Mobile Information Systems

Volume 2016 (2016), Article ID 3723862, 11 pages

http://dx.doi.org/10.1155/2016/3723862

## Iterative MIMO Detection and Channel Estimation Using Joint Superimposed and Pilot-Aided Training

^{1}Department of Electronics, Systems and IT, ITESO Jesuit University, 45604 Tlaquepaque, JAL, Mexico^{2}Department of Electrical Engineering, CINVESTAV-IPN, 45015 Zapopan, JAL, Mexico^{3}Department of Electronics and Communication, CUCEI-Guadalajara University, 44430 Guadalajara, JAL, Mexico^{4}Department of Electrical and Electronic Engineering, ITSON, 85130 Ciudad Obregon, SON, Mexico

Received 10 September 2015; Revised 19 January 2016; Accepted 25 February 2016

Academic Editor: Yuh-Shyan Chen

Copyright © 2016 Omar Longoria-Gandara et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a novel iterative detection and channel estimation scheme that combines the effort of superimposed training (ST) and pilot-aided training (PAT) for multiple-input multiple-output (MIMO) flat fading channels. The proposed method, hereafter known as joint mean removal ST and PAT (MRST-PAT), implements an iterative detection and channel estimation that achieves the performance of data-dependent ST (DDST) algorithm, with the difference that the data arithmetic cyclic mean is estimated and removed from data at the receiver’s end. It is demonstrated that this iterative and cooperative detection and channel estimator algorithm surpasses the effects of data detection identifiability condition that DDST has shown when higher orders of modulation are used. Theoretical performance of the MRST-PAT scheme is provided and corroborated by numerical simulations. In addition, the performance comparison between the proposed method and different MIMO channel estimation techniques is analyzed. The joint effort between ST and PAT shows that MRST-PAT is a solid candidate in communications systems for multiamplitude constellations in Rayleigh fading channels, while achieving high-throughput data rates with manageable complexity and bit-error rate (BER) as a figure of merit.

#### 1. Introduction

Estimation theory deals with the basic problem of inferring a set of required statistical parameters of a random experiment based on the observation of its outcome. It is assumed that it is possible to produce an effect in the experiment by means of a controlled excitation signal. This approach is normally adopted in practical communications systems where channel estimation is an essential part of standard receiver designs [1] and carried out by transmitting training symbols commonly known as pilot symbols [2]. In this case, the random experiment can be seen as an unknown system that is identified by observing how the system reacts to the applied excitation or training signal.

Traditionally, the most widely used channel estimation technique is pilot-assisted training where the pilots are multiplexed in time or frequency. This is widely known in the literature as pilot symbol assisted modulation (PSAM) [2] and is denominated as pilot-assisted transmission (PAT) [3]. This scheme employs a nonrandom training pilot sequence known* a priori* by the transmitter and the receiver. The training pilots are periodically inserted into certain positions in the time (frequency) with the information-bearing symbols, before modulation and transmission. Using the knowledge of the training symbols and the corresponding received signal, the channel estimation block at the receiver is able to make an estimate of the channel impulse response (CIR). Conventional PAT-based channel estimation methods use pilot symbols in time-division multiplexing (TDM) schemes, thus decreasing the effective data transmission rate.

Recently, an alternative channel estimation strategy that circumvents the unwanted effect of data rate reduction has emerged, called implicit training (IT) [4]. Two outstanding IT approaches, known as superimposed training (ST) [5, 6] and data-dependent ST (DDST) [7, 8], achieve higher effective data rates with manageable complexity [9]. These techniques are based on a training sequence added (superimposed) to the information-bearing symbols. Both schemes provide a simple (unsophisticated) channel estimation process [10, 11] and differ only in that the arithmetic mean of the transmitted data of the DDST scheme is superimposed onto the transmitted sequence. Both techniques have been successfully applied to single-input single-output (SISO), as well as multiple-input multiple-output (MIMO) systems [11–17], combined with orthogonal frequency division multiplexing (OFDM) modulations [18–20], and time-varying channels [21–23]. Likewise, there are interesting alternatives to OFDM in [24, 25], where the single-carrier modulation approach is employed, using a joint frequency domain equalization and channel estimation.

Although DDST outperforms ST [12] in terms of channel estimation error, it is worth mentioning that the data decoding under DDST is of an iterative nature, as it needs to remove the data-dependent distortion. Furthermore, DDST [8] performs similarly to TDM-based channel estimation, while saving the overhead in TDM data rate due to pilot transmission. There are, however, some drawbacks that must be taken into consideration when DDST is used. First, this technique introduces a delay in the transmitted data when it calculates the data-dependent signal; second, it assigns less transmission power to the data signal; hence, the symbol demapping operation is not suitable for higher orders of modulation due to identifiability problems, as was highlighted in [26]. This is an important issue, because recent communication standards consider this type of modulation; for example, WiMAX (IEEE 802.16e-2005 standard) uses 64-QAM digital modulation that DDST cannot support. In addition, DDST presents two more drawbacks: its performance is highly sensitive to the data block length used as well as the increased peak-power and peak-to-average ratio (PAPR) in the transmitted signal, as shown in [27].

This paper proposes an iterative detection and channel estimation structure for MIMO systems, which is capable of dealing with the data identifiability problem previously described. The novel algorithm is based on the use of joint (fusion of both techniques) implicit and explicit training for the channel estimation and symbol detection processes. Previous results of the authors related to implicit training for MIMO systems were presented in [28], which introduced the mean removal ST (MRST) technique devoted to estimate the arithmetic cycling mean of the data block signal at the receiver side (instead of at the transmitter side like DDST does). However, later on it was recognized that MRST is not able to deal with the identifiability problem, just like DDST, when the MIMO system employs high-order digital modulation schemes.

The proposal of an iterative detection and channel estimation scheme is hereafter referred to as joint mean removal ST and PAT (MRST-PAT). The method is based on a reliable preliminary channel estimate using PAT with a small number of dedicated pilot symbols. Subsequently, it uses the time-average estimator with the ST signal added to each transmitted data block, achieving an improvement in system throughput. Thus, MRST-PAT merges the best qualities of the two techniques, achieving a better BER performance than if employed separately. In addition, the proposed method eliminates the data identifiability difficulties that DDST exhibits when higher orders of modulation are used [26].

This paper is organized as follows: Section 2 presents the space-time MIMO signal model. Section 3 summarizes the fundamental theory and performance of PAT (TDM), ST, and DDST channel estimation techniques. Section 4 details the structure of the iterative MIMO detection and channel estimation joint MRST-PAT and its theoretical performance analysis. Section 5 depicts the application of the iterative joint MRST-PAT using a 2-OSTBC coder. Section 6 considers the numerical simulation results and performance analysis for the training-based frequency-flat block-fading MIMO channel estimation using TDM, DDST, and MRST-PAT. Finally, some concluding remarks in Section 7 close this paper.

*Notation*. Bold letters in lower (upper) case are used to denote vector (matrices); stands for the complex number field; and represent transpose and conjugate transpose, respectively; denotes identity matrix; and represent Euclidean norm and Frobenius norm, respectively; denotes trace of a matrix; stands for Kronecker product; and denotes a multidimensional complex Gaussian distribution with mean and covariance matrix .

#### 2. Space-Time Signal Model

This section describes the space-time signal model applicable to most existing space-time coding designs such as Vertical Bell Labs Layered Space-Time (VBLAST) [29] and the generalized schemes referred to as space-time block codes from orthogonal designs [30].

With reference to Figure 1, this paper considers a MIMO single-carrier system operating over frequency-flat quasistatic block-fading channel model, with transmit and receive antennas described bywhere is the transmitted vector comprising elements denoted as and is the received vector.