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SINR Analysis and Energy Allocation of Preamble and Training for Time Division CT with Range

Extension Qiongjie Lin and Mary Ann Weitnauer

School of Electrical and Computer Engineering Georgia Institute of Technology, Atlanta, Georgia 30332-0250

Email: lin3@gatech.edu; maweit@gatech.edu

Abstract—In this paper, we investigate the packet decoding performance degradation due to the joint effects of synchro- nization and channel estimation errors in orthogonal frequency division multiplexing (OFDM)-based time-division cooperating transmission (TDCT) for the purpose of range extension. The signal to interference and noise ratio (SINR) of maximal ratio combining (MRC) with OFDM TDCT is analyzed in multipath fading channels. We demonstrate the performance impairment on decoding for different TDCT implementation scenarios with conventional synchronization and different channel estimation schemes through the simulation of the practical system with com- plete synchronization, channel equalization and decoding pro- cesses. We show that when the total energy for synchronization and channel estimation is limited because of the range extension objective, the way energy is distributed between preamble and training sequence plays an important role.

Index Terms—Cooperative transmission, range extension, OFDM synchronization, channel estimation

I. INTRODUCTION

In cooperative transmission (CT), multiple radios in a net- work transmit copies of the same message through differently fading multipath channels, and a receiver combines the copies in the physical layer. The cooperatively transmitting nodes form a virtual array, from which the receiver can derive diversity and array gains [1]. These gains can be used to increase reliability, reduce transmit power, or extend range. In particular, range extension can overcome shadowing and path loss that would otherwise partition the network. CT range extension (CTREX) can benefit many types of wireless networks. For example, it can increase the two-hop coverage area of a single access point [2]. CT can be performed concurrently (CCT) or in different time slots; we call the time-slotted version “time-division CT” (TDCT). Meanwhile, the orthogonal frequency division multiplexing (OFDM) is an efficient technique for mitigating the effects of delay spread in multipath wireless channels. This paper then treats OFDM- based TDCT with the objective of range extension in the multipath fading channel.

For OFDM wireless reception, timing/frequency synchro- nization and channel state information (CSI) estimation are well known to be big issues. Symbol timing offsets larger than the cyclic prefix (CP) will introduce inter-symbol-interference

The authors gratefully acknowledge support for this research from the National Science Foundation under grant CNS-1017984.

(ISI), while carrier frequency offsets (CFOs) will introduce inter-carrier-interference (ICI). Moreover, the packet decoding performance is also affected by the CSI estimation error, which results from both the additive noise and the presence of residual synchronization error.

The bit error rate (BER) impairment caused by CFO is evaluated in [3] in AWGN channels. In [4], the authors evaluate the BER performance degradation, conditioned on the given multipath channel realization, by exploiting the Gaussian approximation of the ICI. However, [3],[4] consider only the performance degradation in terms of synchronization error assuming perfect CSI is available at the receiver. On the other hand, various CSI estimators and their corresponding performance analyses have been studied in the literature. In [5],[6],[7], LS (Least Square) and LMMSE (Linear Mini- mum Mean Square Error) channel estimation algorithms are discussed under the assumption of perfect synchronization. On this subject, Cheon and Hong proposed a BER analysis in Rayleigh fading channel, incorporating both the effects of the CFO and the CSI estimation errors [8]. But they assume the channel estimate and the channel estimation error are uncorrelated when the interference power is small. As indicated in [4], the method presented in [8] may overestimate the BER in some simulations. In [9], the effects of channel estimation error are analyzed in the presence of CFO in the frequency-selective Rayleigh fading channel. However, the effect of synchronization error on received data is ignored in the derivation of BER.

To the best of our knowledge there are few existing works on analyzing the joint impact of synchronization and channel estimation errors on the BER of TDCT in terms of range extension, or equivalently, at very low SNR. The BER perfor- mance of multiple-input and multiple-output (MIMO) OFDM system is analyzed with CFO and CSI estimation errors in [10], where the CFO and CSI estimation errors are modeled as independent zero-mean RVs. In [11], the effect of CFOs estimation error on CSI estimation is discussed, however, the mean square error (MSE) of the channel estimator for SISO/MIMO-OFDM system is addressed instead of BER. Some recent works [12], [13] consider the OFDM channel estimation problem in the presence of CFO and phase noise with focus on the development of new channel estimation algorithms and corresponding BER analyses are missing.

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Fig. 1. Illustration of two-hop TDCT system. Fig. 2. Illustration of the structure of relay nodes and destination.

In this paper, we consider the joint effects of synchroniza- tion and channel estimation errors on TDCT for the purpose of range extension. We analyze the post-combiner signal to inference and noise ratio (SINR) to evaluate the joint impact of residual CFOs and channel estimation errors on decoding numerically. The BER of coded OFDM TDCT in the multipath fading channel is then investigated through the simulation of the entire practical system with complete synchronization and CSI estimation processes. The conventional SISO OFDM synchronization [14] scheme is applied on each relay link. A channel estimator that averages channel estimates over several consecutive subcarriers is also considered. Through the Monte Carlo simulation of the whole OFDM TDCT system, we observe that the CFO and channel estimation errors jointly affect the SINR performance, and the performance degradation factors could be modeled as co-link interference and noise, which is proportional to number of cooperating relays, K and inter-link interference and noise, which is proportional to K2.

The paper is organized as follows. Section II describes the system model considered for this work. Section III presents the SINR analysis for post-combiner OFDM signals in terms of range extension and energy limitation. In Section IV, we show the simulation results of BER of coded BPSK OFDM signals for various TDCT scenarios with different synchronization and channel estimation schemes. Finally, Section V concludes the paper.

II. SYSTEM MODEL

We consider a half-duplex time-division cooperative com- munication system with one source node, S, a relay cluster of K cooperating relay nodes {R1, R2, ..., RK}, and a des- tination node, D, as shown in Fig.1. Either the decode-and- forward (DF) or amplify-and-forward (AF) relaying scheme could be adopted for the relay nodes. We assume direct communication between source and destination is not avail- able. There are two phases of transmission to achieve the communication between source and destination. In the first phase, the source node, S, broadcasts the message to potential relay nodes. All the relay nodes that correctly decode the header (AF) or the packet (DF) from the source node will participate in the second phase, keeping the same offsets for transmission that they learned in reception.

In this work, we focus on the decoding performance at the receiver during the second phase, assuming the original data from the source node has been decoded successfully and is ready to be sent at the relay cluster. The output OFDM symbol of the kth relay is given by the N point complex modulation sequence

xki = 1√ N

N−1∑ n=0

Xne j2πin/N , (1)

where, Xn ∈ {Xpn, Xtn, Xdn} is the modulated symbol in the frequency domain, where Xpn denotes the preamble for synchronization, Xtn denotes the training sequence for CSI estimation, while Xdn denotes the data symbol; i and n are the time and subcarrier indices, respectively; N is number of subcarriers of one OFDM symbol.

Since the OFDM system is not sensitive to the timing offset, we assume the timing error is smaller than the CP length. Let the normalized frequency offset error be denoted �k = ∆fkTs, where ∆fk is the residual CFO of the kth link after the CFO compensation and Ts is the sample duration. Denoting the phase offset θk0 for the kth link, the received OFDM symbol during the kth time slot at the destination can be expressed by

rki = ejθ

k 0

√ N

N−1∑ n=0

HknXne j2πi(�k+n)/N + zki , (2)

where Hkn is the channel response of the nth subcarrier of the kth relay link, and zki ∼ CN (0, σ2Z) is an additive Gaussian noise. With perfect symbol timing, the received data from the kth relay in the frequency domain at the receiver after FFT becomes

Rkn = 1

N

N−1∑ i=0

rki e −j2πin/N + Zkn = H̄

k nXn + I

k n + Z

k n, (3)

where Zkn is a frequency domain additive Gaussian noise, and H̄kn denotes the distorted channel response, which can be written as

H̄kn = Hknsin(π�

k)

Nsin(π�k/N) ej(π�

k(N−1)/N+θk0 ), (4)

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and the ICI due to the residual CFO is

Ikn =

N−1∑ m=0,m6=n

HkmXm sin(π�k)ej(π�

k(N−1)/N+θk0 )