Suboptimal Spatial Diversity Scheme for 60 GHz Millimeter-Wave WLAN
aa r X i v : . [ c s . I T ] N ov Suboptimal Spatial Diversity Scheme for 60 GHzMillimeter-Wave WLAN
Zhenyu Xiao,
Member, IEEE
Abstract —This letter revisits the equal-gain (EG) spatial di-versity technique, which was proposed to combat the human-induced shadowing for 60 GHz wireless local area network,under a more practical frequency-selective multi-input multi-output channel. Subsequently, a suboptimal spatial diversityscheme called maximal selection (MS) is proposed by tracingthe shadowing process, owing to a considerably high data rate.Comparisons show that MS outperforms EG in terms of linkmargin and saves computation complexity.
Index Terms —60 GHz, spatial diversity, millimeter wave, IEEE802.11ad, human-induced shadowing.
I. I
NTRODUCTION T HE EMERGING IEEE 802.11ad wireless local areanetwork (WLAN) standard promises multi-giga bits persecond (Gbps) transmission by exploiting the 60 GHz commu-nications [1]-[3], where beamforming technique is necessaryto compensate for high path loss. Despite this, human-inducedshadowing, especially blocking, may easily break a link due tothe stringent link budget. To cope with this, a re-beamformingprocess can be initiated to find an alternative link [4], ora multihop scheme can be adopted to bypass the blockagethrough one or more relay nodes [3], [5]. These approaches,however, have the problem that the transmitter and receiverdetect that the link is lost only after dropping a large amountof data due to the high data rate and a large packet size [6].To address this problem, a spatial diversity technique wasproposed by Park and Pan in their recent work [6], wheremultiple beams along the N strongest multiple propagationpaths are formed simultaneously during a beamforming pro-cess, so that when one of the propagation paths is blocked by ahuman, there are other propagation paths left to maintain thecommunication link. As the power gain on each path is setto be equal, the scheme is called equal-gain (EG) diversityscheme. Although a frequency-flat multi-input multi-output(MIMO) channel was adopted in their work, the EG schemeis proven effective to combat human-induced shadowing viasimulation and experiments.In this letter the EG scheme is revisited under a frequency-selective (FS) MIMO channel, which is more practical for 60GHz communications, because the bandwidth is sufficientlylarge to resolve multipaths [3]. Moreover, explicit expressionsof total power gain are presented, which are not provided in [6]
This work was supported by the National Natural Science Foundationof China (NSFC) under grant No. 61201189, the Postdoctoral ScienceFoundation under grant No. 2011M500326 and 2012T50094.The author is with the School of Electronic and Information Engineering,Beihang University, Beijing 100191, P.R. China. Note that in [3] the OFDM sample time is 0.38 ns and the single-carrier(SC) sample/chip time is 0.57 ns, both of which are small enough to resolvemultipaths. but necessary in computation of received power. Subsequently,realizing that transmitting a packet is much faster than human-induced shadowing for 60 GHz WLAN owing to the multi-Gbps speed, a suboptimal spatial diversity scheme calledmaximal selection (MS) is proposed by tracing the shadowingprocess. Comparison results on received power and bit-errorrate (BER) show that the proposed scheme not only achievesa higher link margin in both normal and blocked cases, butalso reduces implementation complexity.II. C
HANNEL M ODEL
Let N t and N r denote the number of transmit and re-ceive antennas, respectively. A MIMO FS channel modelis adopted here. Following the conventions used in [6], weassume that the l -th reflector is located in direction ( φ tl , θ tl ) from the transmitter, and ( φ rl , θ rl ) from the receiver. Thetransmit steering vectors, h l , corresponding to the l reflec-tor and associated with direction ( φ tl , θ tl ) , is expressed as h l = √ N t [ e j πf τ ( φ tl ,θ tl ) , ..., e j πf τ Nt ( φ tl ,θ tl ) ] T , where f is the carrier frequency of the signal, τ ( φ tl , θ tl ) = 0 and τ i ( φ tl , θ tl ) is the relative delay for the i -th transmit antennaversus the first transmit antenna to the same receive antennaover the l -th path, ( · ) T is the transpose operator. Similarly,the receive steering vectors, g l , corresponding to the l -threflector and associated with direction ( φ rl , θ rl ) , is expressedas g l = √ N r [ e j πf τ ( φ rl ,θ rl ) , ..., e j πf τ Nr ( φ rl ,θ rl ) ] T , where τ ( φ rl , θ rl ) = 0 and τ i ( φ rl , θ rl ) is the relative delay for the i -th receive antenna versus the first receive antenna to the sametransmit antenna over the l -th path. Thus, the channel matrixover the l -th path can be expressed as C l = g l λ l h Tl , where λ l is the channel coefficient of the l -th path. Subsequently,taking the multipath delay into account, the FS channel matrixis obtained as C [ k ] = P Nl =1 C l δ [ k − ∆ l ] , where N is thenumber of multipaths, ∆ l is the normalized delay from thefirst transmit antenna to the first receive antenna over the l -thpath. It is important to note that ∆ l was not involved in [6];thus, the channel model reduced to a frequency-flat one there.III. EG D IVERSITY R EVISIT
The m -th received sample y [ m ] over the N paths is ex-pressed as y [ m ] = N X l =1 w Tr C l w t p w Ht w t s [ m − ∆ l ] + w Tr n , (1)where s [ m ] is the m -th transmitted sample with an averagepower P , w t and w r are transmit and receive antenna weightvectors (AWVs), respectively, n is a circularly symmetriccomplex Gaussian noise vector with identical variance for each element. Defining the transmit and receive antenna gain overthe l -th path as α l = h Tl w t and β l = w Tr g l , respectively, wehave y [ m ] = 1 p w Ht w t N X l =1 α l β l λ l s [ m − ∆ l ] + w Tr n . (2)Let λ (0) l denote the channel gain, which accounts for theeffect of propagation loss and reflection loss of the l -thpath when beamforming is performed. As EG sets identicalpower gains, which are channel gains multiplied by antennagains over each path, we achieve α l β l = ¯ λ (0) /λ (0) l , where ¯ λ (0) = N P Nl =1 λ (0) l . Hence y [ m ] can be expressed as y [ m ] = 1 p w Ht w t N X l =1 ¯ λ (0) λ (0) l λ l s [ m − ∆ l ] + w Tr n . (3)It is noted that in a non-shadowing case, the channelgains do not vary, i.e., λ l = λ l (0) ; thus, y [ m ] =1 / p w Tt w t P Nl =1 ¯ λ (0) s [ m − ∆ l ] + w Tr n . However, in a shad-owing case it does not hold since λ l = λ l (0) once λ l varies.Taking the number of transmit and receive antennasinto account, one appropriate way to determine α l and β l is to constrain α l /β l = N t /N r . Thus, α l = q ¯ λ (0) /λ (0) l N t /N r and β l = q ¯ λ (0) /λ (0) l N r /N t . With boththe amplitude and phase controlled (APC), the transmit andreceive AWVs are obtained as w t = ( H T ) − α and w r = β T G − , (4)where α = [ α , ..., α N ] T , β = [ β , ..., β N ] T , H =[ h , ..., h N ] , G = [ g , ..., g N ] , ( · ) − is the pseudo-inverseoperation.The total power gain for the EG scheme with APC is G EG − AP C = N X l =1 (cid:12)(cid:12)(cid:12)(cid:12) ¯ λ (0) λ (0) l λ l (cid:12)(cid:12)(cid:12)(cid:12) (cid:14) (cid:0)(cid:0) w Ht w t (cid:1) (cid:0) w Hr w r (cid:1)(cid:1) , (5)which is the power gain observed after the receive antennaarray versus that before the transmit antenna array. Thus, itdepends on the AWVs in both ends and the channel gains λ l ,as shown in (5).Note that in the above derivations, EG with APC is adopted.In the case that only phase can be controlled (PC), the channelgains cannot be precisely set. In such a case, w t and w r areobtained by w t = exp ( j ∠ (( H T ) − α )) and w r = exp ( j ∠ ( β T G − )) , (6)respectively, where ∠ is the phase operation. Thus, y [ m ] isexpressed as (1) instead of (3), and the corresponding totalpower gain is G EG − P C = N X l =1 (cid:12)(cid:12)(cid:12)(cid:12) w Tr C l w t (cid:12)(cid:12)(cid:12)(cid:12) (cid:14) (cid:0)(cid:0) w Ht w t (cid:1) (cid:0) w Hr w r (cid:1)(cid:1) . (7)IV. S UBOPTIMAL D IVERSITY S CHEME
The EGC scheme is efficient when the LOS path is blocked.In the normal case that the LOS path is not blocked, however,it is not optimal because larger antenna gains are set to poorer paths, i.e., transmit power is wasted on the NLOS paths. More-over, FS effect is generated and intensified due to the identical-energy multipath components. In this section, the optimal gainsetting is simply analyzed under an ideal assumption. Based onit, the corresponding suboptimal diversity scheme is proposed.With the 2-norm of the transmit and receive AWVs con-strained to unity, according to (1), the optimal AWVs tomaximize receive signal-to-noise ratio (SNR) is achieved by [ w optt , w optr ] = arg max w t , w r X Nl =1 | w Tr g l λ l h Tl w t | . (8)Thus, the optimal gain setting is α optl = h Tl w optt and β optl =( w optr ) T g l . When N = 1 , the optimal solution is easilyobtained as w optt = h ∗ and w optr = g ∗ , where ( · ) ∗ is theconjugate operation. However, when N > , i.e., multipathexists, the optimal solution of (8) is considerably difficult toobtain. Even though exploiting an iterative approach is ableto achieve the optimal solution [7], it is not necessary toachieve the optimal BER performance, because inter-symbolinterference due to multipath is not involved in (8).To facilitate the analysis, it is natural to assume that themultiple reflection directions do not overlap with each other,i.e., h † l h m = 0 and g † l g m = 0 when l = m , where ( · ) † isthe conjugate transpose operation. In fact, when N t and N r are large, the beamwidth of h l and g l are narrow, and do notoverlap with h m and g m , respectively. Thus, h † l h m and g † l g m will approximately equal 0.Let yet h Tl w t = α l and w Tr g l = β l . Under this idealassumption, we have P Nl =1 α l = 1 and P Nl =1 β l = 1 , dueto the 2-norm constraint of AWVs. Let λ n = max( { λ l }| l =1 , , ..., N ) , we achieve N X l =1 | w Tr g l λ l h Tl w t | ≤ λ n N X l =1 β l α l ≤ λ n N X l =1 β l N X l =1 α l = λ n , where the equality holds when α l = β l = δ [ l − n ] . This isthe optimal gain setting under the assumption, which suggeststhat the antenna arrays in both the transmitter and the receivershould beamform towards the direction of the strongest path.In such a case, the received power is larger, and the FS effectis less, which both contribute to improving the link margin.Now the remaining question is how the antenna arrays canalways beamform to the direction of the strongest path withoutdropping data. Realizing that a 60 GHz WLAN achieves amulti-Gbps speed, much faster compared with a shadowingprocess, we propose the shadowing tracing algorithm for thispurpose, which is described as Algorithm 1.It is clear that for MS the whole shadowing process is traced.Exploiting the shadowing tracing approach, the transceiver canrapidly change its beam towards the current strongest pathwithout dropping data or time-costly re-beamforming once theon-communication path is being blocked. In [6] the typicalshadowing duration is 664 ms. The data octets of the currentIEEE 802.11ad packet are specified to be within the rangeof 0-262143 [3]. Hence, the maximal packet duration is only × / × = 2 . ms if the transmit speed reaches1 Gbps, which means that the packet duration is significantlysmaller than the decay duration and the latter can be well Algorithm 1
The MS Scheme with shadowing tracing
1) Initialize:
Perform beamforming. Sort the channel gains( λ (0) l ) in a descending order. Store them and theircorresponding steering vectors ( H and G ).
2) Normal Communication:
Set k = 1 . The transceiver beamforms to andcommunicate over the 1-st path direction, whichis usually the LOS path. During communication,the channel gain of the path ( λ ) is estimated forevery packet. When the 1-st path is being blocked,the channel gain λ will decrease sharply. Once λ < λ (0)2 , go to .
3) Reselection:
Set k = k + 1 . The transceiver change beam-forming towards the k -th path according to thestored steering vector, and estimate the currentchannel gain λ k . If λ k < λ (0)min( k +1 ,N ) , whichmeans the current path is also blocked, repeat if k < N ; go to to restart beamforming if k = N .Otherwise go to .
4) NLOS Communication:
Communication is continued over the new-selected k -th path. The shadowing on the 1-stpath is traced periodically, i.e., communication onthe current path pauses with a period T P , andthe transceiver beamform to the 1-st path to testwhether the block moves away. If the estimatedchannel gain λ becomes larger than λ (0) k , whichmeans that the block is moving away, go back to . Otherwise the transceiver beamforms towardthe k-th path to continue NLOS communication.If the time for re-beamforming comes, or λ k decreases dramatically due to another block onthe current path, go to for re-beamforming.traced. Therefore, the MS scheme is applicable in practice.When communicating on the k -th path, the weight vectors forMS are w t = h ∗ k and w r = g ∗ k . (9)In such a case the total power gain can be calculated from(7), which is G MS = | w rT C k w t | (cid:0) w Ht w t (cid:1) ( w Hr w r ) (cid:12)(cid:12)(cid:12)(cid:12) w t = h ∗ k , w r = g ∗ k = λ k N t N r , (10)where N t and N r are gains of the transmit and receive antennaarrays, respectively.It can be observed that, compared with the EG scheme,the superior points of MS are (i) it has a lower computa-tion complexity, because there are no matrix inversions andmultiplications when calculating the weight vectors; (ii) itachieves a higher total power gain and does not induce FSeffect, because the antenna arrays always beamform towardsthe direction of the current strongest path. r e c e i v ed po w e r ( d B m ) L r = 16 dBL r = 0 dBL r = 8 dBNon−diversity : EG with PCo o o o : EG with APCx x x x : Proposed MS Fig. 1. Comparison of received signal powers between EG, MS and the non-diversity scheme with different reflection losses. PC denotes phase controlonly, while APC denotes both amplitude and phase control. The drop of thereceived power is caused by human-induced shadowing.
The extra cost of MS is shadowing tracing . The channelgain of the 1-st path needs to be estimated each packet in theNormal Communication state, and with an appropriate period T P in the NLOS Communication state. As a channel estima-tion sequence is defined in the standard IEEE 802.11ad frameformat [3], shadowing tracing in the Normal Communicationstate does not cause additional cost. However, shadowingtracing in the NLOS Communication state will degrade effi-ciency, because communication needs a periodical temporarypause, and antenna arrays in both ends need to change beam-forming between toward the 1-st and the on-communicationpath directions, which may elapse tens or hundreds µ s. Theefficiency degradation is η = 2 T BS /T P , where T BS is thebeam-switching time, and T P is the estimation period, whichshould be significantly smaller than the shadowing duration.As the shadowing duration is about several hundred ms [6],by selecting a relatively large estimation period, e.g., 20 ms,and a common beam-switching time, e.g., 100 µ s, the typicaldegradation of efficiency is only . /
20 = 1% , which isminimal and acceptable.V. P
ERFORMANCE E VALUATION
Received powers are calculated with the same antennaplacement, human-induced shadowing model, path lossmodel, transmit power as that in [6]. The reflection loss ( L r )is set 0 to 16 dB in 8 dB step. A × antenna array is usedin both the transmitter and the receiver. The received signalpower is achieved by adding the transmit power ( P = 10 dBm) and the corresponding total power gain in dB.Fig. 1 depicts the received signal powers for EG, MS andthe non-diversity scheme with different reflection losses. Fromthis figure we observe that, as we expected, when the LOSpath is not blocked, EG receives a lower power than the non-diversity scheme. EG with PC loses more power comparedto that with APC, whereas when the LOS path is blocked,EG with PC receives a higher power than that with APC. By The shadowing duration was 664 msec, the decay time was 55.7 msec,the maximum attenuation was 23.3 dB, and the rise time was 31.8 msec. −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 010 −4 −3 −2 −1 Receive SNR (dB) BE R EG with PC, non−blockedEG with APC, non−blockedEG with PC, blockedEG with APC, blockedMS, non−blockedMS, blocked
Fig. 2. BER performance of EG and MS with L r = 8 dB in both blockedand non-blocked cases. The receive SNR is set the same in the blocked andnon-blocked case to reflect the FS effect more clearly. contrast, the proposed MS scheme receives a higher powerthan the EG scheme in both non-blocked and blocked cases.In the non-blocked case the superiority is more evident whenthe reflection loss is larger; while in the blocked case it is theopposite. We stress that the MS scheme has no power losscompared with the non-diversity scheme when the LOS pathis not blocked.In addition to the received power, the BER performanceis also evaluated via simulation, where carrier and timingsynchronization, as well as channel estimation, are assumedperfect. As the BER comparison here is to evaluate the FSeffect, the receive SNR is set the same for all the cases.The modulation and coding scheme 1 (MCS1) of SC PHYin [3] with a chip time of T c = 0 . ns is adopted andthe SC frequency-domain equalization (SC-FDE) is used inthe receiver to combat the FS effect. The typical reflec-tion loss, i.e., L r = 8 dB, is exploited. For EG, thereare two multipath components. The relative delay for theNLOS path bounced by the ceiling versus the LOS pathis [( p (7 / + 2 × − / (3 × ) / . × − ] = 6 chip intervals, where [ · ] is integer round operation. Thegains for the LOS and NLOS path are h = λ w Tr g h T w t and h = λ w Tr g h T w t , respectively, where h l and g l are determined by the antenna placement, λ and λ arecomputed according to propagation loss and reflection loss, w t and w r are calculated according to (4) for APC and (6)for PC. The equivalent normalized baseband channel responseis ( h , , , , , , h e − j πf T c ) T / p | h | + | h | , where f is the carrier frequency and f = 60 GHz. Note that thechannel responses are different between blocked and non-blocked cases, because λ , the channel gain of the LOS path,varies. For MS, the channel response is similarly set.The BER performance is shown in Fig. 2. It can be observedthat in the non-blocked case, EG with APC has a significantloss compared with MS, while EG with PC has a smallerloss. As SNR becomes larger, the gap between EG with APC According to the model in [6], the LOS distance between the transceiveris 7m, and the height from the antennas to the ceiling is 2m. The propagationspeed of 60 GHz signal is × m/s. and MS becomes larger. Similar results can be observed withdifferent parameter settings, e.g., transceiver distance, heightof antenna, etc. This is because in the non-blocked case EGwith APC leads to two identical-energy multipath components,which strengthens the FS effect. EG with PC cannot strictlysatisfy the target of equal gain on each path due to the phaseoperation. Hence, the two multipath components have actuallydifferent energy, which weakens the FS effect, and thus thecorresponding BER is significantly better than that of EGwith APC. In the blocked case, most channel energy of EGwith PC and APC disperse on the NLOS path, because ithas a larger channel gain and antenna gain than the blockedLOS path. Consequently, the FS effect is little and the BERperformance of EG with PC and APC become close to that ofMS. Moreover, as MS always beamforms to the direction ofthe stronger path, the FS effect is little.The overall link margin performance depends on both thereceived power and BER performance. If we jointly considerFig. 1 and Fig. 2 in the case of L r = 8 dB, in the blockedcase, compared to EG with PC, MS achieves about a 10.3 dBhigher receive power and a 0.1 dB SNR gain at − BER,i.e., a 10.4 dB higher link margin; compared to EG with APC,MS achieves about an 8.8 dB higher receive power and a 1.3dB SNR gain at − BER, i.e., a 10.1 dB higher link margin.In the non-blocked case, MS has no SNR gain according toFig. 2, but yet receives respectively 1.3 and 2.6 dB higher linkmargin compared to EG with PC and APC due to the higherreceived power according to Fig. 1. In summary, MS achievesa higher link margin than EG with PA and APC in both cases,and the superiority is more significant in the non-blocked case.VI. C
ONCLUSION
The EG scheme has been revisited under a frequency-selective multipath MIMO channel for 60 GHz communica-tions, and the total power gain that is necessary in the com-putation of received power has been obtained. Subsequently,the suboptimal MS diversity scheme has been proposed byexploiting the shadowing tracing approach, which exploits themulti-Gbps speed of 60 GHz WLAN. Comparisons on thereceived power and BER show that MS has lower computationcomplexity, and achieves a higher link margin than EG, owingto the higher receive power and less FS effect. The superiorityon link margin is more significant in the normal case, i.e.,when the LOS path is not blocked.R
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