Phase Noise Modelling and Mitigation Techniques in OFDM Communications Systems

Transcription

1 Phase Noise Modelling and Mitigation Techniques in OFDM Counications Systes Ville Syrjälä, Mikko Valkaa, Nikolay N. Tchaov, and Jukka Rinne Tapere University of Technology Departent of Counications Engineering Korkeakoulunkatu 1, FI Tapere, Finland E-ail: Abstract This paper addresses the analysis and itigation of the signal distortion caused by oscillator phase noise (PN) in OFDM counications systes. Two new PN itigation techniques are proposed, especially targeted for reducing the intercarrier interference (ICI) effects due to PN. The first proposed ethod is a fairly siple one, steing fro the idea of linearly interpolating between two consecutive coon phase error (CPE) estiates to obtain a linearized estiate of the tievarying phase characteristics. The second technique, in turn, is an extension to the existing state-of-the-art ethods. Here the idea is to use an additional interpolation stage to iprove the phase estiation perforance around the boundaries of two consecutive OFDM sybols. The paper also verifies the perforance iproveent of these new PN estiation techniques by coparing the to the existing stateof-the-art techniques using extensive coputer siulations. To ephasize practicality, the siulations are carried out in 3GPP- LTE downlink like syste context, covering both additive white Gaussian noise (AWGN) and extended ITU-R Vehicular A ultipath channel types. Index Ters phase noise; OFDM; coon phase error; intercarrier interference; LTE O I. INTRODUCTION RTHOGONAL Frequency-Division Multiplexing (OFDM) is a ulticarrier odulation schee used in any odern and eerging counications standards, e.g., Digital Video Broadcasting (DVB), wireless local area networks such as IEEE g, and 3GPP Long Ter Evolution (LTE). Copared to traditional single carrier odulation ethods, OFDM has its strengths and weaknesses. Steing fro the long sybol duration and thus efficiently ipleentable guard interval (GI), OFDM is relatively iune against inter-sybol interference (ISI). Furtherore, ulticarrier transission enables efficient use of adaptive odulation and coding schees, and also This work was supported by the Finnish Funding Agency for Technology and Innovation (Tekes, under the project Advanced Techniques for RF Ipairent Mitigation in Future Wireless Radio Systes ), the Technology Industries of Finland Centennial Foundation, Finnish Foundation for Technology Prootion, EUREKA CELTIC E!3187 B21C-Broadcasting for 21st Century, and TUT Graduate School. provides robustness against frequency-selective fading in ters of fairly siple equalization. On the other hand, OFDM iposes high deands for the quality of the used radio devices, being especially sensitive, e.g., to oscillator nonidealities. These include different synchronization errors as well as rando phase fluctuations called phase noise [2], [15], [17]. On radio ipleentation side, there are currently big deands for saller and ore energy efficient radio transitters and receivers. Even higher deands for the radios will be set, when any transceivers, or parts of the transceivers, ust be operating siultaneously in a single device. This kind of configuration coes into play, e.g., when ipleenting radio devices for ultiple-input ultipleoutput (MIMO) transission systes. In general, because of these high deands for the transceivers, it is very iportant to understand and try to itigate possible non-idealities in the transission chain coponents. This is called dirty-rf signal processing in general [10]. The ipact of PN on OFDM systes has been extensively studied, e.g., in [2], [12] and [15]. The distortion due to PN can in general be divided into two coponents: coon phase error (CPE) and intercarrier interference (ICI). While CPE refers to the constant phase rotation experienced by all the subcarriers within one OFDM sybol interval, ICI corresponds to neighbouring subcarriers interfering with each other. The itigation of CPE alone has generally been widely investigated. A siple ethod for CPE itigation has been presented in [12], and the sae ethod has been further iproved in [16], also trying to reove soe ICI. In addition, various techniques for ICI itigation have been developed. For exaple, [11] has presented a very illustrative technique for ICI itigation steing fro iterative detection principles. The sae group has also published soe perforance iproveents to their ethods in [4] and [5]. This paper concentrates on enhanced PN odelling and itigation schees. In Section II, odelling of free-running and PLL-based oscillators is shortly addressed. Section III concentrates on the analysis of PN effects on OFDM wavefors. Section IV then gives a short review of essential state-of-the-art in PN itigation including [5], [11], and [16] /09/$ IEEE.

2 Section V is the ain contribution of this paper, introducing two new PN itigation schees. The first one is relatively siple and is based on linear interpolation of the CPE values over adjacent OFDM sybols. The second one concentrates on iproving the perforance of the ethods presented in [11] and [5] by iproving the PN estiation accuracy at sybol boundaries using proper interpolation. Section VI then actually analyzes the itigation perforance of the proposed and reference techniques using coputer siulations. Finally, Section VII concludes the work. II. PHASE NOISE MODELLING In addition to ordinary carrier frequency and phase offsets, the tie-varying phase behaviour of the used oscillator(s) is one of the ost challenging non-idealities in radio devices. In this paper, we focus on the phase noise aspects, and both free-running and phase-locked loop (PLL) type oscillators are considered. A general signal-level odel for a noisy coplex (I/Q) oscillator is typically forulated as j2 π fct jφ () t α (), (1) osc t e e where φ (t) denotes the phase noise and f c is the noinal oscillating frequency, i.e. carrier frequency for oscillators in direct conversion receiver. In the following, ore detailed characteristics of the phase noise φ (t) are addressed for different types of oscillators. A. Free-Running Oscillators Free-running oscillator odel is very siple and illustrative. In the literature [13], the phase noise of a freerunning oscillator is typically assued to follow Brownian otion (also called Wiener Process). Accurately, we can define the PN for a free-running oscillator as φ () t cb() t, (2) in which B(t) denotes standard Brownian otion and c is the so-called diffusion rate [13]. Standard Brownian otion B(t), in turn, is defined as a rando process for which B(t 2 ) B(t 1 ) is Gaussian distributed with zero ean and variance t 2 t 1. Thus, we are able to odel the PN process with a single paraeter c. The process in (2) has a variance that linearly increases with tie [9], written here as σ 2 () t c t. (3) φ Decay of power spectral density (PSD) is a coonly used quantity to define oscillator PN properties. Now, we can ap the diffusion rate c to the PSD in order to siplify the paraeterization of the odel. First of all, one-sided PSD of the oscillator α osc in (1) around the carrier frequency attains the Lorenzian spectru and is given by c S( Δ f) (2 π Δ f) + ( c/ 2) 2 2, (4) where Δf is the frequency offset fro the noinal centre frequency f c of the oscillator [13]. Fro (4), the rate of decay at larger offsets is -20 db/decade, and the 3 db bandwidth of the PSD is given by c β. (5) 4π This 3 db bandwidth in (5) gives us an easily interpretable reference paraeter and is used fro now on in free-running oscillator characterizations. B. Phase-Locked-Loop Oscillators In practice, phase-locked-loop (PLL) based oscillators are typically used. Here, a PLL phase noise odel, which contains both white and flicker noise perturbations to φ (t), is presented. In general, the PLL PN output is doinated by the reference crystal oscillator (CO) below the loop bandwidth f LBW, and by the voltage controlled oscillator (VCO) above f LBW. Conteporary integrated CMOS VCOs can exhibit significant flicker noise contributions that cannot be neglected [6]. For a free-running VCO with flicker noise, the variance of φ (t) over tie t becoes [8] σ t t 2 2 white+ () t (2 π fc ) cωt + c f RN ( t1 t 2) dt1dt2 flicker 0 0, (6) where c ω and c f are the constants describing white and flicker noise perturbations. These constants can, in practice, be found through circuit siulator or spot PN-PSD easureents at large offsets, fro [8] L ( f ) ( ω + ( Δ )) 2 ( ) 2 fc c cfsf f Δ π f c + c S Δ f +Δf ( ω ) c f f. (7) In (7), S f (Δf ) is the flicker noise PSD at offset Δf fro the carrier and can be written as [8] Sf 1 2 tan γ c Δ, (8) Δf πδf 2πΔf 1 ( f ) where γ c specifies the cutoff frequency at which the flicker noise PSD deviates fro its noinal 1/Δf slope. In the PLL odel, the excess phase variance deviates fro (3) depending on the PLL ipleentation and noise type perturbations. In first-order PLL with white noise perturbations only, the variance of φ (t) saturates at [7]

3 2 2 2π fc cω li σφ, white ( t). (9) t f Notice also that, the ipleented PLL odel flattens the VCO and CO excess phase PSD S Φ (Δf ) to constant levels at sall offsets Δf and thus eliinates a singularity at the carrier that is associated with the Brownian otion odel [7]. An exaple generation of the PLL output PN PSD with f LBW 2 khz is shown in Fig. 1. The corresponding PN spot easureents are suarized in Table I. III. OFDM SYSTEM MODELLING In a general OFDM syste with N subcarriers, the tiedoain wavefor saples are obtained by N-point inverse fast Fourier transfor (IFFT) of the subcarrier data sybols [3]. Thus, at -th OFDM sybol interval, these saples can be written as LBW 1 x( n) X ( k) e N N 1 j 2 π nk / N, (10) k 0 where X (k) denotes the k-th subcarrier data sybol during -th OFDM sybol interval. Every OFDM sybol has also a cyclic prefix (CP), which copies the last G saples of (10) before the first saples, giving the extended OFDM-sybol length of N +G saples. [11] After the ipact of a ultipath channel, receiver downconversion with PN, and reoval of the CP, we can write the received saples for -th OFDM sybol as a vector Power Spectral Density [dbc/hz] PLL L(Δf): generated FR VCO L(Δf) 140 FR CO L(Δf) PLL L(Δf): ask Frequency Offset fro Carrier [Hz] Fig. 1. Exaple of PLL output phase noise for centre frequency of GHz. PN spot reading TABLE I EXAMPLE PLL MODEL PARAMETERS Flicker noise perturbation region (-30 db/decade) White noise perturbations region (-20 db/decade) CO No flicker noise region L CO (100 Hz) -90 dbc/hz VCO L VCO (30 khz) -75 dbc/hz L VCO (1 MHz) -110 dbc/hz transfer function, η is the FFT of AWGN, and J is the FFT of exp( jφ ). The J can be written explicitly as 1 J ( k) e e N N 1 jφ ( n) j 2 π nk / N. (13) n 0 j r diag( e φ )( x h ) + n. (11) Here, is a circular convolution operator, x is the vector of saples of -th transitted OFDM sybol, h is the channel ipulse response, and n is Additive White Gaussian Noise (AWGN) vector. In addition, φ is a vector that has PN realization saples within -th OFDM sybol, so φ [φ (0),..., φ (N-1) ] T. In this odel, it is assued that transitter has no PN. This assuption can be ade because receiver PN has been shown to doinate the contribution PN has on the total syste perforance [13]. Also, as entioned in [11], with sall PN bandwidths, the transitter PN can be effectively referred to RX side. Next, the received signal vector is deodulated using FFT. The resulting frequency-doain signal vector, following directly fro (11), is given by R J ( X H ) + η. (12) Here, is an eleent-wise ultiplication operator, X is the vector of transitted subcarrier sybols, H is the channel Now, it can be noted that the coponents of (12) can be written essentially in two parts as R( k) X( k) H( k) J(0) N 1. (14) + X () lh () lj ( k l) + η ( k) l 0, l k This splitting is very iportant for our analysis purposes, because it divides the PN contribution to two different parts. The first and the second parts of (14) are the CPE corrupted and ICI corrupted parts of the signal, respectively. The CPE eans coon phase rotation of every subcarrier data inside one OFDM sybol. ICI, on the other hand, is the intercarrier interference that every subcarrier causes to each other due to frequency spreading by PN. [11], [17] IV. STATE-OF-THE-ART PHASE NOISE ESTIMATION AND MITIGATION TECHNIQUES This Section gives a short overview of state-of-the-art PN itigation techniques, originally presented in [5], [11] and [16], for reference. CPE and ICI itigation schees are considered separately to ephasize readability.

4 A. CPE Estiation As (14) shows, CPE has exactly the sae effect on every subcarrier inside one OFDM sybol. Thus, we can estiate the CPE ter J (0) for an OFDM sybol by using, e.g., preknown pilot subcarriers (S P ). To focus on CPE, we can odify (14) so that the ICI and AWGN are just cobined into one variable ε (k). This results in R ( k) X ( k) H ( k) J (0) + ε ( k). (15) When we consider the case k S P, we can estiate J (0) with, e.g., least squares (LS) estiation, given that also the channel response H (k) is known [16]. This estiate can be forulated as R k X k H k k SP Jˆ(0) 2 X ( k) H ( k) k SP * * ( ) ( ) ( ), (16) where () * is a coplex conjugate operator. In [16], additional eans to iprove this estiate were also introduced for the cases where the nuber of pilot subcarriers (k S P ) is low. In our case though, we are ostly focusing on 3GPP LTE -like syste with large nuber of subcarriers, and thus also any pilot subcarriers per OFDM sybol [1]. Thus, (16) is used as the priary CPE estiation ipleentation in the forthcoing developents. B. ICI Estiation In CPE estiation above, only the first ter of J vector is estiated for each OFDM sybol. All the other ters of J represent ICI as (14) illustrates. The J vector has altogether N eleents in it. With practical nuber of subcarriers, it would be coputationally very heavy to try to estiate all of these values. Gladly, this is not needed. Steing fro the PN odelling in Section II, phase has typically steeply descending low-pass natured spectru around the noinal oscillating frequency. Thus the coponents around the centre frequency are the ost iportant ones in ost practical cases. Thus below, we consider only the spectral coponents near the centre frequency, J (k), k { 0,..., u, N u,..., N 1}, or with circular indexing k { u,..., u } [11]. Now, if we estiate only ICI ters with k { u,..., u }, we can write R (k) in (14) ore conveniently as u R( k) X( k l) H( k l) J( l) + ζ ( k). (17) l u Here, variable ζ (k) has the AWGN ters and all nonestiated ICI-ters in it. Furtherore, if we only consider a subset of the subcarriers k { l 1,..., l P }, P>2u + 1, we can write (17) in a atrix for R( l1 ) A( l1+ u) A( l1 u) J( u) + ζ R( lp) A( lp + u) A( lp u) J( u), (18) or equivalently as R,p A,u J,u + ζ,u, in which A (k)x (k)h (k). In practice, this subset of subcarriers can be selected so that it consists of subcarriers that are the ost reliable after initial detection [11]. Reliability, in turn, can be easured, e.g., with the help of coding [4]. Now assuing that both X (k) and H (k) are known for the considered subcarriers, estiating J,u is easy using, e.g., the pseudo inverse of A,u as ( ) 1 ˆ H H u, u, u, u,, p J A A A R. (19) The resulting PN spectru estiate can then be used to deconvolve the effect of the PN out of the syste, i.e., ICI can be reoved. Notice that instead of the least-squares estiator presented in (19), a ore coplicated iniu ean-squared error (MMSE) estiator was deployed in [11]. MMSE approach requires quite detailed knowledge of the statistical properties of the phase noise at hand [11]. The LS approach is chosen here for coputational siplicity since in 3GPP LTE -like systes with high nubers of subcarriers, the calculation of these statistics is relatively deanding. As the above ethod obviously needs knowledge of the data sybols at the considered subcarriers, the idea is to do the processing iteratively [11]. In the first iteration, only the CPE is reoved fro the received signal and the relevant subcarrier data is detected. These sybol decisions are then used as known sybols in (18)-(19), yielding an estiate of the PN spectral coponents. After reoving the ICI fro the received signal block using this estiate, the subcarrier data is detected again, yielding yet ore reliable data decisions. This whole procedure is then iterated. Steing fro the utilized block-wise or truncated Fourier series approach for PN estiation in [11], and also here in (18)-(19), the resulting PN estiation quality at the tails (close to sybol boundaries) inside each OFDM sybol is very poor. This will be illustrated graphically in Section V. This proble can be relieved with the edge substitution ethod presented in [5]. In the edge substitution technique, the edges of PN estiates for each OFDM sybol are replaced by so called periodic extensions. This periodic extension is calculated by observing the PN estiate saples in different order, so that the interesting edge is apped to the iddle parts of the OFDM sybol. After reordering the PN estiate, the estiated PN in the iddle parts that correspond to the edge parts of the original PN estiate can be used as a substitution for the edges. This is done separately for both, leading and trailing, edges of the PN estiate within each OFDM sybol. [5]

5 V. NEW ICI ESTIMATION AND MITIGATION TECHNIQUES In this Section, new linear interpolation based ICI estiation technique (LI-CPE) and new linear interpolation based tail-estiation technique (LI-TE) are proposed. Here, instead of other ore coplex interpolators, linear interpolation is used as the ain tool to ephasize coputational siplicity. Also, in case of free-running oscillators, linear interpolation has been shown in [18] to be the optiu way to process and estiate tie-doain phase noise values, which further justifies its use in LI-TE approach. In both LI-CPE and LI-TE ethods, after obtaining the final estiate for the tie-doain phase noise behaviour within the processed OFDM sybol, the actual itigation of the ICI is done by deconvolving the corresponding received signal block with the FFT of the estiated phase noise wavefor. A. ICI Estiation Using CPE Interpolation (LI-CPE) The proposed LI-CPE PN estiation technique is based on siple linear interpolation of two consecutive CPE estiates. If we study PN and CPE realizations in Fig. 2, we notice that by linearly interpolating the CPE realization fro the iddle of each sybol to the iddle of the next sybol, our result, on average, is closer to the PN realization than the CPE estiate alone. These interpolated CPE characteristics estiate also the ICI behaviour by trying to reconstruct the phase behaviour inside individual sybols. In addition, the estiation procedure is forulated here so that the CPE of the final interpolated phase atches the original CPE value inside each OFDM sybol. An exaple of the overall estiated phase as a function of tie using the above estiation approach is given in Fig. 2. One drawback of the above estiation procedure is that it iposes an extra delay of one OFDM sybol copared to plain CPE estiation. Notice also that any existing CPE estiation schee, such as the one in (16), can be used to obtain the initial CPE estiates used in the interpolation stage. B. Iterative ICI Estiation Using Tail Interpolation (LI-TE) The new LI-TE PN estiation technique iproves the estiation perforance of iterative technique presented in [11]. As already noted in [5], the ethod does not work perfectly. It has probles especially with the tails of each sybol, because Fourier series approxiation does not give good PN estiates in the edges of an OFDM sybol. This is also deonstrated in Fig. 3. The probles can be reduced siply by linearly interpolating the phase over these badly estiated parts of the PN estiate. The linear interpolation sees to perfor best when using linear interpolation over about 15 % of the total saples fro the end and the beginning of each sybol. Fig. 3 illustrates how the ethod iproves the PN estiate accuracy. Indeed, Phase Error [rad] True phase noise CPE LI CPE estiation Tie in OFDM Sybols Fig. 2. LI-CPE ethod deonstrated for a free-running oscillator with 100 Hz spectral width (β ) over six OFDM sybols. Phase Error [rad] True phase noise PN estiation Tie in OFDM Sybols Fig. 3. LI-TE ethod deonstrated for a free-running oscillator with 100 Hz spectral width (β ) over six OFDM sybols. For deonstration purposes, only one iteration in is used. the earlier ethod gives corrupted ICI estiates, and the interpolation ethod iproves the quality of the estiate noticeably. When LI-TE is applied to the iterative ethod of [11], interpolation can be utilized at each iteration. It should be noted though, that when using only a single iteration, we need estiates of previous and next sybol to do the interpolation, eaning a delay of one OFDM sybol. When using two iterations, we need the second iteration output of the adjacent sybols, thus our delay increases to two sybols and so on. This is not a ajor proble though since the iterative ICI estiation ethod gets altogether coputationally heavier and heavier as the nuber of iterations increases, so any iterations are not feasible anyways. In the forthcoing perforance evaluations, we use interpolation only over two iterations for siplicity.

6 VI. SIMULATIONS AND PERFORMANCE ANALYSIS In the siulations, the perforances of all the presented PN itigation techniques are studied and copared. Siulation odel is based on 3GPP LTE downlink -like syste [1], where 1024 subcarriers with 15 khz subcarrier spacing are used, 600 of which are carrying 16QAM data. The 600 active subcarriers are selected so that 300 of the are on the both sides of the centre subcarrier. Of these 600 active subcarriers, 18 carry pilot sybols, and are not used for data transission. The length of the cyclic prefix is 63 saples. The siulation process is carried out as follows. First, data sybols are generated using 16QAM subcarrier odulation. These are then OFDM-odulated, and send to the channel. As a channel, we use both additive white Gaussian noise (AWGN) channel and extended Vehicular A [14] ultipath channel odels. Extended Vehicular A is used so that the channel is static for blocks of 12 OFDM sybols after which new channel realization is drawn. After the channel, receiver PN is odelled and applied. Both free-running and PLLbased oscillators are applied in the siulations. The PN effect is then itigated with presented techniques, and channel is equalized. In the channel equalization, perfect channel knowledge is assued. After itigation and equalization, the actual sybol detection is done separately for each subcarrier using the well-known iniu-distance principle. For, we use 2 iterations and estiate three PN spectral coponents (u 3) around the DC-bin (CPE). For edge substitution technique of [5] and LI-TE technique, we use edge window length of 70 and 155 saples, respectively. These values were confired by siulations to be, on average, the best window length values for each technique. The used window length of the tail substitution technique also confors to the proposed window length in [5]. In LI-TE, in turn, a relatively long interpolation window is used, copared to tail-substitution reference technique, in order to utilize the neighbouring sybol PN estiates as efficiently as possible. The perforances of PN itigation techniques presented in Sections IV and V are copared to each other. The results for AWGN and extended Vehicular A channels are presented in Fig. 4 and Fig. 5, respectively, for free-running oscillator case. In the siulations, at least fifty-thousand OFDM sybols are transitted for every (SNR, β ) pair. Fro the AWGN channel siulations in Fig. 4, we can see noticeable perforance increase when coparing the perforance of LI-TE ethod over that of the state-of-the-art tail substitution ethod [5]. Also, the siple LI-CPE ethod gives a nice perforance boost over the basic CPE estiation. Fro Fig. 5, it can be seen that the perforance of the best ethods get relatively near to the ideal case, but at the sae tie the significance of the PN itigation ethods decrease copared to AWGN channel case. This is natural because the relative Sybol Error Rate (SER) Sybol Error Rate (SER) No PN CPE est. LI CPE Signal to Noise Ratio (SNR) [db] (a) CPE est. LI CPE Phase Noise Bandwidth β [Hz] (b) Fig. 4. Siulated SER as a function of (a) SNR, and β 200 Hz (b) β, and SNR 20 db. PN is generated with free-running oscillator and AWGN channel is used. contribution of the PN gets saller when the channel becoes ore difficult. Still, LI-TE ethod outperfors the reference ethods. The perforance of LI-CPE ethod, on the other hand, sees to get quite near to the perforance of the state-of-the-art ethods. When siulating the PLL oscillator case, PN of PLL oscillator is generated using the ask in Fig. 1. The itigation results for the PLL case are given in Fig. 6. Copared to the free-running case, the relative perforance differences between the itigation techniques reain alost the sae. LI-TE still outperfors its rivals. It is noticeable though that the LI-CPE ethod works especially well in a PLL case where PN has less high frequency coponents. It gives near the perforance of the basic and tail substitution ethods in high SNR region also, with considerably lower coputational coplexity.

7 Sybol Error Rate (SER) CPE est. LI CPE No PN Signal to Noise Ratio (SNR) [db] Fig. 5. Siulated SER as a function of SNR. PN is generated with freerunning oscillator (β 200 Hz). Extended ITU-R Vehicular A channel odel is used. Sybol Error Rate (SER) 10 3 No PN CPE est. LI CPE Signal to Noise Ratio (SNR) [db] Fig. 6. Siulated SER as a function of SNR. PN is generated with PLL-based oscillator. AWGN channel is used. VII. CONCLUSIONS Phase noise is a critical ipairent in OFDM type ulticarrier systes. We introduced two new linear interpolation based techniques to estiate PN. The first technique, LI-CPE, is a siple way to iprove the perforance of general pilot-based CPE estiate by interpolating the PN estiate over adjacent OFDM sybols. The second technique, LI-TE, iproves the perforance of the state-of-the-art ICI itigation techniques by decreasing the PN estiation error in tail parts of each OFDM sybol. Utilizing both free-running and PLL-based oscillators, the itigation perforances of all the techniques were analyzed using siulations. The siulations showed that LI-CPE gave a very good perforance increase over general CPE itigation. LI-TE, on the other hand, noticeably increased the perforance of the state-of-the-art ICI itigation technique. In addition, we noticed that the significance of ICI itigation is relatively lower under challenging radio propagation environents, copared to plain AWGN. Still, clear perforance iproveent is achieved in high SNR region. REFERENCES [1] 3GPP Technical Specification, TS v Physical Channels and Modulation (release 8), May [2] A. Arada, and M. Calvo, Phase noise and sub-carrier spacing effects on the perforance of an OFDM counication syste, IEEE Counications Letters, Vol. 2, No. 1, pp , January [3] J. A. C. Bingha, Multicarrier odulation for data transission: an idea whose tie has coe, IEEE Counications Magazine, Vol. 28, No. 5, pp. 5-14, May [4] S. Bittner, W. Rave, and G. Fettweis, Joint iterative transitter and receiver phase noise correction using soft inforation, in Proc. IEEE International Conference on Counications 2007 (ICC 07), June 2007, pp [5] S. Bittner, E. Zierann, and G. Fettweis, Exploiting phase noise properties in the design of MIMO-OFDM receivers, in Proc. IEEE Wireless Counications and Networking Conference (WCNC 08), March 2008, pp [6] M. Brownlee, P. K. Hanuolu, K. Mayara, and U. Moon, A 0.5-GHz to 2.5-GHz PLL with fully differential supply regulated tuning, IEEE Journal of Solid-State Circuits, Vol. 41, No. 12, pp , Deceber [7] A. Deir, Coputing tiing jitter fro phase noise pectra for oscillators and phase-locked loops with white and 1/f noise, IEEE Transactions on Circuits and Systes I: Regular Papers, Vol 53, No. 9, pp , Septeber [8] A. Deir, Phase noise and tiing jitter in oscillators with colorednoise sources, IEEE Transactions on Circuits and Systes I: Fundaental Theory and Applications, Vol. 49, No. 12, pp , Deceber [9] A. Deir, A. Mehrotra, and J. Roychowdhury, Phase noise in oscillators: a unifying theory and nuerical ethods for characterization, IEEE Transactions on Circuits and Systes - I: Fundaental Theory and Applications, Vol. 47, No. 5, pp , May [10] G. Fettweis, Dirty RF: A new paradig, in Proc. 16 th International Syposiu on Personal, Indoor and Mobile Radio Counications, 2005, Septeber 2005, pp , Vol. 4. [11] D. Petrovic, W. Rave, and G. Fettweis, Effects of phase noise on OFDM systes with and without PLL: Characterization and copensation, IEEE Transactions on Counications, Vol. 55, No. 8, pp , August [12] P. Robertson, and S. Kaiser, Analysis of the effects of phase-noise in orthogonal frequency division ultiplex (OFDM) systes, in Proc. IEEE International Conference on Counications, June 1995, pp , Vol. 3. [13] T. Schenk, RF Ipairents in Multiple Antenna OFDM: Influence and Mitigation, PhD dissertation, Technische Universiteit Eindhoven, ISBN p. [14] T. B. Sorensen, P. E. Mogersen, and F. Frederiksen, Extension of the ITU channel odels for wideband (OFDM) systes, in Proc. IEEE Veh. Technol. Conf., Septeber 2005, pp [15] L. Toba, On the effect of Wiener phase noise in OFDM systes, IEEE Transactions on Counications, Vol. 46, No. 5, pp , May [16] S. Wu, and Y. Bar-Ness, A phase noise suppression algorith for OFDM-based WLANs, IEEE Counications Letters, Vol. 6, No. 12, pp , Deceber [17] S. Wu, and Y. Bar-Ness, OFDM systes in the presence of phase noise: Consequences and solutions, IEEE Transactions on Counications, Vol. 52, No. 11, pp , Noveber [18] Q. Zou, A. Tarighat, and A. H. Sayed, Copensation of phase noise in OFDM wireless systes, IEEE Translations on Signal Processing, Vol. 55, No. 11, Noveber 2007.