Elsevier

Signal Processing

Volume 167, February 2020, 107298
Signal Processing

A general framework for joint estimation-detection of channel, nonlinearity parameters and symbols for OFDM in IoT-based 5G networks

https://doi.org/10.1016/j.sigpro.2019.107298Get rights and content

Highlights

  • An iterative joint estimation/detection algorithm to jointly estimate channel and nonlinearity parameters and detect symbols.

  • Considering general memoryless nonlinearity models in OFDM systems.

  • A general CRLB is derived for general case of memoryless nonlinearities with real parameters.

  • Considering fast-fading channels and using comb-type pilots.

Abstract

Despite being a strong candidate also for future cellular networks, OFDM’s main drawback is the high peak-to-average power ratio. This requires transmitters to deploy high dynamic range power amplifiers which are difficult to manufacture and thereby expensive. It is particularly problematic in future IoT-based 5G networks, in which a lot of presumably low-cost low-power devices transmit data to a high-quality receiver. In order to make such transmitters as simple and cheap as possible, we consider receiver-side nonlinearity compensation and symbol detection. In particular, we study the problem of joint maximum-likelihood estimation-detection of channel and nonlinearity parameters and symbols using frequency-domain comb-type pilots in multi-path fading OFDM systems, and propose an iterative optimization algorithm to solve it. We also calculate the Cramér-Rao lower bound for a general type of memoryless nonlinearity and show that the proposed algorithm attains it, for high signal-to-noise ratios. We then show by numerical evaluations that the algorithm converges fast and the difference of its performance with the one of the genie-aided scenario, with perfect a priori knowledge of nonlinearity parameters and channel, is negligible.

Introduction

Orthogonal frequency division multiplexing (OFDM) is one of the most popular multi-carrier transmission methods that has been recognised as the most effective technique for high-speed wireless communications. It enjoys being immune to multipath fading channels, having maximal spectral efficiency, and having the capability of being implemented on low-cost embedded devices. Due to these attractive features, OFDM has been adopted in several technologies and standards such as 4G (LTE and its evolutions so far) and IEEE 802.11 (WiFi). More recently, OFDM using cyclic prefix (CP-OFDM) which is the main focus of this paper, has triumphed over other rivals in the race to 5G new radio (NR) [1].

Despite its impressive characteristics, OFDM suffers from a high peak-to-average power ratio (PAPR). One immediate solution to this problem is designing and deploying high power amplifiers (HPAs) with high dynamic range. However, manufacturing such HPAs is expensive which makes using them in low-cost devices economically infeasible. It will also be more problematic in future wireless networks, particularly in case of applying OFDM to millimeter wave (mmWave) spectrum in (IoT)-based 5G NR, since manufacturing efficient HPAs is much more difficult and costly at those frequencies [2]. The other way to overcome the problem of OFDM’s high PAPR is forcing the HPA to work in its linear region by introducing a high input back-off (IBO). However, this not only leads to low signal-to-noise-ratio (SNR) at the receiver side, but reduces the HPA energy efficiency, and hence results in increased energy consumption. This situation prevents the use of OFDM in (Internet of things) IoT-based communication networks such as machine type communications (MTC) [3], which presumably consist of low-power devices working on years-long button batteries, or for vehicle to everything (V2X) services [4]. The third approach which is also the underlying assumption of this paper, is to let the HPA’s operating point be close to its saturation level and the high PAPR OFDM signal get distorted as a result of the nonlinearity introduced by the HPA. This way is conducive to having a highly efficient HPA, and hence less power consumption which makes it usable in low-cost low-power devices. Nevertheless, we need to devise solutions to deal with the distorted transmitted signal since it causes inter-subcarrier interference, and hence degrades the performance of the system.

There are many works in the literature that have proposed solutions to deal with the HPA nonlinearity distortion. These works are mainly categorized into three approaches. The first one is to deploy a pre-distorter just before the HPA in series to make the cascaded system behave as a linear system [5]. The second approach is a low PAPR signal design using signal processing and coding techniques [5]. However, both of these approaches suffer from increased complexity and cost at the transmitter. The third approach which is also the purpose of this paper is to leave the distortion at the transmitter side, but compensate it at the receiver side. It is particularly an attractive solution in uplink transmissions, as we can transfer all the complexity and cost to the receiver side which is a high quality receiver such as a base station (or an IoT gateway), and make the transmitter as simple and cheap as possible. Towards this goal, the first work was introduced in [6], which is an iterative symbol detection algorithm that aims to estimate the distortion and remove it from the received symbols in each iteration at the receiver side. However, in this work, it is assumed that channel and nonlinearity are known a priori, which is not the case in practical situations, especially in IoT-based networks. In particular, the receiver needs to estimate (and re-estimate) the nonlinearity parameters since there are a lot of low-cost devices, each having different manufacturing qualities. Furthermore, measuring and calibrating them would be very costly. Moreover, the HPA characteristics and parameters can change because of environmental conditions such as temperature and humidity [7].

There are several works in the literature that aim to integrate channel or nonlinearity parameters estimation with the iterative symbol detection algorithm [8], [9], [10], [11], [12]. However, all of these works assumed either no multipath channel, or a known multipath channel, or estimating the multipath channel using conservatively low-magnitude pilots not affected by the nonlinearity. The latter limits the practical applicability since using low-magnitude pilots can cause problems with coverage, and also the nonlinearity parameters can be unknown to the transmitter itself a priori. The authors in [7] proposed a joint channel and clipping level estimation using block-type pilots for an OFDM system with a clipper (limiter) at the transmitter side. It is shown that the performance of the proposed algorithm is really close to the iterative symbol detection algorithm with a perfectly known channel and clipping level.

In this paper, we propose an iterative joint estimation-detection algorithm to jointly estimate channel and nonlinearity parameters and detect symbols for a general memoryless HPA model, for an OFDM system which uses comb-type pilots. To the best of our knowledge, there is no other work in the literature which considers such a joint estimation-detection problem for OFDM systems. Next, to demonstrate the applicability of this general proposed algorithm, we apply it to limiters as an example of a non-smooth nonlinearity and also polynomial models by which all smooth memoryless nonlinearities can be approximated. Furthermore, note that there are two reasons that we consider comb-type pilots. The first is that it can better track and estimate channels in fast-fading situations, in which the channel remains the same just for a few OFDM symbols (one OFDM symbol in this work) [13], [14]. Moreover, it is compatible with the existing 4G LTE standards [15] and 5G NR [1]. The comb-type and block-type pilot schemes are illustrated in Fig. 1.

More specifically, the main contributions of this work in comparison to [7] are as follows:

  • 1.

    In [7], block-type pilots are used, i.e., a whole OFDM symbol is dedicated to frequency-domain pilots (Fig. 1a). Therefore, the process of channel and nonlinearity parameter estimation and process of symbol detection are separated. However, here, in this paper comb-type pilots are used, which means that pilot tones and data tones are present together in an OFDM symbol (Fig. 1b). This leads to the need of having a joint estimation-detection algorithm to simultaneously perform the process of channel and nonlinearity parameter estimation and process of symbol detection. This paper proposes such an algorithm.

  • 2.

    The authors in [7] use the iterative detection algorithm proposed in [6] without changing it to detect the subsequent OFDM symbols. The channel and nonlinearity parameter estimates calculated using the previous all-pilot OFDM symbol are incorporated in the iterative detection algorithm. However, in this paper, we modify and propose a novel version of the iterative detection algorithm to make it compatible with the OFDM symbol consisting of pilot and data tones, and combine it with the estimation process. In particular, we devise a decision-directed method in which the estimation process is done using the detected symbols from the previous iteration.

  • 3.

    Moreover, in this paper, we broaden our attention to the whole set of memoryless nonlinearity models.

The remainder of this paper is organised as follows. Section II provides a detailed description of the considered system model in this paper. Section III discusses the proposed estimation-detection algorithm to jointly estimate channel and nonlinearity parameters and detect symbols. Section IV discusses the performance of the estimation part of the algorithm and provides a theoretical lower bound on its performance. Sections V, and VI demonstrate the application of the proposed algorithm for limiters, and memoryless polynomial nonlinearities, respectively. Section VII depicts numerical results and illustrates the performance of the proposed method. Finally, conclusions are drawn in Section VIII.

Section snippets

System model

We consider a baseband-equivalent OFDM system with N subcarriers, as illustrated in Fig. 2, in which s=[s[0],,s[N1]]T is the frequency-domain input vector consisting of multiplexed comb-type pilots and data tones, all drawn from a finite set of constellation points such as QAM denoted by S. The Np pilots are inserted in s in such a way that the total N subcarriers are divided into Np groups with length Lp=N/Np, and in each, the first subcarrier is allocated by a pilot. Therefore, for the k-th

Joint channel-nonlinearity parameters estimation and symbol detection

In this section, we propose an estimation-detection iterative algorithm to jointly estimate channel and nonlinearity parameters and detect symbols with the help of frequency-domain comb-type pilots for a general memoryless HPA nonlinearity model in an OFDM system.

Using frequency-domain comb-type pilots, the problem of joint maximum-likelihood (ML) estimation-detection of channel and nonlinearity parameters and symbols can be formulated as the following least-squares (LS) problem using (6):minθNL

Cramér-Rao lower bound

The Cramér Rao lower bound (CRLB) gives a lower bound on the variance of any unbiased estimator. The ML estimator asymptotically achieves the CRLB under some regularity conditions [29]. Here, we have a hybrid estimation and detection problem. To deal with this, we find the CRLB for estimation parameters under the assumption that the detection parameters are perfectly known a priori, i.e., the data symbols act as pilot symbols thereby providing a lower bound. The estimation parameters comprise

Limiter as the nonlinearity

In this section, we consider clipping as the nonlinearity. There are four reasons that this nonlinearity model requires specific attention.

  • 1.

    Deliberate clipping can be used to reduce the PAPR of the OFDM signal at the transmitter side.

  • 2.

    It is, itself, a simplified yet useful model of nonlinear HPAs.

  • 3.

    In the case of using a pre-distorter, the cascaded combination of the pre-distorter and the HPA is often well-approximated by a clipper.

  • 4.

    Due to its non-smoothness, it cannot be modeled by polynomials.

  • 5.

    It

Nonlinearity modeled by polynomials

Polynomials can give us freedom in modeling smooth memoryless nonlinearities. They can be used for nonlinearities with known models (SSPA, TWTA) and also as a generic model for nonlinearities whose functions are unknown. In this way the nonlinearity function becomes linear in the nonlinearity parameters, which makes it more mathematically tractable. However, when aiming to estimate the polynomial coefficients, working directly with the model given by (15) can cause numerical instability

Numerical results

In this section, the performance of the proposed estimation-detection algorithm is investigated by means of numerical simulations. The subcarrier modulation scheme is 16QAM. Two different number of subcarriers N=128 and 512 are considered here. The subcarrier spacing is 15 KHz, hence the sampling rate of 20 MHz works fine for both cases. Furthermore, two different multipath Rayleigh fading channel models are used here, which are as follows:

  • Exponential power delay (EPD) Model [33]: This model

Conclusion

In this paper, we have studied joint maximum-likelihood estimation of channel and nonlinearity parameters and symbol detection at the receiver side in future IoT-based 5G cyclic prefix based OFDM networks using frequency-domain comb-type pilots. In such networks, there are lots of low-cost low-power nodes transmitting to and receiving from more complex nodes such as a base station, therefore estimation of nonlinearity parameters along with channel estimation and symbol detection greatly matters

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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