Novel Preamble Design for Channel Estimation in FBMC/OQAM Systems

Abstract

The nonorthogonality between the real and imaginary FBMC/OQAM modulated signals complicates the channel estimation (CE) process, and conventional OFDM CE methods cannot be directly applied to FBMC/OQAM. The conventional preamble-based CE schemes in FBMC/OQAM systems are mainly based on the interference approximation method (IAM) to improve the estimation performance. In this paper, we develop a novel preamble structure to improve the CE performance. We exploit the symmetry pattern to cancel interference and take into account the interference weights in this symmetric structure. The conventional preamble and the proposed preamble are compared via simulations in the IEEE 802.22, 3GPP Vehicular A and Pedestrian A channels. Numerical simulation results demonstrate that the proposed preamble can achieve better bit error ratio (BER) and mean squared error (MSE) performance under the three channel models considered.

1. Introduction

Multicarrier communication techniques have been widely adopted in recent years for high data rate transmission. Cyclic prefix-based orthogonal frequency division multiplexing (CP-OFDM) is certainly the most researched and accepted multicarrier technology among the various wireless communications standards [1-3]. With the insertion of some redundancy, the frequency selective channel becomes a frequency flat subchannel. However, the disadvantage of CP-OFDM is a loss in spectral efficiency due to the CP insertion, and a higher sensitivity to narrowband interferers and Doppler spread. As described in Ref. [4], up to 25% transmitted power as well as spectral efficiency is wasted because of the inclusion of CP.

Unlike the CP-OFDM system, FBMC/OQAM well utilizes time frequency localization (TFL) property pulse shaping via an IFFT/FFT-based filter bank, and staggered OQAM symbols, real symbols at twice the symbol rate of FBMC/QAM, are loaded on the subcarriers [5]. Hence, FBMC/OQAM has a theoretically higher spectral efficiency [6,7] and increased robustness to frequency offset and Doppler spread. Moreover, CP is not required in FBMC/OQAM systems, which may lead to even higher transmission rates [8]. Moreover FBMC/OQAM has already been introduced into the TIA’s digital radio technical standards [9].

FBMC/OQAM has its root in the pioneering works of Chang [10] and Saltzberg [11], who introduced multicarrier techniques over two decades ago. Among the various pulse shaping prototype filters with good TEL properties that have been proposed [12-15], FBMC/OQAM has garnered wide attention and has been the focus of extensive research [16-19]. Because of the subcarrier functions, which are only orthogonal in the real field, there always exist imaginary valued intrinsic interference from neighbor symbols. That is why conventional OFDM CE methods cannot be directly applied to FBMC/OQAM.

A number of FBMC/OQAM CE methods have been recently studied for preamble-based and scattered pilot-based training schemes. A pseudo pilot-based CE method has been proposed in Ref. [20], and a preamble-based CE interference approximation method (IAM) has been proposed in Refs. [21-23]; the IAM schemes include IAM-R, IMA-I, IAM-C, and E-IAM-C, and all of these methods can be characterized as aiming at constructively exploiting interference to improve estimation performance. Extended IAM-C (E-IAM-C) [23] has been identified as the best performance gain in all of the proposed IAM preamble structure schemes so far. In contrast to the IAM approach, in which the interference is taken advantage of to improve CE accuracy, the interference cancellation (IC) approach is designed to cancel or avoid the interference. Such a preamble design has been proposed in Refs. [24-27], and a more spectral efficiency preamble design method has been suggested in Ref. [28].

In this paper, we investigate the possible maximum gain from existing preamble structures. The major contributions of this paper are as follows:

1. The conventional IAM and IC preamble-based channel estimation methods for FBMC/OQAM are reviewed.

2. A novel preamble structure for channel estimation in FBMC/OQAM system is proposed.

3. The proposed preamble structure exploits the symmetry pattern to obtain interference cancellation gain and jointly considers the interference weights to obtain a greater interference approximation gain. The idea of the proposed preamble structure is based on a trade-off between IAM and IC, and is called the novel preamble structure (NPS).

4. The superiority of the proposed preamble structure is verified by numerical simulations over IEEE 802.22, 3GPP Vehicular A and Pedestrian A channels.

The rest of this paper is organized as follows: In Sec. 2, we describe the discrete-time baseband equivalent model for FBMC/OQAM systems. In Sec. 3, we review the IAM and IC preamble structures and design the novel preamble structure. The BER and MSE performance of the proposed preamble associated with the conventional preamble-based CE are compared and simulation results for the three aforementioned channel scenarios are presented in Sec. 4. Section 5 concludes the paper.

 

2. System Model

The transmitted signal in FBMC/OQAM systems can be written in the following form [21]:

where dm,n are real valued OQAM symbols, and gm,n(t) represents the synthesis basis which is obtained by the time-frequency translated version of the prototype function g(t) in the following way

with N an even number of subcarriers, F0 = 1/T0 = 1/2 τ0 the subcarrie spacing, and ϕm,n an additional phase term. T0 denotes the OFDM symbol duration, and τ0 denotes the time offset between the real and imaginary parts of the OQAM symbols. The double subscript (.)m,n denotes the (m,n)-th frequency-time (FT) point, m is the subcarrier index and n is the OQAM symbol time index. Fig. 1 shows the FBMC/OQAM lattice. For ease of understanding, the OFDM lattice is also shown in Fig. 1.

Fig. 1.FBMC/OQAM and OFDM lattices [24].

The pulse g is designed so that the associated subcarrier functions gm,n are orthogonal in the real field, that is

where δi,j is the Kronecker delta, δm,p = 1 if m = p and δm,p = 0 if m ≠ p. We can find that even in the distortion-free channel and with perfect time and frequency synchronization, there still will be some purely imaginary intercarrier interference at the output; thus, we set interference weights

with a purely imaginary term for (m,n) ≠ (p,q).

After passing through the channel, the received signal with an additive noise can be written as

with

where h(t,τ) is the channel impulse response. Hm,n(t) is the complex response of the channel at instant t. We assume that we have a flat fading channel at each subcarrier, which means that the channel is constant during the duration of the prototype, then Hm,n(t) = Hm,n. Fig. 2 shows the implementation diagram of the FBMC/OQAM system, which was proposed by Jinfeng Du and Svante Signell [5].

Fig. 2.Implementation diagram of the FBMC/OQAM system [5].

When the output is at the p-th subcarrier and q-th OQAM symbol, the output signal, with the noise separated out, can be expressed as

A common definition is that only the first-order neighborhood Ω1,1 of a given FT point (p,q), Ω1,1 = {(m,n),|m|≤1,|n|≤1,(m,n≠(0,0)}, causes the interference, and assuming that the channel is almost constant over this neighborhood, we can rewrite (7) as

with the increase of m and n, and becomes very close to zero [5]; (8) can then be rewritten as

The zero-forcing (ZF) equalized signal can be written as

As is a pure real term, the estimated symbol is given by

From (11), we can infer that the inter symbol interference (ISI) can be neglected, in practice, with prototype functions well localized in both time and frequency.

Considering Gaussian noise η with zero mean and variance σ2, the CE formula can be expressed as

Note that the larger the power of the better the CE will be. This observation underlies the IAM schemes, which will be discussed in the following section.

 

3. Preamble-based Channel Estimation Methods

Since our focus in this paper is on preamble-based channel estimation in FBMC/OQAM systems, in this section we review the IAM and IC approaches and propose the novel preamble structure.

3.1 Interference Approximation Method (IAM)

The first-order neighborhood is considered, and the preamble length is taken equal to 3τ0 and is assumed to be perfectly known at the receiver. dp,q is located in the middle of the preamble. As introduced in formula (12), the symbols surrounding dp,q should have the same sign so that they can be added together; then, the greater the power of the better the estimation will be.

We should also know the interference weights for neighbors (m,n) ∈ Ωp,q of each FT point (p,q). The values can be computed based on the prototype filter g, and thus, for all q, the interference weights are given by

Details can be found in Ref. [23]. Generally, β,γ > δ. The above quantities can be given by

In Sec. 4, γ = 0.5004, β = 0.3183, δ = 0.2501, and ε = 0 for the design of g.

In order to simplify the maximum preamble magnitude problem, IAM-R was proposed in Ref. [21] to place nulls at the first and third FBMC/OQAM symbols of the preamble,

where dp,0 = dp,2 = 0, dp+1,1 = -dp-1,1 , p = 0,1,2...,N-1, we assume |dp,1|2 = d2, and then the power of can be expressed as

Fig. 3(a) shows an example with N = 8, for OQAM modulation of the IAM-R preamble structure.

Fig. 3.Preamble structures for (a) IAM-R, (b) IAM-C, and (c) E-IAM-C.

Furthermore, one may try to find a complex valued preamble sequence so that the power of will be maximized. With a slight modification, the pilot symbols are either purely real or imaginary at all the subcarriers. This operation is to set the middle FBMC/OQAM symbol equal to that in IAM-R, but with pilots at the odd subcarriers multiplied by j. This preamble structure, proposed in Ref. [28], is called IAM-C. The power of is E{d2|1+2β|2} = d2(1+4β+4β2). Obviously, the power of in IAM-C is larger than that achieved by IAM-R. Fig. 3(b) shows the IAM-C preamble structure, for N = 8, and OQAM modulation.

In IAM-C, nulls are placed in the first and third symbol positions, and thus one may think to utilize the first and third symbols to obtain the maximum possible power of the preamble. Considering the analysis of presented at the end of Sec. 2, an alternative preamble structure that employs the side symbols as well could yield pilots that are stronger than those of IAM-C.

A method based on this idea, proposed in Ref. [23], is called extended IAM-C (E-IAM-C). The preamble magnitude is d|1+2(β+γ)|; clearly, the power of is larger than that achieved by IAM-C. An example of E-IAM-C is given in Fig. 3(c).

3.2 Interference Cancellation (IC) Method

In IAM schemes, inter-pilot interference is removed by an opposite sign between adjacent subcarriers in the frequency domain and inter symbol interference is prevented by an insertion of nulls. An alternative approach is presented to cancel or avoid the intrinsic interference, and is called the interference cancellation (IC) method.

A straightforward way to cancel the interference is to simply null the data surrounding the pilot FT point. IAM-R is considered to be a special IC method. Another way to simplify the interference cancellation is to transmit zeros at the middle symbol, at all odd indexed subcarriers. Such a preamble was proposed in Ref. [27]. Another design, which relies on the symmetries in (13) to cancel the interference from adjacent subcarriers, was suggested in Ref. [24]. Like the idea of E-IAM-C, the neighborhood symbols utilize the symmetries to transmit data at the FT positions instead of nulls [28], which was confirmed to have the better CE performance among interference cancellation methods. Following the pattern in (13), the data modulating the first order neighbors could be structured as

One can use the above structure to design a preamble with the property of interference cancellation by simply applying the pattern for every third subcarrier and resorting to interpolation for the rest. This makes it true that the interference weights are the same for every second subcarrier. Fig. 4 depicts some examples of IC preamble structures, with N = 8, and OQAM modulation.

Fig. 4.Preamble structures for IC methods from (a) Ref. [27], (b) Ref. [24], and (c) Ref. [28].

3.3 Novel Preamble Structure (NPS)

It was shown in Ref. [28] that the preamble structure could have better CE performance in IC methods. However, in contrast with the IAM approach, this method is only considered to cancel the neighborhood interference, and the influence of interference power on CE performance is ignored.

We see in Fig. 4(c) that the interference cancellation is reflected in all subcarriers. The structure with magnitude d is clearly smaller than in IAM approaches. However, simulation results [28] show that, compared to IAM approaches, this preamble-based CE method can achieve better BER and MSE performance.

Based on the idea of maximum interference cancellation gain from all the subcarriers and the larger power of we consider every fourth subcarrier to be modulated, and propose a novel preamble structure. The proposed structure is using symmetry pattern to combine both interference cancellation gaindan interference approximation gain.

In the following equation, we consider the preamble pairs Si,j (i = 0,1, j = 0,1) which cancel each other in order to remove interference at the pilot location:

At an odd-indexed subcarrier, the pilot ±d in the middle, At an even-indexed sub-carrier, with the pilot d in the middle, and with the pilot -d in the middle,

An example is given, at an odd-indexed subcarrier, with the pilots in the middle, and ±d placed at the right and left neighborhood positions. When at an even-indexed subcarrier, the middle pilots are ±d, with d placed at the right neighborhood position, and its negative, placed at the left neighborhood position. Then from calculations, at an odd-indexed subcarrier, when the middle pilot is d, the preamble has magnitude d|1-j2(|β+δ)|, and when the middle pilot is -d, the preamble has magnitude d|1-j2(|δ-β)| ; where β > δ, obviously, the magnitude is larger than d. At an even-indexed subcarrier, with the pilot d in the middle, the preamble has magnitude d|1+j2(|β-γ)|, and with the pilot -d in the middle, the preamble has magnitude d|1+j2β|. It is clear that in a pair of subcarrier pilots, one of its magnitudes is larger than that achieved by conventional interference cancellation. Compared to IAM approaches, the proposed structure has a smaller magnitude, but takes into account interference cancellation. Furthermore, the proposed structure has a larger magnitude than conventional IC approaches. Fig. 5 gives an example of an NPS, with N = 8, and OQAM modulation.

Fig. 5.Novel preamble structure.

 

4. Simulation Results

In this section, we present simulation results to verify our analysis, and the BER and MSE performance of the two conventional preamble schemes (IAM and IC) versus the proposed preamble scheme are discussed. There have been many previous studies [29-31] of CP-OFDM and FBMC/OQAM that have concluded that an FBMC/OQAM system for preamble-based CE obtains better performance than a CP-OFDM system, so our simulation analysis will not include a CP-OFDM system.

The simulations were carried out with three channel models and modulation parameters. The channel models are the IEEE 802.22 A, 3GPP Vehicular A and Pedestrian A channels. The IEEE 802.22 standard aims at constructing wireless regional area network (WRAN) utilizing free TV bands. 3GPP two channel models provide different delay path parameters. Main parameters are inspired from the IEEE 802.22 standard [1]. The three channel profiles and main parameters of the system used are shown in Tables 1 and 2.

Table 1.Profiles of the three channels.

Table 2.Main parameters of the systems.

We utilize prototype filters of finite length, denoted by L, that are well-localized in time and frequency. The prototype filter is obtained from the isotropic orthogonal transform algorithm (IOTA), the design of which is described in Ref. [12]. The truncation of the IOTA prototype function, limiting its duration to 4T0, contains L = 4N = 48192 taps. The bit error ratio (BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. The MSE, where Hm is the m th subcarrier channel value, and its estimated value, is plotted with respect to the signal-to-noise ratio (SNR).

Figs. 6(a) and (b) show the BER and MSE performance of the proposed preamble and conventional preambles in the IEEE 802.22 channel model. It is obvious that, in both the BER and MSE cases, the NPS outperforms the other preamble schemes over the entire SNR range considered. In Fig. 6(a), we see that the NPS is slightly better performing than the IC in Ref. [28] method, but has a gain of about 1 and 3 dB compared to E-IAM-C and IAM-C, respectively, when a BER of 10−2 is considered. IC in the scheme described in Ref. [28] outperforms IC the scheme described in Ref. [27] scheme over the entire SNR range considered. The E-IAM-C method performs slightly better than the IC method described in Ref. [27] for low to moderate SNR values. At higher SNRs, the IC method described in Ref. [27] exhibits the better performance, while the BER curves of the E-IAM-C scheme exhibit an error floor. This phenomenon in FBMC/OQAM is due to the fact that the approximation is not exact for channels with significant time dispersion. The trend of the NPS curve may be due to the fact that the value of is variable in odd and even subcarrier, as the analysis described in Sec. 3 shows, its value is greater than that in the IC method at half of the probability, and the other half is less than that.

Fig. 6.(a) BER and (b) MSE performance of the proposed preamble and conventional preambles in the IEEE 802.22 channel.

It can be seen from Fig. 6(b) that, compared with the conventional IC and IAM methods, the channel estimation is effectively improved by the proposed NPS method. The reason is that the variance of is reduced with the NPS method, which improves the channel estimation accuracy. The NPS method provides a significant SNR gain compared to those of the Ref. [27] IC, Ref. [28] IC, IAM-C and E-IAM-C methods at the same MSE level.

Figs. 7(a) and (b) depict the performance of the preambles under the Vehicular A channel, which has a higher sampling frequency than the IEEE 802.22 model as shown in Table 2. Results show an improved performance of the NPS compared to the other four methods, for both BER and MSE measurements.

Fig. 7.(a) BER and (b) MSE performance of the proposed preamble and conventional preambles in the Vehicular A channel.

From Fig. 7(a), compared to the IC and IAM methods, the BER performance is improved with the proposed NPS method. When BER=10−2, the NPS gives performances that are approximately 0.2 dB better than the Ref. [28] IC method, and 1.2, 1.6 and 3.2 dB better than the Ref. [27] IC, E-IAM-C and IAM-C, respectively. The performances for the schemes get very close to each other, because we have adopted a higher sampling frequency channel model. From Fig. 7(b), compared with the conventional four methods, the channel estimation is effectively improved by the NPS. We can find that the MSE performance gains of the NPS scheme compared to the other schemes are evidently less than that shown in Fig. 6(b). The MSE performance of the proposed scheme is 2, 4 and 3.7 dB better than that of the Ref. [28] IC, Ref. [27] IC and E-IAM-C schemes, respectively, when the target MSE of 10−2 is considered. The IAM-C scheme cannot work due to the limiting effect of the SNR region, and its MSE performance is still the worst.

The Pedestrian A-type channel is considered in Figs. 8(a) and (b), where it is shown that the NPS provides effective channel estimation performance improvement that is greater than the other four methods. Reducing the number of delay paths to four, it can be observed from Fig. 8(a) that the entire BER performance is better than that shown in Fig. 7(a), but worse than that shown in Fig. 6(a). The interval between the NPS and IC curves is wider than in Figs. 6(a) and 7(a). As shown in Fig. 8(b), the MSE performance of the proposed scheme is about 3, 7 and 5.5 dB better than that of the Ref. [28] IC, Ref. [27] IC and E-IAM-C schemes, respectively, when the target MSE of 10−2 is considered; the IAM-C scheme still cannot work due to the limiting effect of the SNR region.

Fig. 8.(a) BER and (b) MSE performance of the proposed preamble and conventional preambles in the Pedestrian A channel.

From the simulation results, it can be verified that the proposed preamble scheme provides performance improvement in the three channel scenarios considered. When under a lower sampling frequency channel, with the same number of delay paths, the superiority is reflected more obviously, with a lower SNR obtaining a smaller BER, and a better MSE. When the channel sample frequency is uniform, the system with fewer delay paths can achieve better BER and MSE performance.

 

5. Conclusions

In this paper, we have proposed a novel preamble structure for channel estimation in FBMC/OQAM systems. The IAM and IC schemes are reviewed along with their associated preamble structures. The proposed preamble is compared with three other conventional preambles under the IEEE 802.22, 3GPP Vehicular A, and Pedestrian A channels. The superiority of the proposed preamble-based CE is verified through simulations in the three channel scenarios considered. In the case of low sampling frequency and fewer multipaths, the superiority is reflected more significantly.