The 11th International Symposium on Communications & Information Technologies (ISCIT 2011) Beamforming Codebook Design and Performance Evaluation for 60GHz Wireless Communication Weixia Zou, Zhifang Cui, Bin Li, Zheng Zhou, Yucong Hu Key Lab of Universal Wireless Communications, MOE Beijing University of Posts and Telecommunications,BUPT Beijing, China 09cui@163.com are taken to compensate the poor link budget in 60GHz, and beamforming techniques which can provide directional communication with high antenna gain have attracted more attention. Abstract—This article puts forward a method for codebook design to support beamforming mechanism in a 60GHz millimeter-wave wireless communication environment. The codebook is designed with only phase shifting but not any amplitude adjustment to meet the low power consumption requirement. IEEE802.15.3c beam MRA (main response axis) directions are taken as the original version to make curve fitting, so that weighting vector based on uniform weighting can be obtained to generate a codebook matrix. The simulation results show that, compared with the codebook in IEEE802.15.3c, similar main lobe patterns can be obtained in the proposed codebook, while the side lobe level is lower and the antenna gain at the direction of MRA is higher. Meanwhile, the interference decreases obviously with an improved network channel capacity in the practice environment, and the codebook is also robust to the beam shifting deriving from phase errors. Beamforming is a versatile and powerful approach to receive, transmit or relay signals of interest in a spatially selective way in the presence of interference and noise. In the last decade, there has been long-term development for the adaptive beamforming technique which can provide optimal communication quality. But the processing of mass data and high overhead in beam searching are time costly, and the exact phase shift and amplitude adjustment are obstacles for lowcomplexity DEVs (devices) to meet the low-power consumption requirement in 60GHz communication [6]. So, 60GHz beamforming prefers a codebook-based solution to achieve a compromise between complexity and highperformance for the system [7]. However, designing codebook in wide band 60GHz WPANs is also a challenge. The steering vector mismatch deriving from change of center frequency over the wide band may result in pattern rotating from the original MRA direction [7]. Hence, the robustness against steering mismatch will be one of the most important considerations in beamforming codebook design. In this paper, we put forward a codebook design scheme based on uniformweighting to support the 60GHz beamforming mechanism. Keywords-millimeter-wave communication; 60GHz; codebook design; beamforming I. INTRODUCTION Due to the increasing market demands for ultra high rate short range wireless applications for WLANs (wireless local area networks), WPANs (Wireless personal area networks), FWA (fixed wireless access), multimedia streaming, vehicular networks and etc [1], the millimeter-wave 60 GHz band with the large swath of available unlicensed spectrum is of a great interest for the development of high data rate short distance communications. Recent advances of using SiGe (silicongermanium) and CMOS (complementary metal oxide semiconductor) to build inexpensive 60 GHz transceiver components has created intense commercial interest to productize and standardize 60 GHz radio technology [2]. Such intense commercial interest led to multiple industrial efforts including standard development efforts including ECMA 387, IEEE 802.15.3c [3] and IEEE 802.11ad [4]. II. A. Network Topology A network is commonly known as a piconet. A piconet consists of several components while the basic component is the DEV. A DEV is required to play the part of the piconet PNC (coordinator) which provides the basic timing for the piconet with the beacon. Additionally, the PNC manages the QoS (quality of service) requirements, power save modes and access control for the piconet to schedule peer-to-peer communications between DEVs. To improve the transmission quality, beamforming technology may be employed for the link between two DEVs. This paper focuses on the beamforming codebook design. The 60GHz system has an ability of providing data rate more than 1Gbps, however, we still face challenges, which of them are limited link budget, reflection loss and other degradation during the transmission. Although the poor quality may provide security communication for BANs (body area networks)[5] and military application, the high pass loss may make the signal drowned in noise and it may be worse in NLOS(non-line of sight)complex environment. A few methods The recent studies show that it is more reasonable to locate the terminals according to a homogeneous Poisson point process for a network topology. We assume that the This work was supported by China Important National Science & Technology Specific Projects (2009ZX03006-006/-009), the Fundamental Research Funds for the Central Universities (G470270, G470415), the BUPT excellent Ph.D. students foundations (CX201122). 978-1-4577-1295-1/11/$26.00©2011IEEE SYSTEM MODEL 30 ⎛d ⎞ PL(dl )[dB] = PL(d 0 )[dB] + 10n log ⎜ l ⎟ + ∑ PAF [dB] (3) ⎝ d0 ⎠ where d0 is the close-in reference distance, n is path loss exponent, PAF (partition attenuation factors), which are the penetration losses due to the drywalls, the people and others between the transmitter and the receiver, can be ignored in a LOS (line of sight) environment. In [10], the channel measurements show that n is approximately 3.5 for NLOS and 2 for LOS at 60 GHz while n is only 2.6 for NLOS at 5GHz. So, it is necessary to apply the beamforming technology into 60GHz communication for the improvement of link budget. DEVs are distributed in a 2- D (dimensional) plane, then, the probability of b DEVs inside a region R only depends on the total area AR and is given by (1) p {b in R} = ( µ AR )b − µ AR e , b≥0 b! (1) where µ is the (constant) spatial density of DEVs per unit area. B. Beamforming Model[7] Referring to Fig. 1, a beamforming system that can achieve beam steering is illustrated in a block diagram format. The BF system can include a digital base-band transmitter with Nt antenna elements and a digital base-band receiver with N r antenna elements. For the link from transmitter to receiver, the signal after base-band processing is up-converted into RF (radio frequency) band. The RF band signal is then transmitted into free space from different antenna elements after weighting by the weight vector. At the receiver, the received RF signal is weighted by the receiver weight vector, and then combined together, down-converted for base-band processing. Therefore, the original signal can be reconstructed through the parameters estimation. We may prefer to emphasize that the weighting vectors are obtained from the codebook in the process of beamforming training in this paper. III. In this section, we will firstly introduce the codebook design principle and the detailed analytic formula in the standard IEEE 80215.3c (hereinafter referred to as “3c codebook design”), and then a codebook design scheme based on uniform-weighting is proposed. The codebooks are generated with only phase shift but without any amplitude adjustment in order to minimize the power consumption of 60GHz RF band electrical devices. The main purpose of our design is to achieve higher antenna gain at the MRA direction with a lower SLL (side lobe level). By this way, the network channel capacity can be improved obviously with the decreased interference in the practice environment. The purpose of beamforming is to select the optimal beam pattern pairs, in other words, the best weight vectors for the transmitter and the receiver antennas with high antenna gains. And the vectors are optimized by a cost function which measures the link quality according to a selected criterion. This criterion can be, for example, SNR (signal noise ratio), SNIR (signal to noise and interference ratio), capacity, etc[7]. In addition, the weight vectors can be adjusted in both phase and amplitude for complex beamforming antenna array. Here, only phase adjustment is taken for a phased antenna array. A. 3c Codebook design Array antenna is used to improve the communication quality in the standard IEEE 802.15.3c and the codebooks are design based on the following principles [3]. 1) The codebooks are designed for a phased antenna array, each column of a codebook matrix specify the phase shift of each antenna element. C. Link Budget model Using the log-distance path loss model, the average path loss PL( d l ) between a transmitter and a receiver separated by 2) The codebooks are generated with a 90-degree phase resolution without amplitude adjustment. d l (m) in free space can be calculated as follows [8]. 3) The codebooks are designed symmetrically spanning the 360 degrees around devices. ⎛ (4π )2 dl 2 ⎞ PL(dl )[dB] = 10log ⎜ 2 (2) ⎟ ⎝ λ Gt Gr ⎠ where λ is the wavelength, Gt and Gr denote the antenna gain at the transmitter and receiver respectively. Then the partition based path loss [9] can be modeled as Wighting Vector RF Channel 4) The codebooks support a multitude of antenna configurations and it is also available for different numbers of antenna elements. As for a 1-D phased antenna array with uniform spacing of λ / 2 , let M denote the number of antenna elements and K denote the beam patterns generated by the codebooks, then when K ≥ M , the beam vectors are given by column vectors of the following matrix shown in (4) Wighting Vector Transmitter Beam Beam BEAMFORMING CODEBOOK DESIGN A codebook is the weighting vector matrix for the array antenna to improve the link quality, and each column of the matrix specifies a beam pattern with a certain MRA direction. Receiver fix ( m× mod( k + ( K / 2), K ) ) K /4 w(m, k ) = j m = 0 : M − 1; k = 0 : K − 1 (4) The function fix( ) returns the biggest integer which is smaller or equal to its value. It is also possible to substitute the function round( ) which returns the closest integer to the input Figure 1. Beamforming system model 31 {θ k | θ k = f (k *64 / K ),k = 0 : K − 1} argument for the function fix(). m = mod( x, y ) is defined as x − n1 y ，where n1 is the nearest integer less or equal to x/ y. For the special case, K = M / 2 , the weighting vectors are given by the column vectors of the following matrix shown in (5). ⎧ (− j ) mod( m , k ) ⎪ ⎪ k = 0, m = 0 : M − 1 m × mod( k + ( K / 2), K ) w(m, k ) = ⎨ ) fix ( K /4 ⎪(−1) ⎪ ⎩ k = 0, m = 0 : M − 1 Considering low power consumption requirement, there is only phase shift but not any amplitude adjustment for the weighting vector values. As for a 1-D phased antenna array with uniform spacing of λ / 2 , when K ≥ M , the beam vectors are given by column vectors of the following matrix shown in (8). w( m, k ) = e jmπ d sin(θk ) (5) IV. PERFORMANCE EVALUATION AND SIMULATION RESULT COMPARISON Generally, there are several metrics used to evaluate the performance of beamformer such as array factor including the main-lobe configuration, HPBW (half power beam width) and SLL, etc, array antenna gain and robustness, which may cause an important effect on the network capacity. In this section, we will evaluate the performance of the proposed codebook design compared with 3c design. According to [4], the number of beams is taken as two times of number of antenna elements for a better cover of the entire user area. Uniform linear antenna is used in the simulation and element spacing is half of the wavelength. B. Uniform-weighting Based Codebook Design Uniform-weighting is a simple window weighting function scheme, and the weighting vector are constituted of the complex numbers that employ the same amplitude and certain phase shift for each antenna element for beamforming at different directions. When the beam MRA direction is θ k , which denotes the angle between the expected direction of k-th beam and the normal line of a 1-D array antenna, the corresponding weighting vector can be derived as follows: w k = a(θ k ) / M k = 0 : K − 1 (6) where a(θ k ) stands for the steering vector at the direction of θ k . Then the problem of codebook design becomes to find out the optimal beam MRA directions. A. Array Factor Array factor is the pattern function associated with the array geometry, that is to say, array factor is dependent on the geometric arrangement of the array elements, the spacing of the elements and the electrical phase of each element. For a uniform N-element linear array which employs the same elements spacing, we can derive the array factor as follows: Draft Standard IEEE 802.llad 1.0, the latest standard worked on spectrum of 60GHz, was released in 2010, and its beamforming training procedure is composed of two subprocedures: SLS (sector level sweep) and BRP (beam refinement). The sector ID (identification) field contained in the frame body of the first sub-procedure indicates the antenna used by the device for transmission and has the length of 6bits, in other words, the possible value of the available antenna patterns range from 0-63[4]. IEEE802.15.3c beam MRA directions are taken as the original version to make curve fitting f ( x ), x ∈ (0, 63) when M = 32, K = 64 , so that the MRA direction set would be obtained as follows. 90 m = 0 : M − 1; k = 0 : K − 1 (8) The above codebook matrix create 16 beam patterns as shown in Fig. 3 when M = 8, K = 16 . The above codebook matrix create 16 beam patterns as shown in Fig. 2 when M = 8, K = 16 . M −1 AF (θ ) = w T a s = ∑w e (9) vector. d is the element spacing and λ is the wave length which the system works on. θ stands for the angle with respect to y-axis while the antenna elements are arranged along the xaxis. Hereon, (•) T indicate the operation of transpose. 90 8 120 60 6 6 4 30 4 150 2 30 2 180 0 180 330 210 240 λ where w is the weighting vector, a s is defined as the steering 60 150 jmπ d sin θ m m =0 8 120 (7) 0 330 210 300 240 270 300 270 Figure 2. Beam patterns generated by the 3c codebook Figure 3. Beam patterns generated by the proposed codebook 32 Similarly, the array factor for a 2-dimension uniformspaced antenna array can be given as follows[11]. N x −1 N y −1 AF (θ , ϕ ) = ∑ ∑w m1 , m2 m1 = 0 m2 = 0 ∑w m1 = 0 j 2π [ m1 ( d x / λ ) cos θ sin ϕ + m2 ( d y / λ ) sin θ sin ϕ ] N y −1 N x −1 = AFx ∗ AFy = e x , m1 Due to the page limitation, we only give the array factor curves for the index k = 2 and k = 9 as shown in Fig.5. when M = 8, K = 16 . HPBW and direction of MRA for each beam are similar for the two design. However, the proposed design obtains a lower SLL which is a significant factor to interference suppression. e j 2π m1 ( d x / λ ) cosθ sin ϕ ∑w y,n e j 2π m2 ( d y / λ ) sin θ sin ϕ m2 = 0 B. Array Antenna Gain The directivity is a measure of how directive an individual antenna is relative to an isotropic antenna radiating the same total power. In other words, the directivity is the ratio of power density of an anisotropic antenna relative to an isotropic antenna radiating the same total power [7], and the directivity is given by (10) where d x denotes antenna element spacing along the x-axis while d y denotes array spacing along the y-axis, as illustrate in Fig.4. ϕ is vertical pitch angle and θ is the horizontal azimuth angle as shown in Fig.4, N x and N y are defined as the numbers of antenna element along x-axis and y-axis respectively. Hereon, the weighting value of wx , m1 and wy , m2 2 Dk (θ ) = w Tk a(θ ) / w Hk Ωw k T where (•) and (•) can be any format according to the designer, also, the weighting vector is available for the 2-D array antenna. So, the codebook design referred in section 3 support a multitude of antenna configurations. The normalized array factor is used to facilitate the beam performance evaluation. H (11) denote operation of transpose and Hermitian transpose respectively, w k is k-th weight vector in the codebook, and matrix Ω is given by[7] sin 2π ( d / λ )(m1 − m2 ) m1 , m2 = 0 : M − 1 (12) 2π (d / λ )( m1 − m2 ) In general, the antenna gain is more reflective of an actual antenna’s performance, which can be seen as the product of directivity and total antenna efficiency including effects of losses and mismatches. In high frequency communication, the value of efficiency is usually taken as 1. Then, the antenna gain is given by Ωn, m = ϕ dy dx • • • • • • • • • • • •θ • • • • • • • • • • • • • • G k (θ ) = eDk (θ ) = Dk (θ ) k = 0 : K − 1 (13) The matrix created by (6) product 16 patterns and the detailed antenna gain parameters of part of the patterns are shown in Table I. where G max ( k ) denote the maximum antenna gain for the k-th beam, and Gintersection (k ) indicate the antenna gain at the intersection between the k-th beam and (mod(k+1,16))-th beam. Due to the page limitation, only half the examples are given in the paper, however, we can find obvious performance differences between the two codebook designs. First, for the array gain at the direction of MRA, the proposed design in this paper is the definitely ideal case where Figure 4. Architecture of planar array antenna Array Factor(dB) 0 −20 SLL=−6.78 SLL=−12.80 −40 −60 −80 −50 0 θ (°) TABLE I. 50 ANTENNA GAIN FOR PART OF BEAMS G max (dB) (a) Beam Pattern when k=2 Index Array Factor(dB) 0 SLL=−6.22 −40 3c design −60 −80 proposed design −50 3c design 3c design Proposed design k=0 9.03 9.03 5.49 6.70 k=2 8.38 9.03 5.73 6.16 k=4 9.03 9.03 5.48 6.54 k=6 8.38 9.03 5.77 6.56 k=9 8.25 9.03 5.56 6.68 k=11 8.18 9.03 5.76 6.45 k=13 8.25 9.03 5.61 6.21 k=15 8.18 9.03 5.72 6.65 SLL=−12.80 −20 0 θ (°) 50 (b) Beam Pattern when k=9 Figure 5. Beam patterns generated by the 3c codebook 33 G intersection (dB) Proposed design (10log 8) dB can be obtained. But we may lose 0.85dB at most at the direction of MRA with 3c design, that is to say, 1-10(8.18-9.03)=18% ideal antenna gain may be lost when M=8. Second, the maximum gain loss at the intersections of any two adjacentbeams is only around 9.03-6.16=2.87 dB for the proposed design while 9.03-5.48=3.55dB will be lost for 3c design at the worst case. It further means that the codebook design in this paper will better cover the entire user areas. 1 0.8 CDF 0.6 std=0.2 3c design std=0.1 proposed design 0 0 0.5 1 1.5 2 2.5 3 3.5 Gain loss at the direction of MRA(dB) 4 4.5 Figure 7. Robustness analysis where (X,Y) denote that gain loss may be below XdB with Y probability.The simulation results show that the performances of the two designs are similar. Concretely, the gain loss of the two codebook designs is lower than 2.5dB with only 90% probability even when standard deviation of phase shift errors is 0.2 [11.5 degree]. And that loss is lower than the gain loss at the direction of intersection of adjacent beams. Obviously, the design is robust to the phase shift errors. There is an obvious performance improvement for the proposed design, and more than 1Gbps can be achieved. In addition, there is a decreasing trend for each performance curve due to the severer interference deriving from the increasing number of devices. V. CONCLUSION This paper briefly reviewed the current codebook design in standard IEEE 802.15.3c and then proposed a codebook design scheme based on uniform-weighting with the same design principle, that’s without any amplitude adjustment but only phase shift to meet the low energy consumption requirement. The simulation results show that higher antenna gain at the direction of MRA and lower SLL can be obtained by the proposed codebook design scheme with the similar equipment complexity. Meanwhile, the proposed design is effective in improving the network capacity and is also robust to the beam shifting deriving from phase errors. In conclusion, the proposed design can provide a preferable candidate for 60GHz codebook design. D. Robustness Analysis There is abundant bandwidth resource in the unlicensed 60GHz band, specifically 59-64GHz in China, 57-64GHz in US,59-66GHz in Europe and Japan, which may make it possible to achieve multi-Gigabit throughput, and wavelength may change a lot over the wide bandwideth. However, all performance simulation are established on the premise of a fixed wavelength 5mm, which may result in phase shifting for the steering vector. So the beams may rotate from the expected direction, and all the conclusions become uncertain for the codebook design. The phase shift errors are modeled as Gaussian distribution with 0 mean and standard deviation (std) proportional to the absolute phase shift. Fig.7 shows the ACKNOWLEDGMENT gain loss at the direction of MRA due to phase shift errors, This research was partly supported by Korean Ministry of Knowledge Economy under the ITRC support program supervised by the NIPA (NIPA-2011-C1090-1111-0007). 10 Channel capacity (Gbps) std=0.1 proposed design 0.2 C. Network Capacity Analysis The above performance including SLL and gain analysis will produce important effect on the received SNIR for the link between the devices which are communicating with each other, and further affect the network capacity. Take 2-D plane for example and assume that L devices are communicating synchronously with LOS mode in a 10*10 area. Set the path loss factor to be 2 according to paper [10]. Channel band width is 1.08GHz for 60GHz communication, so the network capacity is shown as Fig.6. 8 REFERENCES [1] 6 4 m=8 3c design [2] m=8 propose design 2 m=16 3c design m=16 propose design 0 std=0.1 3c design 0.4 0 5 10 15 Number of DEVs [3] 20 Figure 6. 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