OFDM系统中DCT信道估计器优化：阈值设定与泄漏消除

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本文主要探讨了在正交频分复用(OFDM)系统中，基于离散余弦变换(DCT)的信道估计器遇到的两个关键问题：阈值设置和泄漏估计。传统的阈值设置方法虽然可行，但通常依赖于经验法则，缺乏理论基础。作者提出了一个新颖的阈值设定策略，它建立在DCT域中信道脉冲响应(CIR)的解析表达式之上，旨在提供更精确且有理论支持的方法。首先，关于阈值设置，传统方法往往通过观察信号噪声比(SNR)或误比特率(BER)与估计误差的关系来确定，这种方法在一定程度上有效，但并不总是最优。文中提出的新方法旨在通过分析DCT域中的信号特性，找出更符合实际信道状况的阈值，以提高信道估计的精度。这可能包括对DCT系数的统计特性的深入理解，以及如何在不同信噪比条件下选择最合适的阈值点。其次，对于DCT基带信道估计器，存在一个显著的问题是高频区域的泄漏效应。由于DCT在处理非平稳信道时，高频率部分的信息可能会向低频部分泄露，导致估计结果的误差增大，形成所谓的"误差地板"现象。为了解决这个问题，作者在本文中延续了他们之前在基于离散傅立叶变换(DFT)的信道估计器泄漏估计方面的研究。他们提出的策略可能包括设计特定的滤波器或者校正算法，以减少DCT域中的泄漏影响，从而提升信道估计的稳健性和准确性。这篇研究论文针对OFDM系统中基于DCT的信道估计器的关键问题，提出了创新的解决方案。作者不仅关注阈值设置的优化，还着重于解决由DCT特性引起的泄漏问题，以期提高信道估计的整体性能。这对于理解和改进现代无线通信系统的性能至关重要，尤其是在多径衰落和频率选择性衰落等复杂环境下的信号处理。通过这些改进，可以增强OFDM系统的抗干扰能力和传输效率。

DCT-Based Channel Estimator for OFDM Systems:

Threshold Setting and Leakage Estimation

Xin Xiong, Bin Jiang, Xiqi Gao, and Xiaohu You

National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, P. R. China

Email: {xinxiong, bjiang, xqgao, xhyu}@seu.edu.cn

Abstract—This paper addresses the problem of the discrete

cosine transform (DCT)-based channel estimator for orthogonal

frequency-division multiplexing (OFDM) systems in the presence

of virtual subcarriers. We focus on the following two problems.

The ﬁrst issue is the threshold setting. Traditional methods to

set the threshold are reasonable but based on heuristics. We

propose a new threshold based on the analytical expression of

the channel impulse response (CIR) in the DCT domain. The

second issue is the leakage estimation for DCT-based channel

estimators. Recently, we have proposed the leakage estimation for

discrete Fourier transform (DFT)-based channel estimators. It is

well known that there is the channel leakage in the high frequency

region of the DCT domain, and the leakage causes the error ﬂoor.

In order to eliminate the error ﬂoor, we propose to estimate the

leakage in the high frequency region. Simulation results show that

the DCT-based channel estimator with the proposed threshold

achieves better performance and the error ﬂoor is mitigated after

leakage estimation.

I. INTRODUCTION

The orthogonal frequency-division multiplexing (OFDM)

technique has attracted much attention due to its robustness

against frequency-selective fading channels and easiness to

employ the multiple antenna techniques. The OFDM technique

has been employed by commercial systems such as long term

evolution (LTE) and wireless local area networks (WLAN)

due to its simple implementation. For coherent receivers, ac-

curate channel estimation can signiﬁcantly improve the system

performance, especially when the system uses the high-order

modulation. The commercial system adopts the pilot-aided

channel estimation as a result of reliability and simplicity.

Among pilot-aided channel estimators, the discrete cosine

transform (DCT)-based channel estimators have been exten-

sively studied over the past decade [1]–[5]. For the ﬁrst

time, the DCT-based channel estimator was suggested in

[1]. Due to its energy compaction property, the DCT-based

channel estimator generally outperforms the discrete Fourier

transform (DFT)-based channel estimator. The authors in [2]

proposed an improved scheme using truncated singular value

decomposition for DCT-based methods. In [3] and [4], the

DCT-based channel estimator was suggested for cyclically

shifted reference signals. In [3], the channel response of each

user was completely separated by the type-I DCT. The authors

compared the DCT-based channel estimator and DFT-based

channel estimator for the LTE uplink in [4].

In this paper, we focus on two problems. The ﬁrst issue is

the threshold setting. Since the DCT-based channel estimator

was proposed, much literature has addressed the issue on

threshold. The existing thresholds are reasonable but based

on heuristics. Until now, the theoretical analysis on threshold

is not sufﬁcient, and some parameters are determined by

experience. In order to solve this problem, we derive the

precise expression of the channel impulse response (CIR)

in the DCT domain. Based on the expression, we propose

a threshold which is easy to set. The second issue is the

leakage estimation. The CIR energy in the high frequency

region of the DCT domain is small but nonzero. For threshold-

based methods, the leaked energy in the high frequency region

is removed while reducing noise. The removed energy will

cause the error ﬂoor which appears in the high signal-to-noise

ratio (SNR) region. Recently, we have proposed to estimate

the channel leakage for DFT-based channel estimators in [6].

In the similar way, the leakage can be estimated by using

the partial minimum mean-square-error (MMSE) ﬁltering for

DCT-based channel estimators. After leakage estimation, the

error ﬂoor will not exhibit in the SNR region of interest.

This paper is organized as follows. Section II describes the

channel model and the system model. The DCT-based channel

estimators and all kinds of thresholds are presented in Section

III. Section IV introduces the leakage estimation for DCT-

based channel estimators. The simulations are analyzed in

Section V. Finally, the conclusion is drawn in Section VI.

Notations: Matrices are denoted by upper case boldface

(e.g. X), and vectors are denoted by lower case boldface

(e.g. x). An N × N identity matrix is expressed as I

The superscripts T and H denote transpose and conjugate

transpose, respectively. [A]

represents the (i, j)-th element of

the matrix A. x indicates rounding x to the nearest integer

that is greater than or equal to x. |x| denotes the absolute

value of x. We reserve E{·} for expectation with respect to all

random variables within the brackets, diag{x} for a diagonal

matrix with the elements of the vector x on its main diagonal,

and blkdiag {X

, X

, ..., X

} for a block diagonal matrix with

matrices X

,..., X

on its main diagonal.

II. S

YSTEM DESCRIPTION

A. Channel Model

A time-varying multipath channel model composed of L

impulses is given by

h(t; τ )=

L−1



m=0

(t)δ(τ − τ

(t)T

), (1)

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