1 Suboptima Spatia Diversity Scheme for 60 Gz Miimeter-Wave WLAN Zhenyu Xiao, Member, IEEE arxiv:1511.02326v1 [cs.it] 7 Nov 2015 Abstract This etter revisits the equa-gain (EG) spatia diversity technique, hich as proposed to combat the humaninduced shadoing for 60 Gz ireess oca area netork, under a more practica frequency-seective muti-input mutioutput channe. Subsequenty, a suboptima spatia diversity scheme caed maxima seection (MS) is proposed by tracing the shadoing process, oing to a consideraby high data rate. Comparisons sho that MS outperforms EG in terms of ink margin and saves computation compexity. Index Terms 60 Gz, spatia diversity, miimeter ave, IEEE 802.11ad, human-induced shadoing. I. INTRODUCTION TE EMERGING IEEE 802.11ad ireess oca area netork (WLAN) standard promises muti-giga bits per second (Gbps) transmission by expoiting the 60 Gz communications [1]-[3], here beamforming technique is necessary to compensate for high path oss. Despite this, human-induced shadoing, especiay bocking, may easiy break a ink due to the stringent ink budget. To cope ith this, a re-beamforming process can be initiated to find an aternative ink [4], or a mutihop scheme can be adopted to bypass the bockage through one or more reay nodes [3], [5]. These approaches, hoever, have the probem that the transmitter and receiver detect that the ink is ost ony after dropping a arge amount of data due to the high data rate and a arge packet size [6]. To address this probem, a spatia diversity technique as proposed by Park and Pan in their recent ork [6], here mutipe beams aong the N strongest mutipe propagation paths are formed simutaneousy during a beamforming process, so that hen one of the propagation paths is bocked by a human, there are other propagation paths eft to maintain the communication ink. As the poer gain on each path is set to be equa, the scheme is caed equa-gain (EG) diversity scheme. Athough a frequency-fat muti-input muti-output (MIMO) channe as adopted in their ork, the EG scheme is proven effective to combat human-induced shadoing via simuation and experiments. In this etter the EG scheme is revisited under a frequencyseective (FS) MIMO channe, hich is more practica for 60 Gz communications, because the bandidth is sufficienty arge to resove mutipaths [3]. 1 Moreover, expicit expressions of tota poer gain are presented, hich are not provided in [6] This ork as supported by the Nationa Natura Science Foundation of China (NSFC) under grant No. 61201189, the Postdoctora Science Foundation under grant No. 2011M500326 and 2012T50094. The author is ith the Schoo of Eectronic and Information Engineering, Beihang University, Beijing 100191, P.R. China. 1 Note that in [3] the OFDM sampe time is 0.38 ns and the singe-carrier (SC) sampe/chip time is 0.57 ns, both of hich are sma enough to resove mutipaths. but necessary in computation of received poer. Subsequenty, reaizing that transmitting a packet is much faster than humaninduced shadoing for 60 Gz WLAN oing to the muti- Gbps speed, a suboptima spatia diversity scheme caed maxima seection (MS) is proposed by tracing the shadoing process. Comparison resuts on received poer and bit-error rate (BER) sho that the proposed scheme not ony achieves a higher ink margin in both norma and bocked cases, but aso reduces impementation compexity. II. CANNEL MODEL Let N t and N r denote the number of transmit and receive antennas, respectivey. A MIMO FS channe mode is adopted here. Fooing the conventions used in [6], e assume that the -th refector is ocated in direction (φ t,θ t ) from the transmitter, and (φ r,θ r ) from the receiver. The transmit steering vectors, h, corresponding to the refector and associated ith direction (φ t,θ t ), is expressed as h = 1 Nt [e j2πf0τ1(φ t,θ t ),...,e j2πf0τn t (φ t,θ t ) ] T, here f 0 is the carrier frequency of the signa, τ 1 (φ t,θ t ) = 0 and τ i (φ t,θ t ) is the reative deay for the i-th transmit antenna versus the first transmit antenna to the same receive antenna over the -th path, ( ) T is the transpose operator. Simiary, the receive steering vectors, g, corresponding to the -th refector and associated ith direction (φ r,θ r ), is expressed as g = 1 Nr [e j2πf0τ1(φ r,θ r ),...,e j2πf0τnr(φ r,θ r ) ] T, here τ 1 (φ r,θ r ) = 0 and τ i (φ r,θ r ) is the reative deay for the i- th receive antenna versus the first receive antenna to the same transmit antenna over the -th path. Thus, the channe matrix over the -th path can be expressed as C = g λ h T, here λ is the channe coefficient of the -th path. Subsequenty, taking the mutipath deay into account, the FS channe matrix is obtained as C[k] = N =1 C δ[k ], here N is the number of mutipaths, is the normaized deay from the first transmit antenna to the first receive antenna over the -th path. It is important to note that as not invoved in [6]; thus, the channe mode reduced to a frequency-fat one there. III. EG DIVERSITY REVISIT The m-th received sampe y[m] over the N paths is expressed as y[m] = r T t C s[m ]+ r T n, (1) t t =1 here s[m] is the m-th transmitted sampe ith an average poer P, t and r are transmit and receive antenna eight vectors (AWVs), respectivey, n is a circuary symmetric compex Gaussian noise vector ith identica variance for each
2 eement. Defining the transmit and receive antenna gain over the -th path as α = h T t and β = r Tg, respectivey, e have 1 N y[m] = α β λ s[m ]+ r T n. (2) t t =1 Let λ (0) denote the channe gain, hich accounts for the effect of propagation oss and refection oss of the -th path hen beamforming is performed. As EG sets identica poer gains, hich are channe gains mutipied by antenna gains over each path, e achieve α β = λ (0) /λ (0), here λ (0) = 1 N N =1 λ(0). ence y[m] can be expressed as y[m] = 1 N t t =1 λ (0) λ (0) λ s[m ]+r T n. (3) It is noted that in a non-shadoing case, the channe gains do not vary, i.e., λ = λ (0) ; thus, y[m] = 1/ t T N t λ =1 (0) s[m ]+r T n. oever, in a shadoing case it does not hod since λ λ (0) once λ varies. Taking the number of transmit and receive antennas into account, one appropriate ay to determine α and β is to constrain α /β = N t /N r. Thus, α = λ (0) /λ (0) N t /N r and β = λ (0) /λ (0) N r /N t. With both the ampitude and phase controed (APC), the transmit and receive AWVs are obtained as t = ( T ) 1 α and r = β T G 1, (4) here α = [α 1,...,α N ] T, β = [β 1,...,β N ] T, = [h 1,...,h N ], G = [g 1,...,g N ], ( ) 1 is the pseudo-inverse operation. The tota poer gain for the EG scheme ith APC is λ (0) G EG APC = =1 λ (0) λ 2 /(( t t )( r r )), (5) hich is the poer gain observed after the receive antenna array versus that before the transmit antenna array. Thus, it depends on the AWVs in both ends and the channe gains λ, as shon in (5). Note that in the above derivations, EG ith APC is adopted. In the case that ony phase can be controed (PC), the channe gains cannot be precisey set. In such a case, t and r are obtained by t = exp(j (( T ) 1 α)) and r = exp(j (β T G 1 )), (6) respectivey, here is the phase operation. Thus, y[m] is expressed as (1) instead of (3), and the corresponding tota poer gain is G EG PC = 2 /(( )( )) T r C t t t r r. (7) =1 IV. SUBOPTIMAL DIVERSITY SCEME The EGC scheme is efficient hen the LOS path is bocked. In the norma case that the LOS path is not bocked, hoever, it is not optima because arger antenna gains are set to poorer paths, i.e., transmit poer is asted on the NLOS paths. Moreover, FS effect is generated and intensified due to the identicaenergy mutipath components. In this section, the optima gain setting is simpy anayzed under an idea assumption. Based on it, the corresponding suboptima diversity scheme is proposed. With the 2-norm of the transmit and receive AWVs constrained to unity, according to (1), the optima AWVs to maximize receive signa-to-noise ratio (SNR) is achieved by [ opt t, opt r ] = arg max t, r N =1 T r g λ h T t 2. (8) Thus, the optima gain setting is α opt = h T opt t and β opt = (r opt ) T g. When N = 1, the optima soution is easiy obtained as opt t = h 1 and opt r = g1, here ( ) is the conjugate operation. oever, hen N > 1, i.e., mutipath exists, the optima soution of (8) is consideraby difficut to obtain. Even though expoiting an iterative approach is abe to achieve the optima soution [7], it is not necessary to achieve the optima BER performance, because inter-symbo interference due to mutipath is not invoved in (8). To faciitate the anaysis, it is natura to assume that the mutipe refection directions do not overap ith each other, i.e., h h m = 0 and g g m = 0 hen m, here ( ) is the conjugate transpose operation. In fact, hen N t and N r are arge, the beamidth of h and g are narro, and do not overap ith h m and g m, respectivey. Thus, h h m and g g m i approximatey equa 0. Let yet h T t = α and r T g = β. Under this idea assumption, e have N =1 α2 = 1 and N =1 β2 = 1, due to the 2-norm constraint of AWVs. Let λ 2 n = max({λ 2 } = 1,2,...,N), e achieve r T g λ h T t 2 λ 2 n β 2 α2 λ2 n =1 =1 =1 β 2 α 2 = λ2 n, here the equaity hods hen α = β = δ[ n]. This is the optima gain setting under the assumption, hich suggests that the antenna arrays in both the transmitter and the receiver shoud beamform toards the direction of the strongest path. In such a case, the received poer is arger, and the FS effect is ess, hich both contribute to improving the ink margin. No the remaining question is ho the antenna arrays can aays beamform to the direction of the strongest path ithout dropping data. Reaizing that a 60 Gz WLAN achieves a muti-gbps speed, much faster compared ith a shadoing process, e propose the shadoing tracing agorithm for this purpose, hich is described as Agorithm 1. It is cear that for MS the hoe shadoing process is traced. Expoiting the shadoing tracing approach, the transceiver can rapidy change its beam toards the current strongest path ithout dropping data or time-costy re-beamforming once the on-communication path is being bocked. In [6] the typica shadoing duration is 664 ms. The data octets of the current IEEE 802.11ad packet are specified to be ithin the range of 0-262143 [3]. ence, the maxima packet duration is ony 262143 8/10 9 10 3 = 2.097 ms if the transmit speed reaches 1 Gbps, hich means that the packet duration is significanty smaer than the decay duration and the atter can be e =1
3 Agorithm 1 The MS Scheme ith shadoing tracing 1) Initiaize: Perform beamforming. Sort the channe gains (λ (0) ) in a descending order. Store them and their corresponding steering vectors ( and G). 2) Norma Communication: Set k = 1. The transceiver beamforms to and communicate over the 1-st path direction, hich is usuay the LOS path. During communication, the channe gain of the path (λ 1 ) is estimated for every packet. When the 1-st path is being bocked, the channe gain λ 1 i decrease sharpy. Once λ 1 < λ (0) 2, go to 3). 3) Reseection: Set k = k + 1. The transceiver change beamforming toards the k-th path according to the stored steering vector, and estimate the current channe gain λ k. If λ k < λ (0) min(k+1,n), hich means the current path is aso bocked, repeat 3) if k < N; go to 1) to restart beamforming if k = N. Otherise go to 4). 4) NLOS Communication: Communication is continued over the neseected k-th path. The shadoing on the 1-st path is traced periodicay, i.e., communication on the current path pauses ith a period T P, and the transceiver beamform to the 1-st path to test hether the bock moves aay. If the estimated channe gain λ 1 becomes arger than λ (0) k, hich means that the bock is moving aay, go back to 2). Otherise the transceiver beamforms toard the k-th path to continue NLOS communication. If the time for re-beamforming comes, or λ k decreases dramaticay due to another bock on the current path, go to 1) for re-beamforming. traced. Therefore, the MS scheme is appicabe in practice. When communicating on the k-th path, the eight vectors for MS are t = h k and r = g k. (9) In such a case the tota poer gain can be cacuated from (7), hich is G MS = r T C k t ( 2 ) t t ( r r ) = λ 2 k N tn r, (10) t=h k,r=g k heren t andn r are gains of the transmit and receive antenna arrays, respectivey. It can be observed that, compared ith the EG scheme, the superior points of MS are (i) it has a oer computation compexity, because there are no matrix inversions and mutipications hen cacuating the eight vectors; (ii) it achieves a higher tota poer gain and does not induce FS effect, because the antenna arrays aays beamform toards the direction of the current strongest path. received poer (dbm) 45 50 55 60 65 L r = 0 db L r = 8 db 70 : EG ith PC L = 16 db r o o o o : EG ith APC x x x x : Proposed MS Non diversity 75 0 0.2 0.4 0.6 0.8 1 time (seconds) Fig. 1. Comparison of received signa poers beteen EG, MS and the nondiversity scheme ith different refection osses. PC denotes phase contro ony, hie APC denotes both ampitude and phase contro. The drop of the received poer is caused by human-induced shadoing. The extra cost of MS is shadoing tracing. The channe gain of the 1-st path needs to be estimated each packet in the Norma Communication state, and ith an appropriate period T P in the NLOS Communication state. As a channe estimation sequence is defined in the standard IEEE 802.11ad frame format [3], shadoing tracing in the Norma Communication state does not cause additiona cost. oever, shadoing tracing in the NLOS Communication state i degrade efficiency, because communication needs a periodica temporary pause, and antenna arrays in both ends need to change beamforming beteen toard the 1-st and the on-communication path directions, hich may eapse tens or hundreds µs. The efficiency degradation is η = 2T BS /T P, here T BS is the beam-sitching time, and T P is the estimation period, hich shoud be significanty smaer than the shadoing duration. As the shadoing duration is about severa hundred ms [6], by seecting a reativey arge estimation period, e.g., 20 ms, and a common beam-sitching time, e.g., 100 µs, the typica degradation of efficiency is ony 0.2/20 = 1%, hich is minima and acceptabe. V. PERFORMANCE EVALUATION Received poers are cacuated ith the same antenna pacement, human-induced shadoing mode, 2 path oss mode, transmit poer as that in [6]. The refection oss (L r ) is set 0 to 16 db in 8 db step. A 20 1 antenna array is used in both the transmitter and the receiver. The received signa poer is achieved by adding the transmit poer (P = 10 dbm) and the corresponding tota poer gain in db. Fig. 1 depicts the received signa poers for EG, MS and the non-diversity scheme ith different refection osses. From this figure e observe that, as e expected, hen the LOS path is not bocked, EG receives a oer poer than the nondiversity scheme. EG ith PC oses more poer compared to that ith APC, hereas hen the LOS path is bocked, EG ith PC receives a higher poer than that ith APC. By 2 The shadoing duration as 664 msec, the decay time as 55.7 msec, the maximum attenuation as 23.3 db, and the rise time as 31.8 msec.
4 BER 10 1 10 2 10 3 10 4 EG ith PC, non bocked EG ith APC, non bocked EG ith PC, bocked EG ith APC, bocked MS, non bocked MS, bocked 4 3.5 3 2.5 2 1.5 1 0.5 0 Receive SNR (db) Fig. 2. BER performance of EG and MS ith L r = 8 db in both bocked and non-bocked cases. The receive SNR is set the same in the bocked and non-bocked case to refect the FS effect more ceary. contrast, the proposed MS scheme receives a higher poer than the EG scheme in both non-bocked and bocked cases. In the non-bocked case the superiority is more evident hen the refection oss is arger; hie in the bocked case it is the opposite. We stress that the MS scheme has no poer oss compared ith the non-diversity scheme hen the LOS path is not bocked. In addition to the received poer, the BER performance is aso evauated via simuation, here carrier and timing synchronization, as e as channe estimation, are assumed perfect. As the BER comparison here is to evauate the FS effect, the receive SNR is set the same for a the cases. The moduation and coding scheme 1 (MCS1) of SC PY in [3] ith a chip time of T c = 0.57 ns is adopted and the SC frequency-domain equaization (SC-FDE) is used in the receiver to combat the FS effect. The typica refection oss, i.e., L r = 8 db, is expoited. For EG, there are to mutipath components. The reative deay for the NLOS path bounced by the ceiing versus the LOS path is [( (7/2) 2 +2 2 2 7)/(3 10 8 )/0.57 10 9 ] = 6 chip intervas, 3 here [ ] is integer round operation. The gains for the LOS and NLOS path are h 1 = λ 1 r Tg 1h T 1 t and h 2 = λ 2 r T g 2 h T 2 t, respectivey, here h and g are determined by the antenna pacement, λ 1 and λ 2 are computed according to propagation oss and refection oss, t and r are cacuated according to (4) for APC and (6) for PC. The equivaent normaized baseband channe response is (h 1,0,0,0,0,0,h 2 e j2πf6tc ) T / h 1 2 + h 2 2, here f is the carrier frequency and f = 60 Gz. Note that the channe responses are different beteen bocked and nonbocked cases, because λ 1, the channe gain of the LOS path, varies. For MS, the channe response is simiary set. The BER performance is shon in Fig. 2. It can be observed that in the non-bocked case, EG ith APC has a significant oss compared ith MS, hie EG ith PC has a smaer oss. As SNR becomes arger, the gap beteen EG ith APC 3 According to the mode in [6], the LOS distance beteen the transceiver is 7m, and the height from the antennas to the ceiing is 2m. The propagation speed of 60 Gz signa is 3 10 8 m/s. and MS becomes arger. Simiar resuts can be observed ith different parameter settings, e.g., transceiver distance, height of antenna, etc. This is because in the non-bocked case EG ith APC eads to to identica-energy mutipath components, hich strengthens the FS effect. EG ith PC cannot stricty satisfy the target of equa gain on each path due to the phase operation. ence, the to mutipath components have actuay different energy, hich eakens the FS effect, and thus the corresponding BER is significanty better than that of EG ith APC. In the bocked case, most channe energy of EG ith PC and APC disperse on the NLOS path, because it has a arger channe gain and antenna gain than the bocked LOS path. Consequenty, the FS effect is itte and the BER performance of EG ith PC and APC become cose to that of MS. Moreover, as MS aays beamforms to the direction of the stronger path, the FS effect is itte. The overa ink margin performance depends on both the received poer and BER performance. If e jointy consider Fig. 1 and Fig. 2 in the case of L r = 8 db, in the bocked case, compared to EG ith PC, MS achieves about a 10.3 db higher receive poer and a 0.1 db SNR gain at 10 5 BER, i.e., a 10.4 db higher ink margin; compared to EG ith APC, MS achieves about an 8.8 db higher receive poer and a 1.3 db SNR gain at 10 5 BER, i.e., a 10.1 db higher ink margin. In the non-bocked case, MS has no SNR gain according to Fig. 2, but yet receives respectivey 1.3 and 2.6 db higher ink margin compared to EG ith PC and APC due to the higher received poer according to Fig. 1. In summary, MS achieves a higher ink margin than EG ith PA and APC in both cases, and the superiority is more significant in the non-bocked case. VI. CONCLUSION The EG scheme has been revisited under a frequencyseective mutipath MIMO channe for 60 Gz communications, and the tota poer gain that is necessary in the computation of received poer has been obtained. Subsequenty, the suboptima MS diversity scheme has been proposed by expoiting the shadoing tracing approach, hich expoits the muti-gbps speed of 60 Gz WLAN. Comparisons on the received poer and BER sho that MS has oer computation compexity, and achieves a higher ink margin than EG, oing to the higher receive poer and ess FS effect. The superiority on ink margin is more significant in the norma case, i.e., hen the LOS path is not bocked. REFERENCES [1] E. Perahia, C. Cordeiro, M. Park, and L. L. Yang, IEEE 802.11ad: Defining the next generation muti-gbps Wi-Fi, in Proc. IEEE CCNC, Jan. 2010, pp. 1-5. [2] M. Park, C. Cordeiro, E. Perahia, and L. L. Yang, Miimeter-ave muti-gigabit WLAN: chaenges and feasibiity, in Proc. IEEE PIMRC, Cannes, France, Sept. 2008, pp. 1-5. [3] Part 11: ireess LAN medium access contro (MAC) and physica ayer (PY) specifications amendment 3: enhancements for very high throughput in the 60 Gz band, IEEE P802.11ad TM /D9.0, Juy 2012. [4] X. An, C. Sum, R. V. Prasad, etc., Beam sitching support to resove ink-bockage probem in 60 Gz WPANs. In Proc. IEEE PIMRC, Sept. 2009, pp. 390-394. [5] S. Sumit, F. Ziiotto, U. Madho, etc., Bockage and directivity in 60 Gz ireess persona area netorks: from cross-ayer mode to mutihop MAC design. Seected Areas in Communications, IEEE Journa on, vo. 27, no. 8, pp. 1400-1413, Oct. 2009.
[6] M. Park,. K. Pan, A spatia diversity technique for IEEE 802.11ad WLAN in 60 Gz band, IEEE Communications Letters, pp. 1260-1262, Aug. 2012. [7] P. Xia,. Niu, J. Oh, C. Ngo, Practica antenna training for miimeter ave MIMO communication, in Proc. IEEE VTC, Sept. 2008, pp. 1-5. 5
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