Performance Analysis of SC-FDMA and OFDMA in the Analysis of SC-FDMA and OFDMA in the Presence of Receiver Phase Noise Gokul Sridharan and Teng Joon Limy Edward

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  • Performance Analysis of SC-FDMA and OFDMA

    in the Presence of Receiver Phase Noise

    Gokul Sridharan and Teng Joon Lim

    Edward S. Rogers Sr. Department of Electrical and Computer Engineering

    University of Toronto, Canada Department of Electrical and Computer Engineering, National University of

    Singapore, Singapore,


    In this paper we study the effect of receiver phase noise on single carrier frequency division multiple

    access (SC-FDMA) and orthogonal frequency division multiple access (OFDMA). We show that in both SC-

    FDMA and OFDMA, common phase error rotates all the symbols by a certain angle and that the higher order

    frequency components of phase noise result in inter-carrier interference, or ICI. We then study the effect of

    phase noise on the performance of linear receivers that are often used in practice. In particular, we show that

    the amount of ICI affecting the sub-carriers depends closely on the allocation of sub-carriers among different

    users and prove that the performance of linear receivers in the presence of receiver phase noise deteriorates

    much more in the case of interleaved SC-FDMA than in the case of localized SC-FDMA. We identify the

    association of the significant phase noise components with the components of multi-user interference to be

    the fundamental reason behind the performance gap between interleaved and localized SC-FDMA.

    Index Terms

    phase noise, SC-FDMA, inter-carrier interference, linear MMSE receivers.

    Manuscript submitted to the IEEE Transactions on Communications on April 10, 2011. The material in this paper was presented

    in part at the IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) 2011, Toronto, ON,

    Canada, Sept. 11-14, 2011.



    In recent years, many standards have adopted frequency-division schemes such as OFDMA and

    SC-FDMA to serve multiple users in a network, both in the uplink and downlink. It is well known

    that OFDM has a high peak-to-average power ratio (PAPR) which leads to difficulties in transceiver

    design. To address this issue, SC-FDMA has been adopted for uplink transmission in the LTE (3rd

    Generation Partnership Project Long Term Evolution, put forth by European Telecommunications

    Standards Institute) standard [1]. SC-FDMA is essentially a DFT (discrete Fourier transform) precoded

    OFDMA scheme and is known to have a much smaller PAPR than OFDMA [2]. In either scheme,

    sub-carriers can be allocated to users in various ways with channel knowledge at the transmitter of

    varying degrees, it is meaningful to solve a resource allocation problem that optimizes some metric

    of performance such as outage probability or capacity. In this paper however, we focus on the two

    allocation approaches adopted in LTE that does not require channel knowledge of any form at the

    transmitter localized and interleaved. In the former, each user is allocated a set of contiguous

    sub-carriers while in the latter, the users are allocated isolated sub-carriers spaced evenly over the

    transmission bandwidth. Interleaved SC-FDMA offers some diversity benefits over localized SC-

    FDMA. The basic steps involved in SC-FDMA transmission are shown in Fig. 1. The figure also

    includes the use of a linear frequency domain MMSE equalizer at the receiver that compensates for

    the channel on a per carrier basis. Such a structure is widely used in receiver design because of its

    low complexity and ease of implementation. In this paper we focus exclusively on such receivers.

    With multi-carrier systems being widely adopted, it is pertinent for us to study their performance

    under realistic scenarios where receiver impairments play a critical role. In particular, phase noise

    (PHN) is an impairment that needs special attention because unlike other impairments, it changes

    substantially over the duration of a multi-carrier symbol and cannot be compensated for in the training

    stage. In this paper, we present a detailed analysis on the effect phase noise has on an SC-FDMA

    signal and on how it alters the performance of a linear receiver that is oblivious to the presence of

    phase noise. The framework that we use lets us generalize our results to OFDMA as well.

    PHN arises from imperfections in the frequency synthesizer that result in random fluctuations in

    the phase of its output sinusoidal signal. In this paper we assume phase noise to be a first-order

    auto-regressive (AR(1)) process as suggested in [3] for the IEEE 802.11g standard. Further details

    on such a process are given in Appendix A.

    Initial studies on SC-FDMA systems under ideal conditions have shown that SC-FDMA performs

    April 22, 2012 DRAFT


    as well as OFDMA [4] while using frequency domain MMSE equalization. Recent studies have

    also analyzed the performance of SC-FDMA under the influence of different RF impairments such

    as frequency offsets, timing offsets, IQ imbalance etc. In [5] a performance comparison between

    SC-FDMA and OFDMA is presented in the presence of power amplifier non-linearity, where SC-

    FDMA is shown to be better. Performance of SC-FDMA under multi-carrier frequency offsets has

    been simulated in [6]. Antilla et al. [7] discuss the effect of receiver IQ imbalance on SC-FDMA

    waveforms. Sensitivity of SC-FDMA to large frequency and timing offsets was studied in [8]. Priyanto

    et al. [9] show how IQ imbalance, power amplifier non-linearities, as well as phase noise affect the

    SNR of the transmitted signal, but do not discuss the effect these non-idealities have on detection at

    the receiver. To our knowledge, there has been no detailed discussion on how receiver phase noise

    affects an SC-FDMA signal. The effect of PHN on OFDM/OFDMA has been studied extensively

    [10][15] and can be characterized by the rotation of all the sub-carriers by a certain angle called the

    common phase error and the leakage of neighboring sub-carriers resulting in inter-carrier interference

    (ICI). We show that both these effects are also seen in the case of SC-FDMA but are characterized


    The performance of linear MMSE receivers in the presence of phase noise and its dependence

    on sub-carrier allocation among users is the primary subject of this paper and has so far not been

    thoroughly investigated. A surprising result in this context is that although interleaved SC-FDMA

    out-performs localized SC-FDMA under ideal conditions by exploiting frequency diversity, in the

    presence of phase noise, interleaved SC-FDMA may perform worse. Using insights from the signal

    model that we derive, we show how this difference in performance arises and further quantify the

    performance loss through a detailed analysis of the SINR (signal to interference and noise ratio)

    expression in the two cases.

    The paper is organized as follows. In Section II we set up the signal model for a multi-user uplink

    transmission using SC-FDMA and focus on linear MMSE receivers used to detect SC-FDMA signals.

    In Section III we study how phase noise affects the received signal before and after being processed

    by the linear receiver. We then discuss how the SINR of the received signal after receiver processing is

    affected by the choice of sub-carrier allocation among different users and establish that localized SC-

    FDMA is more robust to PHN than interleaved SC-FDMA. Finally, in Section IV we investigate how

    interference resulting because of phase noise depends on various system and phase noise parameters.

    In this paper, all vectors are represented in bold lowercase font and all matrices are represented in

    April 22, 2012 DRAFT


    bold uppercase font. The notation diag(M) is used to represent the column vector formed using the

    diagonal of the matrix M. circ(v) is used to represent the square right circulant matrix formed using

    the vector v. E[.] and V ar(.) are used to denote the expectation and variance of a random variable.


    A. The received signal without phase noise

    We first consider the detection of an SC-FDMA symbol transmitted over a block fading frequency

    selective channel where the channel stays constant over the duration of a whole symbol and there is

    no phase noise. We assume that perfect frame synchronization, including carrier frequency recovery

    has been established in the training stage. We further assume that current channel conditions have

    been estimated during the training phase and that the channel state information is available at the

    receiver. The model established here is essential in understanding the the effect of phase noise on a

    conventional LMMSE receiver for SC-FDMA.

    We consider a wireless network with K users communicating to a base station using SC-FDMA or

    OFDMA, with each user being assigned M sub-carriers. Let the total number of sub-carriers be N ,

    with N = MK. Each user performs an M-DFT precoding of the symbols, maps the M-DFT output

    to its assigned sub-carriers, and then performs multi-carrier modulation with an N-IDFT operation.

    If we let the M 1 symbol vector of the kth user be denoted as dk, the N 1 time domain transmit

    vector xk(after cyclic prefix removal) corresponding to the kth user can be written as

    xk = FHNTkFMdk, (1)

    where Tk is an N M sub-carrie