arXiv:1104.1007v4 [cs.NI] 1 Aug 2012 aldaao his ota inlpoesn tspatial at processing signal multip However, baseband. that digital simply at executed so (or be can chains) domain chains analog downconversion called RF/analog separate via [5]. mmWave [4] some (RFICs) in Circuits and Integrated are standards 16 Radio-Frequency the antennas example, in For supported of range. are number beamform communication antennas the the large exploit space extending A to for free transceiver than gain band. the loss Friis GHz at more placed dB By 2.4 therefore 28 the loss. from at suffer path GHz that 60 signal at high signals formula, its is spectrum mmWave for development requirements active and in protocols are system. the [3], namely, standardize 802.11ad to standards, and IEEE [2] short miniature Consequently, 802.15.3c rather in deployed devices. The be regulatory [1]. consumer to antennas most uses more by allows unlicensed allocated wavelength for is bandwidth worldwide frequency of carrier bodies 7-GHz multipl A GHz realize rate. 60 to data at (Gbps) candidate second viable per a Gigabits as considered been has ytm Inc. Systems olrednmcrneo inl u oba nlsvarying angles beam to due signals packet. i lead training of may packet a range scheme across a dynamic whose within standard large variations 802.11ad to IEEE power the environ flat to non-line-of-sight very contrast in provides robustness angles also techni the training but their BF shows proposed at only The pai code. packets. angle not steering few beam signature a best in and the obtained unique packet, be angles training assigned a beam in is simultaneously multiple angle coding beam By Each protocol. efficient coding. training An (BF) ther BeamForming other. is called pair each angle is beam It best towards needed. the obtain angles to protocol pointing searching beam their eie yia IOagrtm r o applicable. reduce not to are t algorithms designed In MIMO complexity. are hardware typical chains are and regime, analog limited power antennas hi processing RF very the and of fewer recovering transmit and for number while range antennas loss Large communication path of the chains. extend number analog to used RF high of with number regime a at hswr sspotdb ruhrFudto elwhpan Fellowship Foundation Croucher by supported is work This dal,atna hudcnett h aeadprocessor baseband the to connect should antennas Ideally, mmWave the at communicating for problems the of One system communication (mmWave) Wavelength Millimeter hspprpeet e Ftann ehiu aldbeam called technique training BF new a presents paper This eoeaycmuiainsat,dvcsaenee oalig to needed are devices starts, communication any Before Abstract riigi maeCmuiainSystem Communication mmWave in Training oigteBas mrvn Beamforming Improving Beams: the Coding TemWv omncto ytmi operating is system communication mmWave —The eateto lcrclEgneig tnodUniversit Stanford Engineering, Electrical of Department .I I. msn@tnodeu [email protected] [email protected], NTRODUCTION .Mn sn,AaS .Poon Y. S. Ada Tsang, Ming Y. Cisco d ment, can r efore que ing his gh le n n e etprba ari h bv cee,te r categorized are they schemes, i above packet the individual in an pair i Since beam poor stage. per is earlier sent [10] in non-LOS resolubility beams path L-Re identifying multiple multi the in the reduced, as incompetent paths greatly shown (NLOS) is is time are scheme training stage level (H-Re) earlier the in higher-resolution beams While level, L-Re larger searched. selected next the cover the by covered In which beams beam. beams per sta (L-Re) space search The Lower-Resolution standards scheme. the training from and multi-level [9] propose Wang prohibitivel [3] time, is [2] training time the reduce searching fo To packet the long. training exhaustively However, a to pair. sending beam is by [8] each method pairs beam One the suggested. all anten- examine are 16 with beams required. (ULA) 32 the Array [7] nas, Linear coverage on Uniform of depends for (or amount example, beam the directions For and of beam antennas number pre-defined of The number of beams). set called a simply at packets pair. direction training and beam setup same best link the the device-to-device define But a that devices. to training metrics gives and applied other BF that be the (AP) can on Point pair protocol focus Access direction beam we the Also, beam best between gain. the the channel to highest paper, calle the refers this is pair protocol In direction This direction training. beam crucial. (BF) very best is BeamForming the devices discovers between that pair protocol Theref efficient other. each an designs. towards thei pointing if not protocol possible are directions not beam communication are devices two complicates between Communications it but analog patterns. one beam range only directional that highly so create [4] to RF needed the Moreov is from at directions. chain signals applied desired the are the that weights at way at the coherent a are weight such antennas in The all designed all communications. is extension, extension. antenna during range each active range the are for transmission effect antennas limited beamforming regim provides generate this To only for ap- proposed it not was are but [6] techniques selection system Antenna MIMO plicable. typical current chains, in analog found is [5]. chain amount [4] analog substantial design one consumes RFIC mmWave only rate Hence, GHz power. sampling at of and signal frequency mmWave analog at the costly are chains analog h Ftann rcs eiswt h rnmte sending transmitter the with begins process training BF The transmission the improves pattern beam directional The few very and antennas of number high of regime this In y [email protected] aes Addepalli Sateesh ic ytm Inc Systems Cisco ore, rts er, n d y e s r - r wall as Packet-by-Packet (PbP) BF training. a<1 A training packet is required to be sent in PbP training for 4 training a beam pair. This introduces high overheads since 1 4 1 headers and preamble in a packet provide no information for 1 BF training but they are used only for message identification 3 Tx 2 3 Rx 2 purposes. In IEEE 802.11ad, in-packet BF training packet Fig. 1: shows a communication scenario: both devices are allowed to structure is purposed to reduce the overheads in the beam steer at the 4 beams only for communication. refinement step which executes H-Re BF training in multi- level scheme. It allows varying beams within a training packet. Beamforming training section Hence, training multiple beams only requires the amount of ..... network bandwidth equivalent to one packet transmission. Beam 2 Beam K Despite the advantages of using In-packet training, it poses Beams 1 to K Beam 1 some challenges in the implementation. First, the changes of beam directions significantly increase the dynamic range of the signals across a packet. Resetting Automatic Gain Control (AGC) may be needed for every change of beam Fig. 2: shows the packet structure for in-packet training in IEEE direction. Second, even if the AGC is reset for every change 802.11ad: CE represents channel estimation sequences and S1 of beam direction, the timing synchronization point may be through S4 are subfields for estimating the phases and amplitudes of channel taps altered after each AGC re-settling. The relative delays and phase differences among all beam direction pairs may become similar performance. inaccurate [11] (comment 414). Consequently, in the IEEE 802.11ad standard, the change of AGC gain preceding each II.IN-PACKET BF TRAINING beam direction change is disallowed so that the relative delay In this section, the background of in-packet training is information is preserved. To limit the increase of dynamic provided. The packet structure in IEEE 802.11ad for in-packet range, in-packet packet structure is only allowed during beam training is first described. Then we discuss two BF training refinement step in which only a smaller set of beams are algorithms that utilize the packet structure. For the sake of trained. presentation, we restrict the transmitter and the receiver being If the power variations of signal during the BF training in able to steer their arrays at 4 beams specified in Fig. 1. It can an in-packet training packet is reasonably flat, it allows in- be easily generalized to the setup with more beams. In the packet training to be implemented in every stage of BF training example, there are one LOS path and one NLOS path with to unleash the full potential of the in-packet training. The attenuation a< 1. question is how one can provide relatively flat power variations while employing in-packet training. A. IEEE 802.11ad packet structure for in-packet training As it can be observed, receive power variations in PbP IEEE 802.11ad provides the capability for in-packet BF training are very limited as the beam direction is maintained training. The packet structure shown in Fig. 2 begins with the same throughout the packet. To enable this feature for the preamble and header sections which are steered using L- in-packet training, we propose a beam coding scheme in Re beams similar to multi-level PbP training to cover larger which the array is steered at multiple highest-resolution beams space. Following the header section, the BF training section simultaneously. Each beam is assigned an unique signature allows training in H-Re beams. It contains AGC field and sequence for receivers to differentiate beam angles and extract training (TRN) fields. The set of beam directions that are the channel information of all the beam pairs. Since the being trained are changed sequentially within the AGC field covering beam pointing directions are the same throughout the for a receiver to calculate an appropriate AGC gain. Then, a packet, beam coding provides a fairly uniform receive power TRN field is allocated for each beam for channel estimation. It across a packet. contains Channel Estimation(CE) sequence and extra subfields With only one analog chain in the transceiver path, how to improve the accuracy of tap delay estimation. It is worth can beams carry different signature sequences? Instead of noting that even though beams are changed every TRN field, encoding the beams at the baseband processor, the antenna the AGC gain is fixed across all the TRN fields. Hence, larger weights at the RF are manipulated as each antenna is weighted dynamic range of signals can be expected. individually. Antenna weights in an array can be uniform or nonuniform [12] [13]. Non-uniformly weighted array allows B. Exhaustive in-packet training magnitude variations on weights while uniformly weighted The exhaustive search becomes feasible as the overheads in array varies the phases of weights only. The beam coding header and preamble sections are minimized through the use scheme may require nonuniform weighted array for the best of in-packet training. The number of training packets in the performance, which is supported by the circuitry in [14]. In example (Fig. 1) is reduced from 16 to 4. fact, we will show by using specific signature sequences, beam The exhaustive in-packet training procedures are shown in coding in uniformly and nonuniformly weighted arrays have Fig 3. The transmitter sends the same training packet 4 times Tx repeats training packet 4 times III. BEAM CODING

4 Employing in-packet BF training may result in larger dy- 1 3 4 1 2 4 1 2 3 3 Tx 2 namic range across a packet. How can one provide reasonably Rx sweeps its Rx beams packet by packet: flat power variations across a packet? 4 packet 1 1 packet 2 2 packet 3 3 packet 4 Instead of varying the beam pointing directions in each TRN Fig. 3: shows the flow for exhaustive in-packet training field as in the standard, if a scheme allows multiple highest- resolution beams being steered at the same time across all the Stage 1: Tx beam training TRN fields, the receive power variations are greatly reduced and no explicit AGC resettling is needed. The main barrier for 4 1 1 3 4 1 4 Tx Beams 2 2 3 such protocol is the single analog chain that forces signals at 3 Tx 2

4 each beam to be identical. Two transmit beams are therefore Rx Beams 1 3 Rx 2 indistinguishable at the receiver if they are steered at the same

Stage 2: Feed back the best Tx Beam information, i.e. Tx beam 2 time. To shed some light on problem, it can be observed that the weight of each antenna can be adjusted individually by Stage 3: Rx beam training tuning a phase-shifter on each antenna. For instance, if an additional phase π is added to the weight at the nth antenna, all th Tx Beams 2 signals through the n antenna will be negated. We leverage

4 1 3 4 this observation and propose a scheme called beam coding. Rx Beams 1 2 4 1 2 3 3 Tx 2 Beam coding first steers the antenna array towards multiple Fig. 4: shows the flow for feedback in-packet training. beam direction as described in section III-A. By encoding each beam with a signature sequence, a receiver is able to identify while the receiver steers its beams one by one. Since beam the signal strength from each beam direction as illustrated pairs (2, 3) and (1, 4) are both aligned and a< 1, the receiver in section III-B. To further reduce the power variations, the is able to identify (2, 3) as the best beam pair. It is also worth beam directions chosen for training within a training packet noting that since the receiver is able to obtain full channel are designed to be orthogonal as discussed in section III-C. information about all the combinations of Tx and Rx highest- For the sake of presentation, we assume that all antenna resolution beams, this scheme has compelling performance in elements are omnidirectional and the array is a non-uniformly NLOS environment. weighted linear array with constant distance between neighbor- ing antennas. The normalized inter-antenna distance is denoted d C. Feedback In-packet training as ∆d = λ where d is the inter-antenna distance and λ is the wavelength of the signal. We will also show that applying The BF training procedure described previously requires no beam coding in uniform weighted array is also feasible. explicit feedback from the receiver until the end of training. In fact, limited explicit feedback consumes very few resources. A. Transmit at two beams at the same time For example, the association request that is sent for receivers Assume the system with N antennas, if the transmit data to associate with the AP can be used to piggyback the consists of all ones, the signal at angle φ is intermediate training results to improve the training time. N−1 j2πn∆d cos φ The procedure is shown in Fig. 4. The Tx beam is first being x(φ)= wne (1) n=0 trained. The transmitter forms its training packet similar to X th the exhaustive in-packet training while the receiver is steering where wn is the weight at the n antenna. If we want to at all its directions simultaneously. The received signal is steer the angle to the transmit beam direction φ1, the antenna j2πn∆d cos φ1 y = 0.5[a 1 0 0], where y[t] represents the receive signal weight will become wn = e− . amplitude at the TRN field t. Since a < 1, Tx beam 2 is Now, to transmit signal through two beam directions, φ1 chosen. Then, this information is fed back to the transmitter and φ2, at the same time, the antenna weights are − − which then sends a training packet through its beam 2 at 2πn∆d cos φ1 2πn∆d cos φ2 wn = e + e (2) stage 3. Receiver is now varying its beam directions within the packet and detects Rx beam 3 as the best Rx beam. Hence The resulting transmit signal equals to the training can be completed in 2 training packets. N−1 N−1 −2πn∆ (cos φ1−cos φ) −2πn∆ (cos φ2−cos φ) Unlike exhaustive in-packet training, the feedback scheme x(φ)= e d + e d n=0 n=0 does not provide full channel information since only Tx beams X X are trained at stage 1. Moreover, since the receive BF gain This implies that due to the linearity of antenna weights is lowered by having all Rx beams active at stage 1, the in the transmit signal, the weights for the two beams are communication range is reduced. This poses an interesting superimposed and create a new beam pattern which attains the tradeoff between the training time and the range, which cannot maximum points at φ = φ1 and φ = φ2. Antenna weights for be leveraged easily in PbP training. The tradeoff is explored 4 transmit beams are formed similarly. In analogy, the antenna in our future work. weights can be formed at the receiver side for 4 beams. B. Encoding the beams First, each transmit beam p is assigned an unique signature Tx Packet 1: Rx steers at beam 1 Packet 2: Rx steers at beam 2 sequence, sp , for all p ∈{1, 2, 3, 4} as follows: CE fields Tx 1 2 3 4 Tx 1 2 3 4 Tx Tx 1 s = [1 1 1 1] s = [1 1 1 1] 1 1 1 1 1 1 1 1 1 1 1 2 − − Tx Tx 2 1 -1 1 -1 2 1 -1 1 -1 Rx 2 s3 = [1 1 1 1] s4 = [1 1 1 1] Rx − − − − 3 1 1 -1 -1 3 1 1 -1 -1 These signature sequences are derived from Walsh code and y = [0 0 0 0] 4 1 -1 -1 1 y = [0 0 0 0] 4 1 -1 -1 1 2 1 are known to both transmitter and receiver. Let βn(φ) = 2πn∆d cos φ Tx e− . Then, the antenna weights, denoted as wn [t] Packet 3: Rx steers at beam 3 Packet 4: Rx steers at beam 4 for all t ∈ {1, 2, 3, 4}, are calculated for the consecutive CE Tx 1 2 3 4 Tx 1 2 3 4 4 fields in the TRN fields as shown in Fig. 5, where t represents 1 1 1 1 1 1 1 1 1 the CE field index: 1 2 1 -1 1 -1 3 Rx 2 1 -1 1 -1 Tx 1 Tx Tx Tx Tx 3 1 1 -1 -1 3 1 1 -1 -1 Rx w = s βn(φ1)+ s βn(φ2)+ s βn(φ3)+ s βn(φ4) n √ 1 2 3 4 4 4 1 -1 -1 1 y = 0.5[1 -1 1 -1] 4 1 -1 -1 1 3 y4 = 0.5 a [1 1 1 1] Hence, the antenna weights at CE field indexes 1,2,3,4 are:
Fig. 5: shows exhaustive beam coding training procedure. Tx At CE 1: wn [1] = 0.5(βn(φ1)+ βn(φ2)+ βn(φ3)+ βn(φ4)) Tx At CE 2: wn [2] = 0.5(βn(φ1) βn(φ2)+ βn(φ3) βn(φ4)) selected beams, different selections of beams have significant Tx − − At CE 3: w [3] = 0.5(βn(φ1)+ βn(φ2) βn(φ3) βn(φ4)) differences in power variations. To reduce power fluctuation, n − − Tx we show that the beams that are encoded in a packet are At CE 4: wn [4] = 0.5(βn(φ1) βn(φ2) βn(φ3)+ βn(φ4)) − − required to be orthogonal. Then, the transmitter is sending the same packet 4 times while Definition 1: Let βn(φi) and βn(φj ) be the antenna the receiver is switching beams after every packet duration. weights for beams i and j at antenna n respectively with N 1 While the receiver is steering at beam q, it receives yq[t]. 2 n=0− |βn(φk)| = 1, for k = i, j. Beams i and j are At the end of the sweeping, it compares the received signal N 1 orthogonal if and only if n=0− βn(φi)βn∗(φj )=0, where with the signature sequences by calculating the correlations, xP is the complex conjugate of x. 4 Tx ∗ r(p,q) = t=1 sp [t]yq[t]. Since beam pairs (2, 3) and (1, 4) To show that orthogonalP beams reduce power fluctuation, are both aligned, we have r(2,3) = 2 and r(1,4) = 2a. Since the array that steers at beams i and j sets the antenna weights, P w , as 1 (β (φ ) ± β (φ )), where the ± describes the a< 1, the best beam pair (2, 3) is obtained. n √2 n i n j It takes 4 frames to complete the training. We call this signature sequences used for beam coding. Then, as exhaustive beam coding scheme. The feedback scheme N−1 N−1 2 ∗ 1 2 2 described in section II-C can also be leveraged via beam w = wnw = βn(φi) + βn(φj ) | | n 2 | | | | coding in the same way to further reduce the training time. n=0 n=0 X X Walsh code are used to separate beams as its codewords N−1 1 ∗ ∗ are orthogonal to each other. Golay sequences possessing very βn(φi)βn(φj )+ βn(φj )βn(φi) ± 2 n=0 ! good auto-correlation property are used as the CE sequences X [3]. This property also helps protecting the Walsh code from If two beams are orthogonal, |w|2 =1 and the transmission losing orthogonality due to multi-path fading effect. Hence, power is then independent of the codes used. Conversely, if receivers are able to identify the relative delays and signal the beams are not orthogonal, the cross terms are non-zeros. strength in all the channel delay taps among all beam direc- In the extreme case where β (φ )= β (φ ) for all n, the |w|2 tions. n i n j fluctuates between 2 and 0 for different codes. Apart from providing stable dynamic range of signals within In fact, in a system with N antennas, there are at most N a packet, beam coding also provides an essential structure for orthogonal beams [16]. The N antenna weight variables create schemes such as compressed sensing [15] to further reduce the a N-dimensional space, resulting in at most N orthogonal training time. For instance, it can be done by replacing the sig- vectors. nature sequences with Gaussian random sequences. However, since the sample size (i.e. the dimension of the antenna array) D. Uniformly weighted phased array is rather small compared to other applications in compressed sensing, the reduction in training time is insignificant while The beam coding scheme requires non-uniformly weighted the receiver complexity is much increased as computations phased array for the best performance as the beam coding are more involved. Hence, this benefit via beam coding is not scheme varies the amplitudes across antenna weights. In fact, further explored here. the scheme also performs fairly well in uniformly weighted phased array in which only phases of the weights can be C. Orthogonal beam directions adjusted. In general, multiple beam steering creates larger side For each training packet, a set of beams are selected to be lobes in uniform array. It can be showed that steering at two encoded by beam coding scheme. Since the scheme involves beams in uniformly weighted Uniform Linear Array (ULA) additions and subtractions on antenna weights among the introduces -9 dB side lobe level instead of -13 dB in single TABLE I: Channel Model Parameters Path loss exponent 2 The CDF for the receive power ratio (LOS) (Mean, RMS) (-10 dB, 4 dB) 1 4 Cluster reflection loss 2 8 Truncation -2 dB 1 Living room model 16 4 Intra-cluster model 0.8 Section 5.5 in [7] 2 Intra-cluster AoA and 8 Gaussian (0, 5 deg) AoD distribution 0.6 TABLE II: Simulation Parameters

Non-uniformly weighted Probability 0.4 Antenna array (∆d) linear array (0.5) Beam coding Noise figure + implementation loss 12 dB 0.2 802.11ad Signal bandwidth 2 GHz 16

0 beam steering. However, as shown in Fig. 10, this is acceptable 0 1 2 3 4 5 6 7 8 in the BF training because during BF training, all the beams Power ratio (linear scale) are swept to discover the best one for communication. The Fig. 7: shows the CDF of power ratio under LOS enviroment. positions of side lobes will therefore be covered by the main lobes of other beams eventually. 99.5% of signals fall within a desired range. The receiver has In simultaneously training more than 2 beams, if the Walsh only one antenna in order to show the worst case scenario of code is being used as the signature sequences, and the number beam coding as it observes more multiple paths if receiving of antennas is a power of 2, it can be proved analytically omni-directionally. The transmitter has 16 antennas and varies that beam coding is feasible in uniformly weighted ULA. The the number of training beams in a training packet. proof is omitted due to the page limit. Instead, we will show The cumulative density function of power ratios in NLOS by simulation that the performance in uniform array is very and LOS environments are shown in Fig. 6 and 7. In NLOS, close to non-uniformly weighted array. it can be observed that all the training data in beam coding IV. SIMULATIONS is with γ < 1 while the ratios in the 802.11ad scheme sweep from 0 to 6. In LOS, this effect is exaggerated. The ratio in In the simulation, the beam coding is compared with the the 802.11ad scheme can reach 14 for 16 beams in a packet. scheme in the IEEE 802.11ad standard. The beam coding Though the ratio in beam coding reaches 2.5 in LOS, no is demonstrated to provide comparably flat receive power extra AGC resetting is required because 95% of training data variations across a packet. We also show that beam coding has is within power ratio 2 and the existence of the dominant excellent performance even under uniformly weighted array. path in LOS environment allows a small percentage of power Simulations follow the living room model in the IEEE clippings in the training result. Therefore, AGC fields are not 802.11ad channel document [7] and the parameters are shown needed in the beam coding scheme. in Table I and II. Due to the fact that the beam coding scheme does not A. Receive power variations need extra AGC resetting nor extra fields for estimating the The main metric is the power ratio, γ, which is equal to relative delay of channel taps among various beam directions, Ptrain beam coding technique can greatly reduce the size of training where Ptrain is the power of signal in the training 3σprem packets designed in the 802.11ad standard. In the 802.11ad section while σprem is the variance of signal in the preamble. standard, for each beam direction that is being trained, there The 3σprem is used because the AGC gain is to make sure are 4*320 bits for AGC resetting, 4*640 bits for relative delay estimations and 1024 bits for CE sequences in a training packet The CDF for the receive power ratio (NLOS) while in the beam coding scheme, only 1024 bits for the 1 CE sequence are needed. A saving of 4000 bits per beam 16 2 4 direction in the BF training section can be observed by using 0.8 8 8 the proposed beam coding technique. 4 2 16 0.6 B. Uniformly weight linear array with phase quantization 1 Phase quantization is commonly found in the mmWave Probability 0.4 RFIC since the phase shifters in the RFIC are digitally- Beam coding 802.11ad controlled. In Fig. 8 and 9, we compare the exhaustive beam 0.2 coding scheme with the scheme with No beam coding (N- BF). N-BF scheme is the exhaustive PbP scheme that serves 0 as the upper bound of the performance since it has the best 0 1 2 3 4 5 6 Power ratio (linear scale) performance in NLOS environment and does not perform multiple-beam steering. The linear scale of SNR in the figure Fig. 6: shows the Cumulative Density Function (CDF) of power ratio 1 ( log2(1+SNRi)) for two schemes under NLOS environment. The labels on the curves is defined as SNR=2 W i − 1, where W is represent the number of beams (i.e. 1, 2, 4, 8, 16) used in a packet. P SNR vs Phase quantization in ULA for LOS environment the total number of simulation runs and i is the index of 27 a simulation run. In the simulation, transmitter and receiver are having 16 antennas. In each training packet, 16 beam 26.5 directions are trained at the same time in the beam coding scheme so that it gives the worse possible performance of 26 beam coding due to phase quantization.

Even though beam coding scheme is expected to give Beam Coding SNR (dB) 25.5 larger side lobes in ULA, its performance approaches that of No beam coding (N−BF) the optimal exhaustive PbP scheme even with two-bit phase quantization as shown in Fig. 8. In NLOS environment, it 25 is worth noting that when the number of phase quantization bits reaches 3, the beam coding scheme has exactly the 24.5 2 3 4 5 same performance as the exhaustive PbP scheme. This is Number of phase quantization bits explained in Fig. 10. Almost no distortion in the plots of Fig. 8: shows the performance with quantization of phases (LOS) beam patterns can be seen in the beam coding scheme with 4- SNR vs Phase quantization in ULA for NLOS environment bit phase quantization. Though more distortions are observed 15.5 for 2-bit phase quantization, since its pointing directions are maintained correctly, the performance for beam coding is still very satisfactory even with phase quantization in ULA. 15

V. CONCLUSION 14.5 We present the beam coding scheme to unleash the po- Beam Coding SNR (dB) No beam coding (N−BF) tentials of the in-packet BF training packet structures for mmWave system BF training. The scheme provides uniform 14 receive power variations for in-packet training so that no extra AGC resetting is required even though beam directions are 13.5 varied within a packet. This not only allows in-packet BF 2 3 4 5 training protocols to be executed at every stage of BF training, Number of phase quantization bits but also greatly reduces the size of a BF training packet used Fig. 9: shows the performance with quantization of phases (NLOS) in the IEEE 802.11ad standard. More importantly, the beam 0 0 330 30 330 30 coding scheme does not require variable amplitudes of antenna 1.538 1.486 weights and hence only mild modification of mmwave RF 300 1.153 60 300 1.115 60 frontend is sufficient to support the beam coding scheme. 0.769 0.743 0.384 0.372

0 0 REFERENCES 270 90 270 90

[1] S. K. Yong and C.-C. Chong, “An overview of multigigabit wireless through millimeter wave technology: potentials and technical chal- 240 120 240 120 lenges,” EURASIP J. Wirel. Commun. Netw., vol. 2007, no. 1, 2007. [2] IEEE Standards 802.15.3c, October 2009. [3] “IEEE 802.11ad standard draft D0.1,” [Avail- 210 150 210 150 able]:www.ieee802.org/11/Reports/tgad update.htm. 180 180 [4] A. Valdes-Garcia, S. Nicolson, J.-W. Lai, A. Natarajan, P.-Y. Chen, (a) 2-bit phase quantization (b) 4-bit phase quantization S. Reynolds, J.-H. C. Zhan, and B. Floyd, “A SiGe BiCMOS 16-Element Phased-Array Transmitter for 60GHz Communications,” in ISSCC, 2010. Fig. 10: shows the beam pattern after beam coding. [5] E. Cohen, C. Jakobson, S. Ravid, and D. Ritter, “A thirty two element phased-array transceiver at 60GHz with RF-IF conversion block in 90nm [12] C. Balanis, Antenna theory: Analysis and Design, 3rd ed. John Wiley flip chip CMOS process,” in RFIC, 2010. & Sons, Inc, 2005. [6] A. Molisch and M. Win, “MIMO systems with antenna selection,” IEEE [13] H. L. Van Trees, Optimum Array Processing. Wiley-interscience, 2002. Microwave Magazine, Mar 2004. [14] Y. M. Tsang, S. Lin, and A. S. Y. Poon, “Fast Beam Training for [7] A. Maltsec, “Channel Models for 60 GHz WLAN Systems,” IEEE doc. mmWave Communication System: from Algorithm to Circuits,” in 802.11-09/0334r8, May 2010. International Workshop on mmWave Commun., Sept 2010. [8] F. Dai and J. Wu, “Efficient broadcasting in Ad Hoc wireless networks [15] E. J. Candes and M. B. Wakin, “An Introduction to Compressive using directional antennas,” IEEE Trans. on Parallel and Dist. Sys., Sampling,” IEEE Signal Processing Magazine, vol. 21, Mar 2008. vol. 4, 2006. [16] A. S. Y. Poon, R. W. Brodersen, and D. N. C. Tse, “Degrees of freedom [9] J. Wang, Z. Lan, C.-W. Pyo, T. Baykas, C.-S. Sum, M. Azizur Rahman, in multiple-antenna channels: a signal space approach,” IEEE Trans. R. Funada, F. Kojima, I. Lakkis, H. Harada, and S. Kato, “Beam Information Theory, Feb 2005. codebook based beamforming protocol for multi-Gbps millimeter-wave WPAN systems,” IEEE J. Sel. A. Commun., Oct 2009. [10] D. Tse and P. Viswanath, Fundamentals of wireless Communication. Cambridge University Press, 2005. [11] A. Kasher, “D0.1 PHY comment resolution,” IEEE doc. 802.11- 10/0944r1, July 2010.