OFDM-based aalog multibad: a scalable desig for idoor mm-wave wireless commuicatio Hossei Roufarshbaf Dept. of Electrical ad Computer Eg. Uiversity of Califoria, Sata Barbara Email: hroufarshbaf@ece.ucsb.edu Upamayu Madhow Dept. of Electrical ad Computer Eg. Uiversity of Califoria, Sata Barbara Email: madhow@ece.ucsb.edu Sridhar Rajagopal Samsug Research America Dallas, TX Email: sridhar.r@samsug.com Abstract We propose a approach to scalig commuicatio badwidths over dispersive chaels that preserves the advatage of DSP-cetric receiver desig, while sidesteppig the difficulty of scalig aalog-to-digital coversio (ADC) to higher ad higher badwidths. This is accomplished by chaelizig the available badwidth ito cotiguous subbads i the aalog domai, with the width of a subbad chose so that digitizatio is possible at reasoable cost ad power usig existig ADC techology. We illustrate these ideas for multigigabit idoor mmwave commuicatio, with GHz badwidth divided ito subbads of width 25-5 MHz. The chael delay spread eve after beamformig ca be as large as 2 s, hece the chael see withi subbads is dispersive. Further, the cotiguity of subbads ad the sloppy aalog chaelizatio implies that adjacet subbads iterfere with each other. We show that OFDM withi subbads is a attractive approach i these settigs: the chael dispersio withi subbads ca be hadled with a moderate cyclic prefix, while the iter-bad iterferece maifests itself oly o the edge subcarriers. We clarify the structure of the iter-bad iterferece, ad show that it is effectively suppressed by adaptive liear Miimum Mea Squared Error (MMSE) techiques for joit detectio across adjacet subbads. Our performace evaluatio is carried out usig chael models developed for the IEEE 82.11ad 6 GHz stadard. I. INTRODUCTION Millimeter wave commuicatio offers the opportuity of scalig wireless badwidths ad data rates by orders of magitude, to multiples of GHz (e.g., the 6 GHz bad has 7 GHz of ulicesed spectrum). I utilizig such large badwidths, we would still lie to ejoy the ecoomies of scale provided by Moore s law that have drive mass maret WiFi ad cellular techologies, with trasceivers that utilize digital sigal processig (DSP) to the greatest extet possible. However, the cost ad power of aalog-to-digital coverters scale poorly with sigal badwidth [1]. Thus, a atural idea is to brea the available badwidth ito subbads which ca be discretized separately by ADCs of reasoable speed, as determied by curret techology. A ey challege, of course, is the iter-bad iterferece that results from imperfect aalog chaelizatio, as we do ot wish to sacrifice badwidth efficiecy by puttig i large guard bads. However, sice we are able to digitize each subbad, it becomes possible to use DSP techiques to hadle such iterferece, as well as stadard impairmets such as chael dispersio withi a subbad. I this paper, we explore such desig issues i the cotext of a idoor mm-wave commuicatio chael, usig OFDM withi subbads to hadle chael dispersio. Cotributios: Our ey cotributios are as follows. Startig from idoor 6 GHz chael models developed durig the IEEE 82.11ad stadardizatio process, we model the chaels see by idividual subbads, assumig that the trasmitter ad receiver form beams alog a domiat ray. We show that, eve for such beamformed lis, the residual chael dispersio withi a subbad of 25-5 MHz width is still several sigal samples log. Focusig o OFDM as a welluderstood DSP-cetric approach to hadle such dispersio, we the ivestigate the structure of iter-bad iterferece for a system i which there is o guard bad betwee subbads. As expected, we fid that oly the edge subcarriers i a subbad ecouter iterferece from adjacet subbads. More iterestigly, we fid that the th subcarrier i a give subbad ecouters iterferece oly from the th subcarriers i the adjacet subbads to the left ad right. Furthermore, liear MMSE adaptatio applied o a observatio vector obtaied by groupig the frequecy domai samples for subcarrier from adjacet subbads is effective i suppressig iter-bad iterferece. We provide umerical results based o IEEE 82.11ad chael models. Related wor: Aalog multibad trasmissio was proposed may decades ago, but the was redered obsolete by OFDM. It has bee recetly cosidered for wired bacplae chaels [2], [3], but large guard bads are used to avoid iter-bad iterferece. Aalog multibad techiques have also bee cosidered for a idoor 6 GHz chael [4], but a guard bad is implicitly provided by stacig the subbads ext to each other after accoutig for excess badwidth, ad chael dispersio was ot addressed. The applicatio of aalog multibad to outdoor 6 GHz chaels was cosidered i [5] (the approach was termed aalog multitoe i that paper). Lie the preset paper, o guard bad was used, ad DSP techiques were used to hadle both chael dispersio ad iter-bad iterferece. However, sigle carrier modulatio was used withi each subbad, hece the structure of the DSP for iterferece suppressio was differet. The delay spread for the loger rage lie-of-sight (LOS) outdoor lis i [5] was smaller tha i our idoor settig, where it ca be as large as 2 s eve after beamformig alog the domiat ray, which might be o lie-of-sight (NLOS).
Amplitude 1.8 1.6 1.4 1.2 1.8.6.4.2 2 x 1 5 5 1 15 2 25 Delay (s) Amplitude 1.8 1.6 1.4 1.2 1.8.6.4.2 2 x 1 5 5 1 15 2 25 Delay (s) Fig. 1. The coferece room sceario used for stadard modelig of the idoor mm-wave chael [6]. h(t, φ tx, θ tx, φ rx, θ rx ) = i Fig. 2. A realizatio of the chael amplitude vs. delay for the coferece room sceario. Fig. 3. The chael realizatio i Figure 2, beamformed toward the strogest path. A (i) C (i) (t T (i), φ tx Φ (i) tx, θ tx Θ (i) tx, φ rx Φ (i) rx, θ rx Θ (i) rx), (1) C (i) (t, φ tx, θ tx, φ rx, θ rx ) = α (i,) δ(t τ (i,) )δ(φ tx φ (i,) tx )δ(θ tx θ (i,) tx )δ(φ rx φ (i,) rx )δ(θ rx θ rx (i,) ). (2) This paper is orgaized as follows: we first review the mmwave idoor commuicatio chael model used i this paper (Sectio II). The proposed trasceiver architecture is discussed i Sectio III. I Sectio IV, we describe the structure of the iter-bad iterferece i terms of its effect o each OFDM subcarrier, ad i Sectio V, we describe our approach to iterferece suppressio. Simulatio results ad coclusios are provided i Sectios VI ad VII, respectively. II. INDOOR MM-WAVE WIRELESS CHANNEL I the cotext of the IEEE 82.11ad stadard, sigificat effort has bee devoted to modelig the idoor mm-wave wireless chael, based o ray tracig simulatios ad experimetal measuremets [6], [7]. This stadard model draws o the quasi-optical ature of the mm-wave sigal to model the chael based o a small umber of paths (LOS ad reflectios), with each reflected path modeled as a cluster of closely spaced rays [8]. The chael impulse respose is modeled as i (1) ad (2), where A (i) is a 2 2 matrix gai of the i-th cluster that presets polarizatio characteristics, C (i) shows the chael impulse respose for cluster i, δ is the Dirac delta fuctio, T (i), Φ (i) tx, Θ (i) tx, Φ (i) rx, Θ (i) rx are the time ad agular characteristics of the cluster that are termed itercluster parameters, ad α (i,), τ (i,), φ (i,) tx, θ (i,) tx, φ (i,) rx, θ rx (i,) are the amplitude, time, ad agular characteristics of the -th ray i i-th cluster that are termed itra-cluster parameters. The statistical distributios for the iter-cluster ad the itra-cluster parameters are give for various idoor scearios such as the coferece room, livig room, ad cubicle office [6]. Figure 1 shows the coferece room sceario where two statios are located o the coferece room des. The LOS path, the 1st order reflected paths, ad the 2d order reflected paths are plotted for this sceario. A realizatio of the chael impulse respose, assumig that the LOS path is bloced, is plotted i Figure 2. The delay spread of the simulated chael impulse respose is 25 s that represets a dispersive chael withi the subbads. We assume that the trasmitter ad receiver are each equipped with 4 4 square arrays λ/2 elemet spacig (oe of the advatages of the small wavelegth is that such arrays ca be realized with compact form factor), ad that these are both steered towards the strogest path. The beamformed chael for the realizatio we have cosidered is show i Figure 3. While the chael is more cocetrated, we observe that the delay spread is still large (12 s) eve after beamformig. Fig. 4. Aalog multibad structure at the trasmit side. Fig. 5. Aalog multibad structure at the receive side. III. MULTIBAND ARCHITECTURE The purpose of the aalog multibad structure is to brea the available badwidth (e.g. MF s Hz) ito multiple parallel subbads (M subbads), each discretized by a ADC of reasoable speed (F s Hz). As we observed i Sectio II, the chael delay spread is sigificat eve after beamformig, so that OFDM is a attractive sigalig techique for equalizatio withi each subbad. Figure 4 shows the trasmitter
side of the aalog multibad architecture. The trasmit data is demultiplexed ito M parallel subbads. Data over each subbad is modulated through the OFDM trasmitter bloc. The digital to aalog coverter (DAC) blocs ad the trasmit filters stac up the subbads at itermediate frequecy (IF) i the aalog domai, spaced at f: we assume that guard bads are ot used, hece f = F s, the samplig rate withi each subbad. The IF aalog sigal is upcoverted to the carrier frequecy bad ad trasmitted over the directioal commuicatio chael. At the receiver (Figure 5), the received sigal is dowcoverted to IF, the demultiplexed usig a set of parallel aalog receive filters, each tued to pass the associated subbad sigal. The received sigal o each subbad is dowcoverted to basebad ad discretized usig ADCs. These parallel discretized sigals are demodulated at the OFDM receivers (which, as we shall see, do eed to be coupled lightly i order to suppress iter-bad iterferece) ad are multiplexed to form the received data stream. IV. INTERFERENCE STRUCTURE Suppose that the iput data stream is demultiplexed ito M subbads. The OFDM trasmitter for each subbad wors at a samplig rate of F s Hz ad cotais N subcarriers. The OFDM data stream for subbad m is deoted by b (m) = [b (m),1,, b(m),n ], (3) where deotes OFDM symbol idex. After taig the iverse discrete Fourier trasform (IDFT) ad addig the cyclic prefix, the time domai samples for the OFDM trasmitted symbol are deoted by B (m). As discussed before, we cosider a guard bad free chaelizig scheme to use all available spectrum. Therefore, we expect that the eighbor subbads sigals (subbads m 1 ad m + 1) iterfere with the curret subbad due to o-ideal trasmit ad receive filters used i aalog chaelizatio. Oce we iclude iter-bad iterferece (we assume this is restricted to the two adjacet bads), the received sigal of subbad m after aalog to digital coversio is modeled as r (m) = h (m) B (m) (4) +h (m ) B (m 1) + h (m+) B (m+1) + w (m), where deotes the circular covolutio, h (m) is the impulse respose of the equivalet chael impulse respose for subbad m, h (m ) is the impulse respose of the equivalet iterferig chael from subbad m 1, h (m+) is the equivalet iterferig chael from subbad m + 1, ad w (m) is the additive white Gaussia oise. We have assumed here that the OFDM trasmitted symbols over parallel subbads are sychroized i time ad have the same legth of cyclic prefix. With these assumptios, the circular covolutio operatio i (4) is valid for the iterferig subbads as well. The equivalet chael impulse respose for subbad m ad iterferig subbads are related to the stadard mm-wave chael impulse respose (1) at the subbad symbol rate through h (m) = p T x h p Rx (5) h (m ) = (p T x e j2π ft ) h p Rx (6) h (m+) = (p T x e j2π ft ) h p Rx, (7) where deotes the covolutio operatio ad p T x ad p Rx deote the impulse respose of the trasmit ad receive filters (Figures 4 ad 5), respectively. Withi the OFDM symbol, the received samples after removig the cyclic prefix ad taig the discrete Fourier trasform (DFT) are give by R (m) = H (m). b (m) (8) +H (m ). b (m 1) + H (m+). b (m+1) + W (m), where. deotes elemet by elemet multiplicatio of two vectors, H (m) is the DFT of the equivalet trasmit chael, ad H (m ) ad H (m+) deote the DFT of the equivalet iterferig chaels. We observe that, by virtue of the cyclic prefix, the iterferece see by OFDM symbol is oly due to OFDM symbol from each of the eighborig subbads. We ca therefore restrict attetio to oe OFDM symbol at a time, ad drop the idex from our otatio. Rewritig (8) for OFDM subcarrier, the received sigal is give by R (m) = H (m).b (m) +H (m+) + H (m ).b (m 1).b (m+1) + W (m). (9) The precedig iterferece model shows that subcarrier ecouters iterferece oly from subcarrier of the adjacet subbads. Hece, the iterferece across subbads ca be hadled by joit detectio for each subcarrier over all subbads. The received sigal o subcarrier of all the subbads is modeled as where H = R = H b + w, (1) R = [R (1), R (2),, R (M) ] T, (11) b = [b (1), b (2),, b (M) ] T, (12) w = [W (1), W (2),, W (M) ] T, ad (13) H (1) H (1+) H (2 ) H (2) H (2+) H (3 ) H (3). H (M). (14) Data trasmitted o subcarrier ca ow be joitly detected across subbads usig the model (1). For M parallel subbads ad N subcarriers per subbad, the maximum umber of o-zero chael coefficiets is N (3M 2). Of course, we expect iter-bad iterferece to be sigificat oly at the edges of the subbads, hece the effort o iterferece suppressio eed oly be expeded o edge subcarriers, as discussed i more detail i the ext sectio.
Fig. 6. Basebad equivalet model for subbad m ad the iterferig subbad m + 1 A. Variatio across subcarriers From (9), we fid that the -th subcarrier i a give subbad ecouters iterferece oly from the -th subcarrier of the adjacet subbads. iter-bad iterferece occurs sice, oce we accout for the frequecy separatio betwee subbads, the aalog trasmit filter for subbad m ± 1 ad the receive filter for subbad m overlap oly i their trasitio bads. Therefore, we expect that the subcarriers at the edges ecouter more iterferece tha those i the middle of the subbad. I order to develop more specific isight, cosider the basebad equivalet model for the iterferece due to subbad m + 1 see by subbad m (the iterferece due to subbad m 1 follows a etirely aalogous patter). Followig (4), the coefficiets of the effective iterferig chael discrete Fourier trasform (DFT) with size N, i.e. H m+, determies the amout of iterferece for each subcarrier. The effective iterferig chael impulse respose is defied i (7). The frequecy respose of the effective iterferig chael is the product of the frequecy resposes of the receive filter (subbad m), trasmissio chael h, ad the trasmit filter (subbad m + 1). Figure 6 shows the frequecy respose of the receive filter for subbad m ad the trasmit filter for subbad m + 1. The cotiuous time Fourier trasform (CTFT) of the effective iterferig subbad (Hc (m+) ) is approximately zero except for the overlappig regio { Hc (m+) (f) for f < F s f/2 Hc (m+) (f) for F s f/2, (15) < f < F s + f/2 where f deotes the amout of frequecy overlap betwee subbads m ad m+1. The frequecy respose of the sampled effective chael (Hs (m+) ) is related to the cotiuous time Fourier trasform (CTFT) of the chael through aliasig: Hs (m+) (f) = F s + l= Hc (m+) (f lf s ). (16) The discrete Fourier trasform (DFT) with legth N is derived by taig samples from oe period of the sampled CFTF (16) at the samplig rate of N/F s H (m+) = Hs (m+) (F s /N) (17) = + = Hs (m+) ( F s N F s) for =,, N 1. Usig (15) ad (17), the DFT coefficiets of the iterferig chael are H (m+) for < fn 2F s H (m+) for N fn 2F s < N H (m+) elsewhere. (18) We observe that, due to aliasig, the effective iterferece from subbad m + 1 hits the OFDM subcarriers i subbad m o both the left ad right boudaries. Aalogously, the iterferece from subbad m 1 also hits the OFDM subcarriers o both boudaries. However, the middle subcarriers do ot see iterferece (uder reasoable assumptios o filter trasitio bads), hece the chael matrix (14) is diagoal for them. Thus, the receiver eeds to perform joit data detectio, or iterferece suppressio, oly for boudary subcarriers. V. INTERFERENCE SUPPRESSION We ivestigate two liear chael equalizatio scearios for joit detectio of the boudary subcarriers. I the first sceario, we assume that the chael is perfectly ow ad we use a zero-forcig liear chael equalizer. I the secod sceario, we cosider a MMSE liear equalizer implemeted usig least squares adaptatio based o a traiig sequece. a) Zero-Forcig Liear Equalizer: Assumig that the chael matrix for each subcarrier (H ) is ow at the receiver, a zero-forcig (ZF) liear equalizer for each OFDM subcarrier ca be applied for joit detectio of the trasmittig symbols over the subbads. For the iterferece model (1), the ZF liear equalizer joitly estimates the symbols of subcarrier through ˆb = H 1 R. (19) The ZF equalizer icurs oise ehacemet, but based o the per-subcarrier iterferece model (1) ad (14), we expect this to be sigificat oly for the boudary subcarriers. b) MMSE Liear Equalizer: The ZF equalizer requires explicit chael estimates, whereas the MMSE equalizer ca be implemeted adaptively based o a traiig sequece. The estimated symbols are related to the received symbols for each subcarrier through ˆb = C H R, (2) where H deotes matrix Hermitia operatio, ad C is the equalizer matrix, chose to miimize the mea squared error (MSE) give by mi C E{(b ˆb ) 2 }, (21) where E{.} deotes the expectatio operatio. Substitutig (2) ito (21) ad miimizig the mea square error by taig the derivative with respect to matrix C, we get the stadard solutio: C = R 1 P, (22)
OFDM symbol rate TABLE I OFDM PARAMETERS USED IN SIMULATIONS. Number of subcarriers Subcarrier spacig CP legth Modulatio scheme 256 MHz 64 4 MHz 16 16-QAM where R = E{R R H } is the correlatio matrix of the observatios ad the cross correlatio matrix P = [E{(b (1) ) R } E{(b (m) ) R } E{(b (M) ) R }]. As usual, for a least squares implemetatio, the precedig expectatios are replaced by empirical averages, with the estimatio of P requirig a traiig sequece. VI. NUMERICAL RESULTS The performace of the proposed architecture is evaluated through simulatios usig the stadard IEEE 82.11 mm-wave idoor chael model. Throughout the simulatios, the OFDM symbol rate (or subbad symbol rate) is F s = 256 MHz ad the carrier frequecy is 6 GHz. Sice the iterferece is ecoutered oly from adjacet subbads, we cosider a simulatio sceario of three cosecutive subbads (M = 3) ad focus o the performace of the middle subbad. The middle subbad represets the full iterferece sceario sice it receives iterferece from both the left ad the right adjacet subbads. The mm-wave chael is geerated usig the coferece room sceario as described i IEEE 82.11-9 for 6 GHz carrier frequecy [6]. Throughout the simulatios, we assume that the lie of sight path is bloced ad the trasmitter ad receivers are steered toward the strogest o- LOS path. We modeled the trasmit ad the receive filters, used i evaluatig the basebad equivalet chaels (5), (6), ad (7), by the squared root raised cosie (SRRC) filter with excessive badwidth of 12.5%. The OFDM trasmitter for each subbad has 64 subcarriers (N = 64), with a cyclic prefix of 16 samples (the overhead due to the cyclic prefix ca be reduced by icreasig the umber of subcarriers). Cosiderig 256 MHz OFDM samplig rate, the chael spacig betwee subcarriers is 4 MHz (Table I) ad we use 16-QAM modulatio o each subcarrier. Chael codig is ot cosidered, sice our focus is o iter-bad iterferece. I Figure 7, we compare the bit error rate (BER) performace of a system with o iterferece suppressio with a bechmar ISI-oly system (i.e., oly oe subbad is trasmitted). The BER is averaged over 1 idepedet realizatios of the idoor coferece room chael. Clearly, while OFDM with the give cyclic prefix is effective i dealig with the ISI of the beamformed chael, iter-bad iterferece ca sigificatly degrade performace (error floor of 3 1 2 after 2 db SNR) uless suppressed. Figure 1 shows the BER v.s. OFDM subcarrier idex for two specific SNR values (6 db ad 2 db). We observe that if the iterferece suppressio is ot applied, as SNR icreases, the BER decays except for boudary subcarriers. This cofirms that the iterferece ecoutered from adjacet subbads appears oly at the boudary subcarriers. BER 1 1 1 1 2 1 3 ISI oly chael Without iterferece suppressio 1 4 1 2 3 4 5 SNR (db) Fig. 7. Bit error rate (BER) vs. SNR for the middle subbad with ad without iter-bad iterferece, averaged over 1 idepedet chael realizatios. No iterferece suppressio is applied. Bit Error Rate (BER).15.1.5 SNR 2dB SNR 6dB 1 2 3 4 5 6 OFDM Subcarrier Idex Fig. 8. Bit error rate (BER) vs. OFDM subcarrier for oe realizatio of the chael whe iter-bad iterferece is ot suppressed. BER decays with icreasig SNR except for boudary subcarriers, which ecouter iterferece from adjacet subbads. Figure 9 shows BER performace vs. SNR whe the ZF ad MMSE liear equalizers are applied. For the ZF equalizer, we assumed that the chael state iformatio for each subcarrier is ow at the receiver. However, the MMSE liear equalizer is traied based o 5 OFDM traiig symbols. For the quasi-static idoor chaels of iterest, we expect that such traiig would be eeded quite seldom (e.g., whe startig up a li), with cotiuig adaptatio i decisio-directed mode. Eve though we assume ideal chael estimatio for the ZF equalizer, the pealty from oise ehacemet is evidet from Figure 9, where it is compared with the MMSE liear equalizer ad the ISI-oly bechmar. This is because we are usig a relatively large 16QAM costellatio, for which oise ehacemet ca severely impact performace eve at moderately large SNRs. Figure 1 shows the amout of oise ehacemet per subcarrier for the ZF equalizer. We observe that while the oise ehacemet is egligible for the middle subcarriers, it is as large as 4 db for the boudary subcarriers. However, i the overall system performace, the oise ehacemet effect is ot sigificat, sice it oly affects a few OFDM subcarriers. I compariso with the ISI oly sceario (Figure 7), we see that usig a liear equalizer wors well for iterferece
suppressio ad the performace results are close to that of the ISI-oly bechmar. A error floor of 1 4 is also observed i the ISI-oly bechmar, ad is probably due to scearios i which the legth of the effective beamformed chael (desired or iterferig) exceeds that of the cyclic prefix. This is bore out by Figure 11, which shows that the error floor falls to 1 5 whe the cyclic prefix is icreased from 16 to 2 samples. BER 1 1 1 2 1 3 1 4 CP legth = 16 samples ISI oly chael ZF iterferece suppressio MMSE iterferece suppressio 1 15 2 25 3 35 4 45 5 SNR (db) Fig. 9. BER vs. SNR whe zero-forcig liear equalizer with ow chael ad MMSE equalizer with uow chael are applied. The BER is averaged over 1 idepedet chael scearios ad trasmit data streams. Noise ehacemet (db) 5 4 3 2 1 1 2 3 4 5 6 OFDM subcarrier Fig. 1. The amout of oise ehacemet for each subcarrier whe zeroforcig liear equalizer is applied for iter-chael iterferece. BER 1 1 1 1 2 1 3 1 4 1 5 CP legth = 2 samples ISI oly chael ZF iterferece suppressio MMSE iterferece suppressio 1 6 1 2 3 4 5 SNR (db) Fig. 11. The effect of icreasig the CP legth by 25% o system performace i compariso with Figure 9. VII. CONCLUSIONS Our results show that aalog multibad with OFDM is a attractive optio for very high rate commuicatio over dispersive chaels. For the idoor mm-wave commuicatio system ivestigated here, liear MMSE adaptatio is effective for suppressig the iterferece see by the edge subcarriers. We view this wor as oly the first step i a comprehesive ivestigatio of the potetial for our approach for sigificatly icreasig data rates, or reducig trasceiver power cosumptio, relative to existig desigs for IEEE 82.11ad. For the simple beamformed li cosidered here, it is importat to develop coded modulatio strategies potetially spaig multiple subbads for providig frequecy diversity. We would also lie to uderstad the source of the error floors. Are they because of the desired or the iterferig subbad s chael legth exceedig the cyclic prefix, ad is there some hybrid iterferece suppressio/cacellatio strategy for removig it? Of course, these error floors are low eough that they ca be hadled with light chael codig. A importat topic for future wor is the combiatio of diversity ad multiplexig with beamformig (e.g., whe there are multiple subarrays, each capable of beamformig idepedetly) [9] i the cotext of aalog multibad. ACKNOWLEDGMENT This research was supported i part by Samsug Research America - Dallas. We acowledge the help ad feedbac from researchers i Samsug Research America - Dallas o this wor. REFERENCES [1] B. Murma. ADC performace survey 1997-214. [Olie]. Available: http://www.staford.edu/ murma/adcsurvey.html. [2] A. Amirhay, V. Stojaovic, ad M. Horowitz, Multi-toe sigalig for high-speed bacplae electrical lis, i Proc. of the IEEE Globecom, vol. 2, March 24, pp. 1111 1117. [3] A. Amirhay, A. Abbasfar, J. Savoj, M. Jeeradit, B. Garlepp, R. Kollipara, V. Stojaovic, ad M. Horowitz, A 24 Gb/s software programmable aalog multi-toe trasmitter, IEEE Joural of Solid-State Circuits, vol. 43, o. 4, pp. 999 19, February 28. [4] V. Dyadyu, J. D. Buto, J. Pathiulagara, R. Kedall, O. Sevimli, L. Stoes, ad D. A. Abbott, A multigigabit millimeter-wave commuicatio system with improved spectral efficiecy, IEEE Tras. o Microwave Theory ad Techiques, vol. 55, o. 12, pp. 2813 2821, December 27. [5] H. Zhag, S. Veateswara, ad U. Madhow, Aalog multitoe with iterferece suppressio: Relievig the ADC bottleec for widebad 6 GHz systems, i Proc. of the IEEE Globecom, 212, pp. 235 231. [6] Chael models for 6 GHz WLAN systems, IEEE 82.11-9/334r8, 21. [7] A. Maltsev, R. Masleiov, A. Lomayev, A. Sevastyaov, ad A. Khoryaev, Statistical chael model for 6 GHz WLAN systems i coferece room eviromet, Radioegieerig, vol. 2, o. 2, pp. 49 422, Jue 211. [8] H. Xu, V. Kushya, ad T. S. Rappaport, Spatial ad temporal characteristics of 6 GHz idoor chaels, IEEE Joural of Selected Areas i Commuicatios, vol. 2, o. 3, pp. 62 63, April 22. [9] E. Torildso, U. Madhow, ad M. Rodwell, Idoor millimeter wave MIMO: Feasibility ad performace, IEEE Trasactios o Wireless Commuicatios, vol. 1, o. 12, pp. 415 416, December 211.