Carrier frequency offset estimation method for 2 × 1 MISO TDS-OFDM systems
© Oh et al.; licensee Springer. 2013
Received: 14 February 2013
Accepted: 23 August 2013
Published: 28 August 2013
In time-domain synchronous (TDS)-orthogonal frequency division multiplexing (OFDM) systems, a pseudo noise (PN) sequence is inserted instead of the cyclic prefix. The PN sequence is used not only as a guard interval but also as a training sequence for channel estimation and synchronization in the time domain. Recently, research studies on 2 × 1 multi input-single output (MISO) TDS-OFDM systems have been conducted, and different PN sequences (which are orthogonal to one another or cyclically shifted) are transmitted at each transmit antenna for channel estimation, which are modulated by binary phase shift keying in the same phase angle. However, when the absolute phase difference among the transmitted PN sequences is π, a PN sequence cancellation problem occurs, making the estimation of an accurate carrier frequency offset (CFO) difficult. In this paper, a CFO estimation method with the aid of PN sequences for 2 × 1 MISO TDS-OFDM systems is proposed. In the proposed method, the phase of the PN sequences at each antenna is rotated differently and transmitted to prevent a PN sequence-canceling problem. In addition, a CFO estimation scheme using channel state information is proposed to estimate an accurate CFO in time-varying channels. We show by computer simulations that the mean square error performance of the proposed method over an additive white Gaussian noise environment and time-varying Rayleigh channel is higher than that of the conventional method.
KeywordsTDS-OFDM MISO Carrier frequency offset estimation PN sequence
Orthogonal frequency division multiplexing (OFDM) systems  are popular broadband communication systems and have been well known to be effective against multipath distortion. In general OFDM systems, cyclic prefix (CP) is inserted as a guard interval to efficiently combat multipath channel, and a pilot signal is inserted into the subcarriers for channel estimation and carrier recovery. In time-domain synchronous (TDS)-OFDM systems, a pseudo noise (PN) sequence is employed instead of the CP, which is modulated by binary phase shift keying (BPSK) . The PN sequence is used not only as a guard interval but also as a training sequence for channel estimation and synchronization in the time domain . Thus, it is not needed in the transmission of the pilot signal among subcarriers, and the spectral efficiency of the TDS-OFDM systems is higher than that of the CP-OFDM systems. Currently, digital TV broadcasting services in China employ TDS-OFDM systems .
Recently, research on the transmit diversity scheme of the TDS-OFDM systems has been conducted in [5–7], and it mainly focused on the 2 × 1 multi input-single output (MISO) systems to achieve diversity gain. The Alamouti code  is a well-known transmission method for 2 × 1 MISO systems and can achieve good spatial diversity gain with minimal decoding complexity. Thus, 2 × 1 MISO TDS-OFDM systems are promising and reliable systems to achieve better performance. In these systems, different PN sequences (which are orthogonal to one another or cyclically shifted) are transmitted at each transmit antenna for channel estimation, which are modulated by BPSK in the same phase angle. However, when the absolute phase difference among the transmitted PN sequences (which are transmitted in the same phase angle) is π, a PN sequence cancellation problem occurs and makes the estimation of an accurate carrier frequency offset (CFO) difficult.
In this paper, a CFO estimation method with the aid of PN sequences for 2 × 1 MISO TDS-OFDM systems is proposed. In the proposed method, the phases of the PN sequences at each antenna are rotated differently and transmitted to prevent the PN sequence canceling problem. After the modulations of the received PN sequences are removed, the CFO is estimated using the L&R algorithm , which is a type of a maximum likelihood (ML) method with several numbers of auto-correlators. In addition, a CFO estimation scheme using channel state information (CSI) is proposed to estimate an accurate CFO in time-varying channels. Using computer simulations, the mean square error (MSE) performance is measured by employing the proposed transmission method and the L&R algorithm over an additive white Gaussian noise (AWGN) environment and a time-varying Rayleigh channel. The rest of this paper is organized as follows: in Section 2, the PN cancellation problem is analyzed when the transmitted PN sequences have the same phase angle, and the CFO estimation method is introduced even under the presence of the PN cancellation problem; in Section 3, the CFO estimation method and a scheme that uses the CSI are proposed; the computer simulation results of the MSE performance are presented in Section 4; and conclusions are drawn in Section 5.
2 PN cancellation problem and CFO estimation method in conventional 2 × 1 MISO TDS-OFDM systems
2.1 System model
where PN1(k) and PN2(k) are the transmitted PN sequences from the first and second transmit antennas, respectively, ƒ c is the CFO, T s is the sampling period, θ is an unknown phase offset, and n(k) is the AWGN at the receive antenna.
2.2 Transmitted PN sequence cancellation problem and CFO estimation method
where and n' ' ' = arg[n' '].
Only when (2a) and (2b) exist continuously, as shown in Figure 3a,d, can the CFO be estimated normally. However, when (2c) exists, as shown in Figure 3b,c, the phase difference between successive PN symbols cannot be used for the CFO estimation. Therefore, all the PN symbols may not be used for the CFO estimation, and the CFO cannot be estimated accurately using more than one auto-correlators, similar to that in the data-aided (DA)-ML methods [9, 11, 12].
where Narg is the number of arg[z(k)z*(k − 1)] calculations.
3 Proposed PN sequence transmission method and CFO estimation method in 2 × 1 MISO TDS-OFDM systems
In this section, the CFO estimation method is proposed, which rotates each phase of the transmitted PN sequences and employs the L& R method in Section 3.1. Furthermore, a CFO estimation scheme that uses the CSI is proposed in Section 3.2 for accurate estimation in the Rayleigh channel.
3.1 Phase rotated PN transmission method and CFO estimation method employing L&R algorithm
In this section, a transmission method that rotates each phase of the transmitted PN sequences to prevent the PN sequence cancellation problem is proposed. In addition, a CFO estimation method employing the L&R algorithm  is proposed.
where and n‴ = arg[n″].
3.2 Frequency offset estimation scheme using CSI
where h11 is the channel impulse response (CIR) from the first transmit antenna to the receive antenna and h12 is the CIR from the second transmit antenna to the receive antenna. In the Rayleigh channel, h11 and h12 are time varying, and the variation rate depends on the Doppler frequency.
The proposed scheme consists of the coarse carrier frequency recovery (CFR), which is a feedback structure, fine CFR, which is a feedforward structure, and phase calculator that uses CSI. For the estimation scheme, the proposed PN sequence rotation and the CFO estimation method are employed for the coarse CFR, and the pilot block correlation method in  can be employed for the fine CFO estimation algorithm. In the proposed scheme, the fine CFR estimates the CFO and applies it to the compensator using the PN sequence at every frame. On the other hand, the coarse CFR first estimates the CFO at every frame and applies it to the compensator using the CSI. The phase estimator estimates the CSI using PN sequences over one PN block (guard interval) after the CFR and applies the estimated CFO to the phase locked loop (PLL) only when the absolute phase difference between h11 and h12 is smaller than π/4. If the absolute phase difference between h11 and h12 is greater than π/4, zero is applied to the PLL.
The PN cancellation problem in the conventional method can also be solved by employing the proposed frequency estimation scheme. For the conventional system, if the absolute phase difference between h11 and h12 over one block is greater than π/4, the CFO is estimated by employing several auto-correlators and applying them to the PLL. However, the proposed PN sequence transmission method that uses the proposed scheme is suitable for both the AWGN and time-varying Rayleigh channels, whereas the conventional method that uses the proposed scheme only works well in the time-varying channel.
4 Computer simulation results
Computer simulation parameters
Symbol rate ƒ s
Center frequency ƒ c
Size of PN sequence
Size of data symbol
Carrier frequency offset
1% of symbol rate
Maximum Doppler frequency
17.64 Hz (40 Km/h), 35.28 Hz (80 Km/h), 52.93 Hz (120 Km/h)
Number of auto-correlators
In this paper, we have proposed a PN sequence phase rotation transmission method and a frequency estimation scheme using CSI. The proposed PN transmission method rotated the transmitted PN sequences differently from one another to prevent the PN sequence cancellation problem and made possible the use of all consecutive PN sequences for the CFO estimation. In addition, the CFO was accurately estimated by the L&R algorithm, which is a type of DA-ML algorithm with multiple auto-correlators. For the time-varying Rayleigh channel, the frequency estimation scheme using the CSI has also been proposed. The simulation results show that the MSE performance of the proposed transmission method and estimation scheme over the AWGN and Rayleigh channels is higher than that of the conventional method.
This paper was supported by Konkuk University in 2010.
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