncated discrete Fourier bases (DFB), unlike the existing approaches [1]-[2] [5]-[6] [16], cover multiple OFDM symbols. Then, a two-step channel estimation approach is adopted for LTV channel estimation. Furthermore, a closedform expression of the estimation variance is derived, which provides a guideline for designing the superimposed pilot symbols. We demonstrate by analytical analysis that the estimation variance, unlike that of conventional ST-based schemes [8]-[19], approaches to a fixed lower-bound as the training length increases. Second, for wireless communication systems with a limited transmission power, unlike [10] where the issue of ST power allocation is derived by optimizing the SNR for equalizer design, we provide an optimal solution of ST power allocation with a different point of view by maximizing the lowerbound of channel capacity. Comparatively, the training power allocation scheme [10] can be otherwise considered as a special case compared with the proposed approach. In simulations presented in this paper, we compare the results of our approach with that of the FDM training approaches [5] as latter serves as a "benchmark" in related works. It is shown that the proposed algorithm outperforms that of FDM training, and yields higher transmission efficiency.

The rest of the paper is organized as follows. Section II presents the system and channel models. In Section III, we estimate the LTV channel coefficients with the proposed two-step channel estimation approach. In Section IV, we derive the closed-form expression of the channel estimation variances. Section V determines the optimal ratio of the ST power to the total transmission power by maximizing the lower-bound of channel capacity. Section VI reports on some simulation experiments in order to test the validity of theoretic results, and we conclude the paper with Section VII.

*Notation:* The letter *t* represents the time-domain variable and *k* is the frequency-domain variable. Bold letters denote the matrices and column-vectors, and the superscripts[ ]*<sup>T</sup>* and [ ]*<sup>H</sup>* represent the transpose and conjugate transpose operations, respectively. , [ ]*k t* denotes the (*k*, *t*) element of the specified matrix.
