Phase Noise Estimation and Compensation Algorithms for 5G Systems

Phase noise, introduced by the receiver local oscillator, has severe effects on the performance of orthogonal frequency division multiplexing (OFDM) systems. The common compensation method can only correct common phase error (CPE) caused by the low-frequency part of the phase-noise spectrum, and cannot compensate phase noise thoroughly. A new method, per-symbol phase noise detection and compensation method, is proposed. Based on a frequency-domain linearized parametric model for phase noise, the method not only deals with CPE more effectively, but also compensates most of the intercarrier interference (ICI) induced by the high-frequency part of the phase-noise spectrum. This method well compensates phase noise in higher SNRs and lower quality tuners.

Orthogonal frequency division multiplexing (OFDM) systems work well if the subcarriers are orthogonal to each other. However, the orthogonality among subcarriers may not exist and result in inter-carrier interference (ICI) at the receiver. This may cause by residual carrier frequency offset, time variations due to Doppler shift or phase noise. Further developing the parallel cancellation (PC) scheme to mitigate the ICI of OFDM systems, we expand this OFDM symbol-based PC scheme into a space-frequency (SF) coded system. This new simple space- frequency parallel cancellation (SFPC) scheme is a technique that combines the SF and PC schemes together. Computer simulations indicate that OFDM systems using the SFPC scheme outperform the regular PC and SF systems in slow and fast frequency selective fading channels, specifically at a high signal-noise-ratio (SNR). Furthermore, the error floor of the SFPC-OFDM system is significantly lower than that of the PC and SF systems without increasing computational load. Additionally, the SFPC scheme is a simple multiple input and multiple output (MIMO) system.

OFDM (orthogonal frequency division multiplexing) systems are very sensitive to carrier frequency offset. Although frequency offset is generally compensated for by an automatic frequency control (AFC), residual frequency offset remains after the AFC. Moreover, OFDM signals are also affected by phase noise. Thus, a kind of phase tracking is needed to compensate for these effects. In an OFDM system such as IEEE 802.11a, a phase tracking scheme that uses pilot subcarriers to detect the phase rotation caused by residual frequency offset and phase noise is employed. However, the spectrum of the AFC output signal is shifted by residual frequency offset. That is, the detected phase is the composite phase of the pilot subcarrier and the adjacent subcarrier because of inter-carrier interference (ICI). The compensation based on the composite phase sometimes overcorrects or undercorrects the phase rotation. In this paper, we propose a phase tracking scheme using iterative estimation of residual frequency offset in OFDM systems. The proposed phase tracking scheme estimates residual frequency offset in the frequency domain, and compensates for it in the time domain. The compensation in the time domain mitigates the spectrum shift of the AFC output. Therefore, the proposed scheme can reduce ICI, and track phases more accurately than the conventional phase tracking scheme.

The time-varying nature of multipath channels in Orthogonal Frequency Division Multiplexing (OFDM) systems causes intercarrier interference (ICI) and complicates the channel estimation at the receiver. The introduction of the local oscillator phase noise further destroys the orthogonality between subcarriers, thus increasing the ICI contribution. In this paper, we investigate the combined effects of channel estimation errors and receiver oscillator phase noise. Furthermore, the common phase error (CPE) is also accounted for in the OFDM system. Using M-QAM modulation in Rayleigh fading channels, we also compare the system performance when the phase noise process assumes different distributions, and present analytical results for illustration, followed by simulation results for validation.

It is well known that Orthogonal Frequency Division Multiplexing (OFDM) systems suffer from intercarrier interference (ICI) in mobile environment due to loss of orthogonality among subcarriers caused by Doppler shifts. There exist many ICI mitigation techniques in the literature to improve the performance of OFDM systems. However, most of the existing ICI mitigation techniques assume the OFDM transmission bandwidth is narrow enough that the frequency offsets on all subcarriers are identical. In a wideband OFDM transmission or a non-contiguous OFDM spanning over large bandwidth, the Doppler shifts on different subcarriers are different, especially in high speed aerial vehicle communication systems. In this paper, we analyze the wideband OFDM system in high mobility environment where the frequency offsets vary from subcarrier to subcarrier. We then propose a novel ICI cancellation scheme to eliminate the ICI effect and offer the wideband OFDM system significantly improved BER performance. Simulation results in AWGN channel and multipath fading channel confirm the effectiveness of the proposed scheme in the presence of frequency offset and time variations in the channel, offering the best BER performance available which matches the BER performance of wideband OFDM system without ICI. To our knowledge, this paper is the first to address the ICI problem of varying frequency offsets across subcarriers in wideband OFDM system.

Low complexity blind detection in OFDM systems with phase noise

Orthogonal frequency division multiplexing (OFDM) is a method suitable for high-rate data transmission in wireline and wireless communications. However, it is very sensitive to frequency offset due to Doppler shifts and carrier synchronization errors. This frequency offset results in inter-carrier interference (ICI) and, as a result, the performance of the OFDM system degrades drastically. Consequently, it, is necessary to remove as many ICI effects as possible to achieve the desired OFDM system performance. Therefore, in this paper, we propose a new method based on a nonlinear adaptive filter to suppress these ICI effects. In addition to showing that the ICI effects can be reduced significantly, the results also demonstrate that the nonlinear filter scheme is superior to the conventional linear filter.

This paper considers the problem of analytically assessing the maximum achievable rates (capacity) of orthogonal frequency division multiplexing (OFDM) transmissions when the receiver, for complexity reasons, only accounts for the common phase error (CPE) effect due to phase noise impairments with inter-carrier interference (ICI) treated as noise. By recognizing that the functional form of the CPE with respect to the phase noise realization is actually a free design parameter, determination of the capacity is posed as a functional optimization problem with respect to the, so-called, CPE function. A simple lower bound of the capacity is obtained, revealing the performance degradation due to the unknown CPE at the receiver, as well as the suboptimal performance achieved in severe phase noise conditions by the conventional CPE function that is routinely employed in previous works. The existence of an optimal number of subcarriers that balances the effects of the (unknown) CPE and ICI is highlighted and critical system design/operation issues, such as selection of the CPE function and effect of unknown channel on the achievable rate, are discussed. The analysis in this paper can be employed for determining the suitability of OFDM in phase noise channels and provides a tractable utility function for resource allocation purposes.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

Orthogonal frequency division multiplexing (OFDM) systems are very sensitive to phase noise caused by oscillator instabilities. In this paper the phase noise is resolved into two components, namely the common phase error (CPE), which affects all the subchannels equally and the intercarrier interference (ICI), which is caused by the loss of orthogonality of the subcarriers. We present a technique to estimate and correct the CPE component and demonstrate its effectiveness when applied to a broadband fixed wireless access (BFWA) data transmission system for the multichannel multipoint distribution service (MMDS) band. We show a performance increase up to 6 dB when applying the CPE correction in terms of the tolerance to the phase noise variance, /spl sigma//sub /spl psi///sup 2/.

ABSTRACTWhile inter-symbol interference is not of concern, inter-carrier interference that is caused by carrier frequency offset (CFO) is more concerned in orthogonal frequency division multiplexing (OFDM) systems. The estimation of channel impulse response (CIR) is another important parameter of interest in the system. Recently, a number of approaches for the joint estimation of CFO and CIR in OFDM systems have been proposed in the literature, and most of them are traditional maximum-likelihood-based approaches. In this paper, we propose a number of mixture cost-reference particle filtering (CRPF) approaches for joint estimation of CIR and CFO, and a couple of them can be applied without the knowledge of both state and measurement noise statistics. Conventional least mean squares algorithm or recursive least squares algorithm is jointly employed with recently developed CRPF for nonlinear and multiple parameters estimation in OFDM systems. The computer simulation results show that mixture CRPFs are more robust against particle impoverishment (PI) problem than standard mixture particle filtering (PF) and mixture regularized PF (RPF) approaches although RPF was particularly developed to tackle the PI problem. In this paper, we investigate a number of mixture PF approaches including ones that do not need the information of noise statistics for the joint estimation of CFO and channel in OFDM systems.

Orthogonal frequency-division multiplexing (OFDM) is robust against frequency selective fading because of the increase of the symbol duration. However, the time-varying nature of the channel causes inter-carrier interference (ICI) which destroys the orthogonal of sub-carriers and degrades the system performance severely. To alleviate the detrimental effect of ICI, there is a need for ICI mitigation within one OFDM symbol. We propose an iterative Inter-Carrier Interference (ICI) estimation and cancellation technique for OFDM systems based on regularized constrained total least squares. In the proposed scheme, ICI aren’t treated as additional additive white Gaussian noise (AWGN). The effect of Inter-Carrier Interference (ICI) and inter-symbol interference (ISI) on channel estimation is regarded as perturbation of channel. We propose a novel algorithm for channel estimation o based on regularized constrained total least squares. Computer simulations show that significant improvement can be obtained by the proposed scheme in fast fading channels.

On the basis of the analysis of the effect of PHase Noise (PHN) and Common Phase Error (CPE) on Orthogonal Frequency Division Multiplexing (OFDM) systems, a cost function is constructed. By the cost function and the idea of Least-Mean-Square (LMS) adaptive algorithm, the adaptive algorithm for the correction of CPE is presented. The simulations have been performed to investigate the performance for tracking PHN and estimating CPE, the results show that the algorithm performs soundly.

The nonlinearity of high power amplifiers (HPAs) exhibits amplitude and phase distortions, which cause loss of orthogonality among the subcarriers in orthogonal frequency division multiplexing (OFDM) systems, and hence, inter-carrier interference (ICI) is introduced in the transmitted signal. The ICI power is proportional to the amplitude of the signal at the amplifier input and it may cause a considerable bit error rate (BER) degradation. Due to the ICI is a random process and has unknown distribution function, it is difficult to evaluate the theoretical BER when the ICI is taken into account. This paper evaluates the BER analytically using sequence development approach (SDA) for OFDM systems perturbed by the HPA. In comparison to the state-of-the-art technique, the evaluation of the BER using this approach achieves superior approximation at the expense of additional computational complexity.

OFDM(Orthogonal Frequency Division Multiplexing) 시스템에서 직교 불균형 문제는 송수신기의 front-end에서 발생하며, 성상도에 영향을 주게 되어 BER(Bit Error Rate)을 증가시킨다. 또한, 위상 잡음은 송수신시 국부 발진기에서 발생되는 잡음으로 각 부반송파의 직교성을 깨뜨림으로써 시스템 성능을 크게 저하시킨다. 기존 방식인 PNS(Phase Noise Suppression) 알고리즘은 이러한 위상 잡음을 효과적으로 제거하는 방법이지만 직교 불균형 이동시에 적용되면 오히려 성능이 감소된다. 본 논문에서는 OFDM 시스템의 수신기에서 하향 변환 시 발생하는 직교 불균형과 위상 잡음의 영향을 분석하고, 수신기 FFT(Fast Fourier Transform) 후단에서 파일럿 심볼을 사용하여 CPE를 먼저 제거하고 직교 불균형과 위상 잡음의 성분을 검출하여 등화기의 판정 기준으로 사용하여 보상하는 방법을 제시하였다. 또, 다른 기존 방식들은 FFT 후단에서 추정하고 피드백 시키거나 프리엠블과 같은 시퀀스를 사용하는 방식이지만, 본 논문에서는 FFT 후단에서 MMSE 등화기만을 사용하여 제거하므로 기존의 방법보다 복잡도가 줄어든다. 기존의 위상 잡음 제거 방식에 ICI(Inter Carrier Interference) 제거 기능을 추가하고 직교 불균형 성분을 추출하여 MMSE(Minimum Mean Square Error) 과정 중에 적응 forgetting factor를 적용하면 성능 개선과 직교 불균형 성분의 영향이 줄어들며 성능이 개선됨을 보인다. In the OFDM system, IQ imbalance problem happens at the RF front-end of transceiver, which degrades the BER(bit error rate) performance because it affects the constellation in the received signal. Also, phase noise is generated in the local oscillator of transceivers and it destroys the orthogonality between the subcarriers. Conventional PNS algorithm is effective for phase noise suppression, but it is not useful anymore when there are jointly IQ(In-phase and Quadrature) imbalance and phase noise. Therefore, in this paper, we analyze the effect of IQ imbalance and phase noise generated in the down-conversion of the receiver. Then, we estimate and compensate the IQ imbalance and phase noise at the same time. Compared with the conventional method that IQ imbalance after IFFT is estimated and compensated in front of FFT via the feedback, this proposed method extracts and compensates effect of IQ imbalance after FFT stage. In case IQ imbalance and phase noise exist at the same time, we can decrease complexity because it is needless to use elimination of IQ imbalance in time domain and training sequences and preambles. Also, this method shows that it reduces the ICI and CPE component using adaptive forgetting factor of MMSE after FFT.