Frequency synchronization for interleaved OFDMA uplink systems☆
Introduction
Multicarrier systems (MCSs) have attracted considerable attention in recent years, because of their flexible frequency resource allocation, robustness in addressing multipath fadings, and ability to provide high throughput in deteriorated communication channels [1]. Based on the different modulation schemes and baseband pulse waveforms employed, MCSs can be classified into orthogonal modulation and nonorthogonal modulation categories. For example, orthogonal frequency division multiplexing (OFDM) and single carrier frequency division multiplexing (SC-FDM) are orthogonal modulation systems, whereas the generalized frequency division multiplexing (GFDM) systems and filter bank multicarrier systems (FBMC) [2] are nonorthogonal modulation systems.
Currently, MCSs are the most promising candidates for next-generation wireless systems because downward compatibility is a key feature being sought in future wireless communication standards [3], [4]. However, MCSs are sensitive to carrier frequency discrepancies between the transmitter and receiver, which misalign the modulated signals in the frequency domain, and produce interferences among the data streams [5], [6], [7]. Frequency synchronization is particularly important for orthogonal MCSs. For example, orthogonal frequency division multiple access (OFDMA) systems, which are an extension of the OFDM system for multiuser communication, use rectangular pulse waveform and rely heavily on exact frequency synchronization because their negligible spectral sidelobes produce substantial multiple access interference (MAIs) when frequency misalignment occurs.
Although the frequency synchronization can also be performed at the user equipment (UE) in which only one single frequency error is estimated [8], [9], [10], [11], the key drawback is the power consumption issues that reduces the battery life of hand held devices. In uplink systems, frequency synchronization is complicated because the base stations (BSs) must manage multiple frequency errors caused by different users. For OFDMA uplink systems, direct frequency compensation is infeasible, because the BS only compensates for the frequency bias of one user; the others are misaligned [7]. Generally, frequency synchronization in OFDMA uplink systems is divided into two stages: (1) carrier frequency offset (CFO) estimation and (2) MAI suppression based on the frequency estimates. This study presents an frequency synchronization algorithm for interleaved OFDMA uplink systems by using a backward prediction system (BPS). Linear prediction (LP) is a digital filtering technique where a discrete-time signals are estimated as a linear function of previous samples [12], [13]. It has been found in many applications of signal processing, such as the direction of arrival of electromagnetic waves, speech waveform compression and blind identification of noisy communication channels [13]. When the collected samples are used to estimate history values of the observed signal, the LP is called a BPS. For interleaved OFDMA systems, the CAS classifies all subcarriers into a set of subchannels each containing a number of contiguous subcarriers. Data symbols of all user are transmitted through subchannels, ensuring an improved system performance in data detection because of the frequency diversity [7]. A key feature of interleaved OFDMA system is that the transmitted signal of each user is periodic in the time domain with a period inversely proportional to the subchannel size. As the system experiences carrier frequency discrepancy, the CFO turns these periodic time samples into a CFO-bearing ones. Accordingly, the proposed approach firstly takes advantage of the periodic structure to construct snapshot vectors through a decimation process where the signals received at the base station are down sampled and then fed into the BPS for CFO estimation. This study illustrates that in the case of noise-free, the BPS can perfectly estimate the past values of the receive time samples, and as a result the CFOs of all users can be found in the zeros of the transfer function of the BPS. In the presence of noise, this study determines the weights of the BPS under the MMSE criterion, and invokes the Wiener–Holf equation to yield the optimal solution. In addition, based on the unit modulus property of the CFO-bearing zeros, the proposed algorithm selects the zeros closest to the unit circle in the z-plane to obtain the corresponding CFO estimates. In contrast to the search-based algorithms in [14] and [16] that require high computational overheads, the proposed CFO estimation algorithm is computationally efficient because of its close-form solution of a polynomial of moderated order.
Base on the CFO estimates, this study presents a three stage frequency synchronization process. First, a set of MAI suppression filters are used to separate the signal of each active user, and then the CFO compensation is performed on the outputs of the MAI suppression filters, followed by a fast Fourier transformation (FFT) for data decoding in the frequency domain. This study develops two types of MAI suppression filters, the ZF and the linearly constrained minimum variance (LCMV) filters. The ZF filter directly removes the MAIs by projecting the multiuser signal to the null space of the CFO signature vectors of the MAI users. The null space projection renders the ZF filter suffering from noise enhancement problem, especially when two users posses close by physical frequency errors. To this end, using the second order statistics of the received multiuser signal, the LCMV filter removes the MAIs while constraining the desired user to unit response under the criterion of minimum mean square error. In contrast to the traditional MMSE-based MAI suppression filter [17], which constrain only the desired user with a distortionless response, the proposed method also imposes zero-response on all the users contributing MAI. Computer simulations show that, in terms of SER, the proposed MAI suppression techniques have at least a 3-dB power gain over the MMSE-based method. The proposed approach possess several distinctive features: (1) the proposed BPS-based CFO estimation algorithm has a reduced computational overhead as compared to traditional algorithms, such as the MUSIC [14] and the ML algorithms [16]; (2) in addition to having a reliable performance in CFO estimation, the proposed MAI suppression technique possesses a better performance in data decoding over the traditional subspace-based approaches, such as the SBMMSE and SBZF algorithms [17]; and (3) the proposed MAI suppression schemes is applicable to an OFDMA system with a moderate number of subcarriers, in which the traditional algorithms [17] suffer a deteriorate SER performance.
The rest of this paper is organized as follows. Section 2 introduces the interleaved OFDMA uplink system model, and the periodic property of the transmit signals. Section 3 presents the proposed Wiener-filter-based CFO estimation algorithm and the MAI suppression algorithms. The computer simulation results used to compare the proposed algorithm with the benchmarks of CFO estimation and MAI suppression for OFDMA uplink systems are described in Section 4, and the conclusion is presented in Section 5.
Section snippets
System model
Fig. 1 shows the block diagram of the OFDMA uplink system with the proposed BPS for frequency synchronization. Consider a system with M active users; the transmit time sequence of user m can be expressed through the inverse fast Fourier transform (IFFT) as [7]where N is the total number of subcarriers, is the data symbol modulated at subcarrier l, and κm is the index set of the subcarriers assigned to user m. Assuming a subchannel size of L for an
Method
In this section, we first introduce the proposed CFO estimation algorithm. Then the ZF and LCMV MAI suppression methods are presented, followed by the analytical derivations of the MSE of the CFO estimates.
Results and discussion
This section presents the computer simulation results along with the discussion on the computational complexity of the proposed algorithm. Consider an OFDMA system with the following settings: and . For all numerical examples, independent Rayleigh fading channels were assumed for each user with in which denotes the power delay profile of hm,n. For user m, was given byThe channel response was assumed to be constant
Conclusions
This study presents a frequency synchronization method for interleaved OFDMA uplink systems. The proposed approach first decimates the received signal to form snapshot vectors, which are the inputs for the BPS. CFOs can then be obtained from the zeros of the BPS through a polynomial rooting process. Based on the CFO estimates, the proposed algorithm suppresses MAI in the time domain by using a set of MAI suppression filters that are under ZF and LCMV criteria, respectively. Computer simulation
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This research was supported by Ministry of Science and Technology, ROC, under the contract MOST 106-2221-E-182-011.