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Beamforming Effects on Measured mm-Wave Channel Characteristics

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Beamforming Effects on Measured mm-Wave Channel Characteristics
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  IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 10, NO. 11, NOVEMBER 2011 3553 Beamforming Effects on Measured mm-Wave Channel Characteristics Shurjeel Wyne,  Member, IEEE,  Katsuyuki Haneda,  Member, IEEE,  Sylvain Ranvier,Fredrik Tufvesson,  Senior Member, IEEE,  and Andreas F. Molisch,  Fellow, IEEE   Abstract —Beamforming is an important feature of   󰀶󰀰  GHzcommunications. We present an analysis of the in ß uence of beamforming in indoor ultrawideband radio channels measuredin the mm-wave 60 GHz band. The performance of narrowbandand wideband direction-based beamformers is investigated interms of improving channel metrics such as the delay spread,excess delay, and the signal-to-noise ratio (SNR). The perfor-mance of the direction-based beamformers is compared withdominant eigenmode transmission and statistical beamforming.Our analysis reveals that in line-of-sight (LOS) scenarios, thetwo direction-based beamformers have a similar performancethat approaches the upper bound set by dominant eigenmodetransmission. In non-LOS (NLOS) scenarios, the direction-basedbeamformers show a performance degradation in relation to theupper bound, with the narrowband beamformer worse off thanthe wideband variant. The array gain in our measured NLOSscenarios is observed to exceed the theoretical upper limit validfor a rich scattering environment. We show that this result followsfrom the spatial structure of the measured NLOS channels thathas only a few strong re ß ected components. We investigate thein ß uence of array size on beamforming performance;  󰀵 󰃗 󰀵  planararrays are observed to improve the channel’s delay metrics aswell as the larger  󰀷 󰃗 󰀷  planar arrays.  Index Terms —60 GHz communications, beamforming, radiochannel, delay spread, measurements. I. I NTRODUCTION O VER the years various approaches have been proposedto overcome the limitations of data transmission speedimposed by current wireless systems. Recently, the area of 60 GHz communications has attracted signi Þ cant researchinterest as one alternative to overcome spectrum congestion atlower bands. The universal availability of   󰀷  GHz unlicensedbandwidth in the  󰀶󰀰  GHz band [1] allows the design of  Manuscript submitted February 9, 2010; revised September 4, 2010 andMay 28, 2011; accepted July 26, 2011. The associate editor coordinating thereview of this paper and approving it for publication was L. Yang.This work was partly  Þ nanced through the Swedish Foundation for StrategicResearch, the High Speed Wireless Center at Lund University, and a grantfrom Vetenskapsr û adet, the Swedish Science Council. K. Haneda would liketo acknowledge the  Þ nancial support of the post-doctoral research project of the Academy of Finland, Helsinki, Finland.S. Wyne was with the Dept. of Electrical and Information Technology, LundUniversity, Lund, Sweden. He is now with the Dept. of Electrical Engineering,COMSATS Institute of Information Technology, Islamabad, Pakistan (e-mail:shurjeel.wyne@comsats.edu.pk).K. Haneda is with the SMARAD Center of Excellence, Aalto University,Helsinki, Finland (e-mail: katsuyuki.haneda@aalto. Þ ).S. Ranvier was with SMARAD Center of Excellence, Aalto University,Finland, and is now with the Belgian Institute of Space Aeronomy, Brussels,Belgium (e-mail: sylvain.ranvier@aeronomie.be).F. Tufvesson is with the Dept. of Electrical and Information Technology,Lund University, Lund, Sweden (e-mail: fredrik.tufvesson@eit.lth.se).A. F. Molisch is with the Dept. of Electrical Engineering, Uni-versity of Southern California, Los Angeles, CA, USA (e-mail: an-dreas.molisch@ieee.org).Digital Object Identi Þ er 10.1109/TWC.2011.083111.100195 relatively simple radio transceivers that can support data rateson the order of several Gbit/s. Standardization activities suchas that of IEEE 802.11 task group ad, to extend the existingwireless local area network (WLAN) standard to the  󰀶󰀰  GHzband, suggest that indoor WLANs will be one of the mainbene Þ ciaries of 60 GHz communications.For the same transmit power and antenna gains, the powerreceived in the 60 GHz band is less than the power received inthe 2/5 GHz bands due to a smaller receive antenna aperturein the 60 GHz band. Additionally, most materials have ahigh penetration loss at  󰀶󰀰  GHz compared with lower bands,leading to a low power of multipath components propagatingthrough building walls [2]. Furthermore, as the dimensions of physical objects are typically large in relation to the operatingwavelength, sharp shadow zones are formed in the  󰀶󰀰  GHzband such that diffraction is not a signi Þ cant propagationmechanism, a fact also veri Þ ed experimentally [3]. In viewof these propagation characteristics, the establishment of areliable communication link in the  󰀶󰀰  GHz band requireshighly directional antennas or steerable antenna beams [4].While directive antennas are prone to misalignment issues,steerable antenna beams have the  ß exibility to be directedtowards the LOS path in a LOS connection, and if the LOSpath is blocked, e.g., by human activity, the beam may besteered towards a strong  Þ rst-order re ß ection in such a NLOSscenario [4]. Furthermore, the small operating wavelengthsin the  󰀶󰀰  GHz band result in small form factor antennassuch that communicating devices may incorporate arrays withpotentially many elements. Real implementations of largearrays in the  󰀶󰀰  GHz band is an area of active researchwhere issues such as the design of high-frequency feedingnetworks and polarization-mismatch are being addressed [5].A collective consideration of all these factors leads to theconclusion that beamforming, i.e., electronic steering of theantenna array patterns to accomplish array gain, is a necessaryfeature of   󰀶󰀰  GHz communications.Extensive measurements and analysis of propagation char-acteristics in the  󰀶󰀰  GHz band are required to evaluatebeamforming performance under realistic channel conditions.Previous work has carried out experimental analysis to in-vestigate different aspects of   󰀶󰀰  GHz channels, see [6],[7], [8] and references therein. In [6] the authors employdirectional antennas with mechanical steering to investigatethe spatial structure of the propagation channel. In [8] theauthors investigate the effect of antenna directivity on delayspreads by using a combination of omni- and directionalantennas, and comparing the analysis results with ray tracing.The applicability of ray-tracing techniques in modeling  󰀶󰀰 GHz channels is an active research area. See e.g., [9] and 1536-1276/11$25.00 c ⃝  2011 IEEE  3554 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 10, NO. 11, NOVEMBER 2011 references therein. Standardization activities in the  󰀶󰀰  GHzband have so far lead to a channel model for wireless personalarea networks [10] that supports beamforming with somelimitations. Ongoing activity by IEEE 802.11 task group ad,aims to extend the existing WLAN standard to the  󰀶󰀰  GHzband and provide a generic channel model for evaluation of system proposals see [11] and references therein.This work presents an analysis of the in ß uence of beam-forming in measured indoor ultrawideband radio channels inthe 60 GHz band. Virtual antenna arrays are used in the mea-surements and beam steering is applied as a post processingstep. The performance of narrowband and wideband direction-based beamformers is investigated in terms of improvingchannel metrics that are important for communications systemdesign such as the root mean square (RMS) delay spread,excess delay, and SNR. The performance of the beamformersis compared with various theoretical bounds. The in ß uence of array size on the beamforming results is also investigated togive an idea of practical array sizes suf  Þ cient for beamforming.The remainder of the paper is organized as follows, themeasurement setup and post processing is described in sectionII, section III contains the results and discussion. Finally, thepaper is concluded in section IV.II. M EASUREMENT  S ETUP AND  P ROCESSING  A. Scenario The measurements were performed in a conference/meetingroom located on the 3rd  ß oor of the Department of RadioScience and Engineering building at Espoo campus of AaltoUniversity, Finland. During measurements the position of theRX array remained  Þ xed in one corner of the room, while anew measurement was recorded by placing the transmit (TX)array at one of   󰀲󰀲  prede Þ ned positions located on two tabletops, refer Fig. 1 for a measurement layout. Apart from theLOS measurements, an NLOS scenario was also measuredat all positions except at A1, B1, and C1 where furnitureplacement prevented the NLOS measurement. The measuredNLOS scenarios were created by blocking the  Þ rst Fresnel-zone with a laptop screen. The screen was of the dimensions 󰀰 󰀮 󰀲󰀷  m  󰃗  󰀰 󰀮 󰀳󰀳  m and was placed at  󰀰 󰀮 󰀴󰀲  m from the initialelement position of the TX array. The shadowing of the directpath by the laptop screen was veri Þ ed by investigating theattenuation of the main peak in the power delay pro Þ le; thelevel of the main peak was observed to decrease by  󰀱󰀶    󰀱󰀷 dB when the screen was in place. Most of the measurementswere performed during the night when there were no otherpeople in the building, and when measuring during the daythe movement of people was prevented in the vicinity of the measurement area to maintain a time-static measurementenvironment.  B. Equipment  The channel transfer functions were measured with avector network analyzer (VNA) based system developed atSMARAD [12]. The TX power was set to  󰀫󰀷  dBm, andthe measured frequency range  󰀶󰀱    󰀶󰀵  GHz was spanned by 󰀱󰀰󰀰󰀱  equidistantly-spaced frequency tones; this setup gave atime of arrival (TOA) resolution of   󰀰 󰀮 󰀲󰀵  ns and a maximummeasurable excess delay of 250 ns. At the TX side a  󰀷  󰃗  󰀷 virtual planar array was scanned in the horizontal plane usinga 2-D electromechanical positioner. The TX element wasa vertically polarized biconical antenna (Flann MD249-AA)with an omnidirectional pattern in azimuth and a nominalgain of 2 dBi [13]. At the RX side a  󰀷  󰃗  󰀷  virtual planararray was scanned in the vertical plane using another 2-Dpositioner, and a vertically polarized open waveguide as theRX element. This orientation of the arrays was selected tomodel the practical case of transmission from a DVD player orsimilar device, placed on the table, to a high-de Þ nition displaydevice placed in the corner of the room. The virtual arraysat TX and RX had an inter-element spacing of   󰀲  mm suchthat the length of one side of the  󰀷  󰃗  󰀷  planar array was  󰀱󰀲 mm. The TX antenna when placed on the table surface, hada height of   󰀱 󰀮 󰀰󰀷  m above the  ß oor whereas the top edge of the vertically oriented RX array was  󰀱 󰀮 󰀱  m above the  ß oor.At each TX position the transfer functions for  󰀲󰀴󰀰󰀱 󰀨󰀴󰀹 󰃗 󰀴󰀹󰀩 channel combinations were recorded. The measurement SNRwas in the range of   󰀴󰀰    󰀶󰀸  dB where the worst case SNRvalues were observed in the NLOS scenarios at the largestTX-RX separations. Prior to measurements the equipment wasback-to-back calibrated; the response of the VNA, frequency-converters, and cables/waveguides etc. were then removedfrom the measured frequency responses in a post-processingstep, before the analysis. C. Post Processing At each TX position the VNA recorded the transfer func-tion     󰀨 󰀬󰀬   󰀩 , where    ∈  󰁛󰀱 󰀬 󰀲 󰀬󰀮󰀮󰀮󰀬   󰀽 󰀴󰀹󰁝  and    ∈ 󰁛󰀱 󰀬 󰀲 󰀬󰀮󰀮󰀮󰀬   󰀽 󰀴󰀹󰁝  represent indices on the RX and TX arrays,respectively, and      corresponds to frequency at the   -thfrequency bin,    ∈  󰁛󰀱 󰀬 󰀲 󰀬󰀮󰀮󰀮󰀬   󰀽 󰀱󰀰󰀰󰀱󰁝 . The    󰃗    channeltransfer matrix at      is written as, 󰁈 󰀨    󰀩 󰀽 󰁛    󰀨 󰀬󰀬   󰀩󰁝  󰀽󰀱 󰀮󰀮󰀮  󰀻  󰀽󰀱 󰀮󰀮󰀮   󰀬  (1)where the channel sample     󰀨 󰀬󰀬   󰀩  lies at the intersectionof the   -th row and   -th column of   󰁈 󰀨    󰀩 . For furtherprocessing, the channel matrix measured at each position wasnormalized such that E 󰁛    󰀨 󰀬󰀬   󰀩󰁝 󰀽 󰀱  after normalization.The statistical expectation E 󰁛  󰁝  is taken over the full range of  󰀬󰀬  and      at each position. 1 The subsequent beamforming was performed in the fre-quency domain, thus the results of the analysis are applicableto the practical case of multicarrier systems. The beamformedchannel at      is written as,   BF  󰀨    󰀩 󰀽  󰁷   󰁶󰁥󰁣 󰁻 󰁈 󰀨    󰀩 󰁽∥ 󰁷 ∥   󰀬  (2)where  󰀨  󰀩   denotes conjugate transpose, the operator  󰁶󰁥󰁣 󰁻󰁽 stacks the columns of its matrix argument on top of eachother, and  ∥∥    denotes the Frobenius norm of its matrix 1 Prior to a statistical analysis, the stationarity of channel samples wasvalidated separately over the spatial regions spanned by the TX and RXvirtual arrays, as well as the measured frequency band. By de Þ nition, theaverage channel gains observed over a stationary region should have minimalvariations. Practically, the variations were observed to be on the order of   󰀵 dB or less in each domain such that the assumption of stationary channelsamples in all domains is reasonably justi Þ ed.  WYNE  et al. : BEAMFORMING EFFECTS ON MEASURED MM-WAVE CHANNEL CHARACTERISTICS 3555 Fig. 1. Scenario and measurement scheme. All dimensions are in meters. argument. Furthermore,  󰁷  is the joint TX-RX beamformingvector written as the column-wise Kronecker product, 󰁷 󰀽 󰁷 TX  ⊗ 󰁷 RX 󰀬  (3)of the column vectors 󰁷 TX  and 󰁷 RX  that represent beamform-ing weights at TX and RX, respectively. Note that this is a gen-eral mathematical formulation, which makes no assumptionsabout whether the channel itself has a Kronecker structure ornot. A brief description of the various beamformers consideredin the analysis is provided below. 1) Direction based beamformers:  A spatio-temporal beam-forming was performed to determine the directions at TX andRX of the strongest path in the channel. For this purpose, 󰁷 TX  was obtained by vectorizing the array factor matrix 󰁁 󰀨  TX 󰀬 TX 󰀬   󰀩  of the TX planar array in response to amultipath component with azimuth angle   TX  and zenith angle  TX  at TX. The matrix is written as [14], 󰁛 󰁁 󰀨  TX 󰀬 TX 󰀬   󰀩󰁝   󰀬  󰀽 exp 􀁻    󰀲    􀀨    󰀫 〈 󰁵 󰀨  TX 󰀬 TX 󰀩 󰀬 󰁤     〉  􀀩􀁽 󰀬  (4)where     and     are indices of array-element positionsalong x- and y- spatial coordinates, respectively, of the hor-izontally oriented array;  󰁵 󰀨  TX 󰀬 TX 󰀩 󰀽 󰁳󰁩󰁮  TX  󰁣󰁯󰁳  TX 󰁵   󰀫󰁳󰁩󰁮  TX  󰁳󰁩󰁮  TX 󰁵  󰀫󰀰 󰁵   is a unit vector representing the phasevariation for a speci Þ c direction of departure of the path; 󰁵  󰀬 󰁵  󰀬  and 󰁵   are unit vectors along x, y, and z coordinates,respectively; 󰁤      󰀽      󰁵   󰀫     󰁵   󰀫 󰀰 󰁵   is a positionvector of the antenna element relative to srcin of the array,and     and     are inter-element spacings along the x- andy-coordinates. Furthermore,    denotes velocity of light and ⟨ 󰁰 󰀬 󰁱 ⟩  represents an inner product of the vectors  󰁰  and  󰁱 . Ina similar way, the weight-vector 󰁷 RX  was de Þ ned for the RXside. 2 The TOA of the strongest path,    peak , was determinedas   peak  󰀽 󰁡󰁲󰁧󰁭󰁡󰁸   󰁻   ℎ  󰀨   󰀩 󰁽 󰀬  (5)where   ℎ  󰀨   󰀩 󰀽 󰀱   ∑  ∑  ∣ ℎ 󰀨 󰀬󰀬  󰀩 ∣ 󰀲 󰀬  (6)is the average power delay pro Þ le (APDP) of the measuredchannel;  ℎ 󰀨 󰀬󰀬  󰀩  is the channel impulse response obtainedas the inverse Fourier transform of      󰀨 󰀬󰀬   󰀩 . A rectangularwindow was applied in the transform as it gives the bestresolution for peak-search purposes.To create the beamformed channel according to (2) and (3)the dominant path’s zenith and azimuth angle-pairs at TX andRX were jointly estimated as, 󰀨 󰋆  TX,RX 󰀬  󰋆  TX,RX 󰀩 WB 󰀽󰁡󰁲󰁧󰁭󰁡󰁸 󰀨  TX,RX 󰀬 TX,RX 󰀩 ∑    󰁷   󰁶󰁥󰁣 󰁻 󰁈 󰀨    󰀩 󰁽∥ 󰁷 ∥    exp 󰀨   j 󰀲      peak 󰀩  󰀬  (7)where  󰋆  󰀬  denotes the pair of angles  󰋆   󰀬  󰋆    andthe subscript  󰀨󰀩 WB  on the set of four estimated angles de-notes the wideband case, i.e., the summation in (7) is overthe range of       that covers the full measurement band-width of   󰀴  GHz. When the direction based beamformeruses 󰀨 󰋆  TX,RX 󰀬  󰋆  TX,RX 󰀩 WB in constructing the weight-vectoraccording to (3), the beamformer will subsequently be referredto as wideband beamformer (WB-BF).For communications in the  󰀶󰀰  GHz band, the RMS delayspread will typically be small due to strong pathloss for long 2 The reference for zenith-angles:   TX  󰀽 󰀰 , and   RX  󰀽 󰀰 , points towardsthe ceiling.  3556 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 10, NO. 11, NOVEMBER 2011 traveling multipath components, leading to a large coherencebandwidth. Hence channel samples will be highly correlatedover small bandwidths. With an aim to investigate beam-forming performance with a limited number of decorrelatedfrequency tones; we compare the WB-BF that utilizes thefull bandwidth, with a narrowband beamformer (NB-BF)characterized by:1) Calculating the joint weighting vector in (3) once atthe center frequency and using the same vector forbeamforming at all frequencies.2) Estimating directions of the strongest path according to, 󰀨 󰋆  TX,RX 󰀬  󰋆  TX,RX 󰀩 NB 󰀽󰁡󰁲󰁧󰁭󰁡󰁸 󰀨  TX,RX 󰀬 TX,RX 󰀩 ∑    ∈  󰁷   󰁶󰁥󰁣 󰁻 󰁈 󰀨    󰀩 󰁽∥ 󰁷 ∥    exp 󰀨   j 󰀲      peak 󰀩  󰀬  (8)where   󰀽  󰁻     󰀺 󰀨       󰀱󰀰󰀰  MHz 󰀩  ≤     ≤  󰀨     󰀫 󰀱󰀰󰀰  MHz 󰀩 󰁽 󰀮  (9)The coherence bandwidth observed in our measured NLOSchannels was around 6 MHz leading to 33 decorrelated tones,on-average, over a span of 200 MHz. For LOS channels thecoherence bandwidth was in excess of 20 MHz leading tothe availability, on-average, of 10 or less decorrelated tonesover the 200 MHz operating bandwidth of the NB-BF. Thesecoherence bandwidth values were based on analyzing thenormalized (unity peak at zero-lag) frequencycorrelation func-tions, and de Þ ning decorrelation at a normalized correlationvalue of 0.9. 2) Dominant eigenmode transmission:  At each frequencytone a singular value decomposition (SVD) of the channelmatrix was obtained as [15], 󰁈 󰀨    󰀩 󰀽 󰁕Σ󰁖   󰀮  (10)The column of   󰁕  and row of   󰁖   that were associatedwith the largest singular value of   󰁈 󰀨    󰀩  were then used as 󰁷   and 󰁷  , respectively, in (3). This scheme, also knownas Dominant eigenmode transmission in the literature, isoptimal in terms of maximizing the SNR [15]. Thus the SVDbeamformer (SVD-BF) upper bounds the SNR improvementperformance of the other beamformers. 3) Statistical eigenvector beamforming:  Another variationof   narrowband   beamforming was investigated in which theeigenvectors were obtained from channel statistics rather than instantaneous  channel realizations as was the case for theSVD-BF discussed above. Speci Þ cally, the vectors  󰁷 TX  and 󰁷 RX  in (3) were de Þ ned by the eigenvectors associatedwith the largest eigenvalues of the (frequency-averaged) TXand RX antenna correlation matrices,  󰁒 TX, NB  and  󰁒 RX, NB ,respectively. These two matrices were in turn estimated as, 󰋆 󰁒 TX, NB  󰀽 󰀨󰀱 󰀯 󰋜  󰀩 ∑    ∈  󰁈 󰀨    󰀩   󰁈 󰀨    󰀩 󰀬  (11) 󰋆 󰁒 RX, NB  󰀽 󰀨󰀱 󰀯 󰋜  󰀩 ∑    ∈  󰁈 󰀨    󰀩 󰁈 󰀨    󰀩   󰀬  (12)where the summation is over the index    such that      belongsto the set    de Þ ned in (9) and  󰋜   denotes cardinality of s. Inthe remainder of the paper, this beamforming will be referredto as TX-EIG RX-EIG BF.III. R ESULTS  A. RMS Delay Spread  The RMS delay spread,    RMS , is conventionally de Þ nedas the square-root of the second central moment of thenormalized APDP (unity area enclosed by APDP) [16]. Thisparameter gives an idea of the self-interference to the receivedsymbols that is caused by multipath in the channel. For amulticarrier system, the delay spread gives an idea of the datarates that can be supported with a given number of carriers.The delay spread calculations in this work were based ondiscarding APDP values below a  󰀳󰀰  dB threshold relativeto the main peak of the APDP; given the dynamic range of  󰀴󰀰  󰀶󰀸  dB observed in the measured APDPs, this threshold-value minimizes the in ß uence of measurement noise in thedelay spread calculations. Figs. 2 and 3 show cumulativedistribution functions (CDFs) of the delay spreads for themeasured LOS and NLOS scenarios, respectively. Each  Þ gureshows three families of CDF curves corresponding to thethree array sizes (common for TX and RX) considered inthe investigations; e.g., the family of CDFs labeled  󰀹  󰃗  󰀹 MIMO in the  Þ gure correspond to  󰀳  󰃗  󰀳  planar arrays usedat both TX and RX. For the LOS scenarios the measuredRMS delay spreads, with a median value of around 1 ns,were quite small. The accuracy of measuring these smallvalues is governed by the well-known limits on resolution of a Þ ltered measurement system, i.e., the square of the measureddelay spread is the sum of the squares of delay spreadsof the (receive)  Þ lter and the channel. The measured delayspreads were, in general, similar to those reported by IEEE802.11 task group ad for identical scenarios; see [17] andreferences therein. For the LOS scenarios shown in Fig. 2 bothdirection based beamformers and the statistical eigenvectorbased beamformer exhibited an identical performance thatapproached the performance of SVD-BF for larger arraysizes. This behavior follows in part from the large coherencebandwidth of the LOS scenarios in that the average gain inperformance accomplished by SVD-BF is not signi Þ cant inrelation to the other beamformers. Additionally, larger arraysizes result in more accurate angle estimates for the direction-based beamformers and more samples to average for theantenna correlation matrices leading to better weight vectorsand improved performance for these beamformers at largerarray sizes. The observed RMS delay spreads were around  󰀱 ns or less in  󰀷󰀰󰀥  of the beamformed LOS channels. For theNLOS scenarios shown in Fig. 3, the WB-BF outperformedthe NB-BF due to a better estimate of the directions (based onthe full bandwidth) that lead to better beamforming weights.The differences in performance of the various beamformerswere reduced with increasing array sizes, though most of theperformance improvement was already achieved with the  󰀵 󰃗 󰀵 arrays. The RMS delay spreads were observed to be around 󰀵  ns or less in  󰀷󰀰󰀥  of the beamformed NLOS channels.  WYNE  et al. : BEAMFORMING EFFECTS ON MEASURED MM-WAVE CHANNEL CHARACTERISTICS 3557 TABLE IC UMULATIVE  P ROBABILITIES OF THE  󰀱󰀰 -  B  DELAY WINDOW . Probability Measured Channel NB-BF WB-BF SVD-BF TX-EIG RX-EIG BF 󰀹 󰃗 󰀹 󰀲󰀵 󰃗 󰀲󰀵 󰀴󰀹 󰃗 󰀴󰀹 󰀹 󰃗 󰀹 󰀲󰀵 󰃗 󰀲󰀵 󰀴󰀹 󰃗 󰀴󰀹 󰀹 󰃗 󰀹 󰀲󰀵 󰃗 󰀲󰀵 󰀴󰀹 󰃗 󰀴󰀹 󰀹 󰃗 󰀹 󰀲󰀵 󰃗 󰀲󰀵 󰀴󰀹 󰃗 󰀴󰀹 󰀹 󰃗 󰀹 󰀲󰀵 󰃗 󰀲󰀵 󰀴󰀹 󰃗 󰀴󰀹 LOS100%  󰀱󰀴 󰀮 󰀳 󰀱󰀴 󰀮 󰀳 󰀱󰀴 󰀮 󰀳 󰀱󰀳 󰀮 󰀰 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀱󰀰 󰀮 󰀳 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀱󰀰 󰀮 󰀳 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 90%  󰀱󰀳 󰀱󰀳 󰀱󰀲 󰀴 󰀮 󰀲 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀹 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀱 󰀮 󰀱 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 70%  󰀵 󰀮 󰀴 󰀵 󰀮 󰀵 󰀵 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 50%  󰀰 󰀮 󰀶 󰀰 󰀮 󰀶 󰀰 󰀮 󰀶 󰀰 󰀮 󰀳 󰀰 󰀮 󰀳 󰀰 󰀮 󰀳 󰀰 󰀮 󰀳 󰀰 󰀮 󰀳 󰀰 󰀮 󰀳 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀳 󰀰 󰀮 󰀳 󰀰 󰀮 󰀳 NLOS100%  󰀳󰀲 󰀮 󰀸 󰀳󰀰 󰀮 󰀸 󰀳󰀰 󰀮 󰀳 󰀲󰀲 󰀲󰀸 󰀮 󰀳 󰀱󰀲 󰀮 󰀵 󰀲󰀲 󰀱 󰀮 󰀵 󰀱 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀲󰀷 󰀮 󰀵 󰀱󰀴 󰀮 󰀸 󰀱󰀴 󰀮 󰀵 90%  󰀳󰀰 󰀮 󰀴 󰀲󰀹 󰀮 󰀵 󰀲󰀸 󰀮 󰀹 󰀱󰀵 󰀮 󰀳 󰀱󰀳 󰀮 󰀴 󰀲 󰀮 󰀴 󰀱󰀰 󰀮 󰀱 󰀰 󰀮 󰀹 󰀰 󰀮 󰀶 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀲󰀲 󰀮 󰀵 󰀱󰀳 󰀮 󰀴 󰀱󰀳 󰀮 󰀳 70%  󰀲󰀸 󰀮 󰀵 󰀲󰀸 󰀮 󰀱 󰀲󰀷 󰀮 󰀹 󰀵 󰀮 󰀹 󰀱 󰀮 󰀴 󰀰 󰀮 󰀸 󰀲 󰀮 󰀱 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀱󰀵 󰀮 󰀸 󰀳 󰀮 󰀹 󰀳 󰀮 󰀶 50%  󰀲󰀵 󰀮 󰀶 󰀲󰀵 󰀮 󰀶 󰀲󰀵 󰀮 󰀶 󰀲 󰀮 󰀵 󰀰 󰀮 󰀷 󰀰 󰀮 󰀵 󰀰 󰀮 󰀹 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀰 󰀮 󰀵 󰀱󰀱 󰀮 󰀶 󰀱 󰀮 󰀴 󰀱 󰀮 󰀳 Tabulated delay windows are in units of ns. Furthermore,     󰃗   abbreviates     󰃗   MIMO. 0.20.40.60.810.20.40.60.81    P  r   (      τ    R   M   S       ≤    A   b  s  c   i  s  s  a   ) 012345670.20.40.60.81 RMS Delay Spread [ns]   measNB − BFWB − BFSVD − BFTX − EIG RX − EIG BF 25x25 MIMO9x9 MIMO 49x49 MIMO Fig. 2. CDF of delay spreads in the LOS scenarios. 0.20.40.60.810.20.40.60.81    P  r   (      τ    R   M   S       ≤    A   b  s  c   i  s  s  a   ) 0510150.20.40.60.81 RMS Delay Spread [ns]   measNB − BFWB − BFSVD − BFTX − EIG RX − EIG BF 9x9 MIMO 25x25 MIMO49x49 MIMO Fig. 3. CDF of delay spreads in the NLOS scenarios.  B. Excess Delay The maximum excess delay is conventionally de Þ ned asthe runtime difference between the LOS and the longest-delayed multipath component that is above a prede Þ ned noisethreshold. In this work a slightly modi Þ ed metric based onwindow parameters [16] was used; the  󰀱󰀰 -dB delay window,   10-dB , was used to gauge the improvement (reduction) inexcess delay effected by beamforming. For a given APDP,   10-dB  was de Þ ned as the shortest delay interval of the APDPsuch that the power within the interval was  󰀱󰀰  dB higher thanthe power outside the interval. This de Þ nition is intended togive a quantitative measure of the self-interference caused bydelay dispersion, or the required length of the cyclic pre Þ x of an orthogonal frequency division multiplexing system [16]. 3 Furthermore, the    10-dB  metric also provides some insight intothe possible trade-off between the desire to use a small numberof taps in a time domain equalizer and the need to capturemost of the RX signal energy. A similar trade-off appliesto the selection of the number of   Þ ngers in a Rake receiver.Table I lists values of     10-dB  for the measured and beamformedchannels at the median,  󰀷󰀰 th,  󰀹󰀰 th, and  󰀱󰀰󰀰 th percentile of thecorresponding data sets. Each column in Table I correspondsto a unique pair of (beamformed) channel and array size.From the LOS measurements listed in Table I, it was ob-served that all beamformers show similar performance;    10-dB was minimized to  󰀰 󰀮 󰀵  ns or less in almost all beamformedchannels, the few occurrences of larger  󰀱󰀰 -dB delay windowswere only observed when using the  󰀳  󰃗  󰀳  planar arrays.For measured NLOS scenarios the WB-BF outperformed theNB-BF and the statistical eigenvector beamformer. As thelatter two beamformers have their weight-vector parametersestimated from a narrow bandwidth, the parameter estimatorsare unable to utilize the larger number of independent samplesmade available over the full bandwidth due to the smallercoherence bandwidth of the NLOS channel. Considering anysingle beamformer, the reduction in    10-dB  was not signi Þ cantat the  󰀷󰀰 th percentile when going from  󰀵  󰃗  󰀵  arrays to  󰀷  󰃗  󰀷 arrays. C. SNR Improvement  The investigated beamformers provide the link with an arraygain relative to the case of single antennas at both ends of thelink. The SNR improvement (array gain) achieved throughbeamforming was de Þ ned as,    󰀽  E 󰁛  ∣   BF  󰀨    󰀩 ∣ 󰀲󰀱    ∥ 󰁈 󰀨    󰀩 ∥ 󰀲   󰁝 󰀬  (13)where the expectation is taken over the frequency domain. Asstated previously, the per-tone SVD-BF is the optimal solutionin terms of attaining the theoretical upper-limit on achievablearray gain.In the measured LOS scenarios, the array gains achieved byall of the considered beamformers were found to approach theupper-bound    , valid for a highly correlated channel [18]. 3 The ratio between the power in the interval and the power outside theinterval is called the  interference quotient   [16].
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