Massive MIMO and HetNets: Benefits and Challenges

Transcription

1 Massive MIMO and HetNets: Benefits and Challenges Jakob Hoydis Bell Laboratories, Alcatel-Lucent, Stuttgart, Germany Newcom# Summer School Interference Management for Tomorrow s Wireless Networks Eurecom, Sophia-Antipolis, France May 29, 2013 Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS 13 1 / 96

2 Some figures, industry trends, and the data explosion Today, 66 % sleep with smart phone (USA) 84 % choose Internet over partner or car (Germany) 67 % would cut anything but mobile broadband (UK) By 2017, there will be 1 13 more mobile data traffic than in , 000, 000, 000 connected devices 2/3 of the total traffic generated by mobile video streaming and communications 1 Source: Cisco, Yankee Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS 13 2 / 96

3 Challenges for the next years How can we provide the necessary area spectral efficiency? Without new spectral resources ( 6 GHz) or technological breakthroughs. avoid that the backhaul becomes the bottleneck? While increasing the flexibility and cost of access point deployment. keep the energy consumption in the infrastructure and the terminals low? Mobility is not anymore limited by coverage but rather by the battery duration. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS 13 3 / 96

4 Possible solutions Today, network densification is the only answer to the capacity crunch: Small cells: Network capacity scales linearly with the cell density. Massive MIMO: Interference can be almost entirely eliminated. Fortunately, both technologies can also significantly reduce the radiated power. Increasing capacity while simultaneously reducing the energy consumption is possible! Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS 13 4 / 96

5 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS 13 5 / 96

6 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS 13 6 / 96

7 The benefits of MIMO Spectral efficiency (bits/channel use) x1 2x2 3x3 8x SNR (db) Outage probability x1 2x2 3x3 8x SNR (db) Spatial multiplexing: C min(n tx, N rx) log 2 (SNR) as SNR Diversity: P out SNR NtxNrx N rx-fold receive and N tx min(n rx,n tx) -fold transmit beamforming gain Spatial division multiplexing (SDMA) or Multi-user (MU) MIMO Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS 13 7 / 96

8 Scaling things up Source: Massive MIMO is nothing new; but it takes MIMO to an entirely new level: A base station (BS) with hundreds or even thousands of antennas simultaneously serves tens of user equipments (UEs) on the same time-frequency resource. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS 13 8 / 96

9 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS 13 9 / 96

10 Massive MIMO: Uplink benefits y = h 1x 1 + h 2x 2 + n Assumptions h 1, h 2 C N 1 have i.i.d. entries with zero mean and unit variance h 1, h 2 perfectly known at the base station (BS) E [ x 1 2] = E [ x 2 2] = SNR n CN (0, I N ) Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

11 Massive MIMO: Uplink benefits The BS applies a simple matched filter to detect the symbol of UE 1: 1 1 N N hh 1 y = x 1 h 1i 2 N i=1 }{{} useful signal By the strong law of large numbers: 1 + x 2 N N i=1 h 1ih 2i } {{ } interference + 1 N N i=1 h 1in i } {{ } noise Thus, 1 N 1 N N i=1 N i=1 h 1ih 2i h 1in i a.s. E [h 11h 21] = 0 (interference vanishes) N a.s. E [h 11n 1] = 0 (noise vanishes) N 1 [ N hh a.s. 1 y x1e h 11 2] = x 1 (SNR can be made arbitrarily small) N Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

12 How fast can the SNR be scaled down with N? The received SINR of UE 1 can be written as: SINR MF 1 = 1 N hh 1 h 2 h 1 1 N hh 1 h NSNR Average signal power: Average interference power: Average noise power: [ ] 1 E N hh 1 h 1 = 1 [ 1 E N hh 1 h 2 2] = 1 h 1 N 1 NSNR The SNR can be made inversely proportional to N without performance loss. Remark The matched filter is optimal: 1 for any N, if SNR 0, 2 for any SNR, if N. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

13 Is the matched filter really optimal? Rate (bits/channel use) MF MMSE SNR = 10dB SNR = 10/N ~3 b/ch.u Number of antennas N With a MMSE detector the following ergodic rate for UE 1 is achievable ( ( R1 MMSE = E [log h H 1 h 2 h H ) )] 1 SNR I N h 1 How much do we gain over the matched filter R1 MF = E [ log 2 (1 + SINR MF 1 ) ]? For SNR = P, one can show that lim N N R1 MF = lim N R1 MMSE = log 2 (1 + P). For SNR = P, we have lim N R1 MMSE R1 MF > 0. The MF can be far from optimal [1], but can be implemented in a distributed manner. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

14 Massive MIMO: Downlink benefits All of the previous conclusions hold similarly for the downlink [2]: Noise and interference vanish as N. The transmit power per UE can be scaled down as 1/N without performance loss. Maximum ratio transmission (MRT) is optimal if the power is scaled down. However, regularized zero-forcing can achieve the same performance with a significantly reduced number of antennas [1]. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

15 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

16 On favorable propagation conditions Whenever 1 N hh 1 h 2 0 as N, we speak about favorable propagation conditions [3]. Definition To measure the orthogonality between two N-dimensional channel vectors, we define the average correlation factor as [ ] h H 1 h 2 2 δ N = E [0, 1]. h 1 2 h 2 2 How does δ N behave for i.i.d. fading channels? when there are line-of-sight components? with antenna correlation? channels obtained from ray-tracing? for measured channels? Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

17 Channel orthogonality for the i.i.d. model Let h 1, h 2 C N 1 have i.i.d. elements with zero mean, then δ i.i.d. N = E [ h H 1 h 2 2 h 1 2 h 2 2 ] = 1 N. Is this the best we can hope for? Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

18 Channel orthogonality for LOS links N antennas φ 1 d 1 UE 1 h i = a i }{{} attenuation e i2π d i λ }{{} phase offset e (ϕ i ) }{{} array response vector λ/2 φ 2 d 2 UE 2 λ is the wavelength uniform linear array: e (ϕ) = [1, e iπ cos(ϕ),..., e i(n 1)π cos(ϕ)] T One can show that (e.g., [4, (7.35)]) δn LOS sin ( N π [cos(ϕ2) cos(ϕ1)]) 2 = N sin ( π [cos(ϕ2) cos(ϕ1)]) 2 2 ( ) 1 = O, ϕ N 2 1 ϕ 2. Remark For sufficiently large angular separation, the correlation factor decays much faster than for i.i.d. channels. Thus, LOS can be desirable for massive MIMO. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

19 Channel orthogonality with antenna correlation Let 2 h 1 = R 1 1 w 1, h 2 = R w 2 w 1, w 2 have i.i.d. elements, distributed as CN (0, 1) R 1, R 2 C N N are deterministic Hermitian nonnegative-definite One can show that Examples: Remark δn cor tr R1R2 tr R 1tr R 2 R 1 = R 2 = UU H, where U C N L has orthonormal columns. Then, δ cor N Let R 1, R 2 such that tr R 1R 2 = 0. Then, δ cor N = 0 δ iid N. = 1 L > δiid N. Antenna correlation can either increase or decrease the channel orthogonality. This can be, for example exploited by smart user scheduling algorithms. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

20 Two useful results of random matrix theory Lemma ([5, Lemma B.26], [6, Lemma 14.2]) Let A C N N and x = [x 1... x N ] T C N be a random vector of i.i.d. entries, independent of A. Assume E [x i ] = 0, E [ x i 2] = 1, E [ x i 8] <, and lim sup N A <, almost surely. Then, 1 N xh Ax 1 N tr A a.s. 0. N Lemma ([6, Lemma 3.7]) Let y be another independent random vector with the same distribution as x. Then, Remark 1 N xh a.s. Ay 0. N For A = I N, these results are simple consequences of the strong law of large numbers: 1 N xh I N x = 1 N N i=1 [ xi 2 a.s. E x i 2] = 1, N 1 N xh I N y = 1 N N i=1 xi a.s. y i E [x i y i ] = 0. N Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

21 A simple correlation model r N antennas φ 1 d Δ Δ UE 1 φ 2 λ/2 d Δ Δ r UE 2 One-ring model (see, e.g., [7]): elevated BS, UE surrounded by local scatterers [R l ] k,j = 1 ϕl + 2 ϕ l e iπ(k j)sin(α) dα, 1 k, j, N It was recently shown [8] that tr R 1R 2 N 0 if [ϕ 1, ϕ 1 + ] [ϕ 2, ϕ 2 + ] =. It also holds that rank (R l ) N cos (ϕ l ) sin ( ), tan 1 (r/d) Example: ϕ l = 0, r = 50 m, d = 250 m rank (R l ) N 5. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

22 Channel orthogonality: Ray tracing and measurements Ray tracing: Channel impulse responses created by ray tracing (WISE Tool [9]) Very detailed 3D model of the ALU campus Average correlation factor computed over random position-pairs Channel measurements: m Channel impulse responses taken from a measurement campaign on the ALU campus [10] Virtual antenna array with up to 112 antennas Average correlation factor computed over random pairs of measurement positions Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

23 Channel orthogonality: Theory versus reality Average correlation factor δn i.i.d. LOS, ϕ 1 = 0, ϕ 2 = 20 Raytracing measured Number of antennas N Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

24 Impact on achievable rates bits/channel use measured i.i.d. C sum R MMSE R BF bits/channel use measured i.i.d. C sum R MMSE R BF SNR (db) SNR (db) Achievable rates with different precoding schemes for a broadcast channel with K = 8 UEs over i.i.d. and measured channels for N = 10 (l.) and N = 112 (r.) BS-antennas. 4 db performance loss for the measured channels (MMSE precoding, N = 112) MRT (or beamforming (BF)) highly suboptimal for large N and SNR Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

25 Lessons learned I 1 With very large antenna arrays, noise and interference vanish and the SNR can be made inversely proportional to the number of antennas N without performance loss. This holds for the uplink and downlink. 2 The above conclusions hold with perfect CSI at the BS and under favorable propagation characteristics, i.e., the channel vectors between to different UEs become orthogonal as N grows. 3 The channel orthogonality factors scales as 1/N for the i.i.d. model and as 1/N 2 for pure LOS links. 4 Antenna correlation can have positive or negative effects depending on how UEs are scheduled. For a the one-ring model, the larger the angular separation between two UEs, the more orthogonal the subspaces spanned by the correlation matrices. 5 Ray tracing and channel measurements show that we can expect favorable propagation conditions in practice. However, the orthogonality scaling is slower than predicted by theory. What happens if the channel must be estimated? What is the impact of hardware imperfections? Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

26 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

27 Channel estimation and the role of TDD Channel knowledge at the BS is a must for precoding/beamforming and coherent detection. The channel coherence time fundamentally limits the number of BS-antennas and/or UEs: Remark FDD: Downlink training + feedback as well as uplink training necessary Pilot overhead proportional to the number of antennas (unless certain channel conditions hold [8]) TDD: Only uplink training needed Pilot overhead proportional to the number of UEs We can add antennas at the BSs for free [11] TDD relies on reciprocity of the uplink and downlink channels. While reciprocity holds without doubt for the physical propagation channel, it does not without calibration for the transceiver RF chains. However, end-to-end reciprocity can be established by different internal and external calibration mechanisms, as has been demonstrated in practice (see, e.g., [12]). Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

28 Uplink channel training The UEs transmit mutually orthogonal pilot sequences φ i C τ 1 of length τ: Y = ( ) ( ) φ T h 1h 1 2 φ T + N 2 where Y, N C N τ and vec(n) CN (0, I Nτ ). The BS correlates Y with φ i φ i 2 : where ñ i CN (0, φ i 2 I N ). φ i Y φ i = h 2 i + ñ i Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

29 Uplink channel training (cont.) Let h 1, h 2 be independent and denote R i = E [ ] h i h H i for i = 1, 2. The BS calculates the linear MMSE estimate of h i based on Y φ i φ i 2 : ( ĥ i = R i R i + 1 ) 1 φ i I 2 N Y φ i φ i 2 We can now decompose h i = ĥi + h i ] ( ) 1 ] where E [ĥi ĥ H i = R i R i + 1 I φ i 2 N Ri = Φ i and E [ h i h H i = R i Φ i. ] Due to the orthogonality principle of the MMSE estimator, E [ĥh i hi = 0. If h i CN (0, R i ), then ĥi CN (0, Φ i ) and h i CN (0, R i Φ i ). Assumptions for asymptotic considerations (as N ): tr R i = c i N for some 0 < c i 1 (linear energy growth) lim inf N 1 N rank(r i) > 0 (infinite degrees of freedom) lim sup N R i < (finite energy per degree of freedom) Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

30 Achievable rates with imperfect CSI During T τ channel uses, the UEs transmit their data: y(t) = 2 h i x i (t) + n(t) = i=1 2 i=1 (ĥi + h i ) x i (t) + n(t) The BS estimates x i (t) after the projection of y(t) on ĥi. An achievable rate for UE 1 is given as [13] ( R 1 = 1 τ ) E log 1 + ĥ1 4 ] ) T ĥ H 1 (h 2h [ h1 hh1 H2 + E ĥ1 + 1 I SNR N ĥ1 For large N, we can find the following approximation: ( R 1 1 τ ) ( 1 log T 1 + tr ) 2 N Φ1 1 tr Φ1R2 + 1 tr Φ1 (R1 Φ1) tr Φ1 N2 }{{} N2 }{{}} NSNR {{ N } interference imperfect CSI noise Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

31 How does imperfect CSI affect the power scaling? Remark Let R 1 = R 2 = I N. Then, one can show that: ( R 1 1 τ ) log T 1 + Let φ 1 2 N a, SNR N b 1 + }{{} N interference Only if a + b 1, we have lim inf N R 1 > 0. 1 ( ) + 1 φ 1 2 N SNR NSNR }{{}}{{} imperfect CSI noise With imperfect CSI, the rate at which the transmit power can we reduced with the number of antennas is smaller than for the case of perfect CSI. For equal pilot and data power, i.e., a = b = 1 2, the power can be made only proportional to 1/ N in contrast to 1/N for perfect CSI. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

32 Pilot contamination The number of orthogonal pilot sequences is limited by the channel coherence time. Thus, the pilot sequences must be reused in neighboring cells. Assume that both UEs transmit the same pilot sequence φ 1 C τ 1 : Remark The BS correlates Y with φ 1 φ 1 2 : Y = ( h 1h 2 ) ( φ T 1 φ T 1 ) + N Y φ 1 = h1 + h2 + ñ1 φ and calculates the linear MMSE estimate ( ĥ 1 = R 1 R 1 + R φ I 1 2 N E [ĥ1 ĥ H 1 ) 1 }{{} = S1 Y φ 1 φ 1 2 ] ( ) 1 ] = Φ 1 = R 1 R 1 + R I φ 1 2 N R1 and E [ h1 hh 1 = R 1 Φ 1. The channel estimate ĥ 1 is correlated with h 2. This effect is called pilot contamination. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

33 Achievable rate with pilot contamination Similar to the case without pilot contamination, an achievable rate is given by ( R 1 = 1 τ ) E log 1 + ĥ1 4 ] ) T ĥ H 1 (h 2h [ h1 hh1 H2 + E + 1 I SNR N ĥ1 where γ 1 = (N large) ( 1 τ ) log (1 + γ 1) T ( R N 2 tr }{{} interference As N, ( 1 N tr Φ 1) 2 ) φ 1 2 I N S H 1 R 2S N 2 tr Φ 1 (R 1 Φ 1 ) NSNR N tr Φ N tr S 2 1R 2 }{{}}{{}}{{} imperfect CSI noise pilot cont. ( 1 lim γ 1 = lim tr ) 2 N Φ1 N N ( ) tr N R1 R 1 + R I φ 1 2 N R2 (R 1 =R 2 =I N ) = 1 Remark As N, pilot contamination can become a limiting factor. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

34 When does pilot contamination become dominating? Power (dbm) Signal Interference Imperfect CSI Noise Pilot contamination Number of antennas N Powers of different parts of the received signal at the BS for R i = d 3.6 i I N with d 1 = 200 m, d 2 = 500 m, and φ 2 = SNR = 121 db. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

35 What can we do against pilot contamination? Correlation helps [14]: Let R 1 = U 1D 1U H 1 and R 2 = U 2D 2U H 2 such that U H 1 U 2 = 0 N. Then, R 1 as N grows. Idea: Assign pilot sequences based on second-order channel statistics in order to reduce pilot contamination. Blind or EVD-based channel estimation [15, 16]: Let R i = β i I N for i = 1, 2 and assume β 1 > β 2. The BS observes the data transmissions during T time slots: Y = ( h 1h 2 ) ( x 1(1)... x 1(T ) x 2(1)... x 2(T ) ) + N where x i (t), i, t, are i.i.d with zero mean and unit variance and N i,j CN (0, 1). Let Y = [u 1... u N ] DV H. Then, as T, N, N/T c and β 1 > c, 1 N u H 1 h 2 a.s. 0, 1 u H 1 h 1 2 N,T N a.s. N,T β1. Thus, the BS can detect x 1(t) either blindly based on u H 1 Y or estimate the effective channel u H 1 h 1 from pilots without pilot contamination. Other techniques: Pilot contamination precoding (multi-cell precoding based on channel statistics and user data sharing) [17], Time-shifted pilots (UEs in different cells transmit the pilots at different times) [18], many more... Pilot contamination is not a fundamental limitation and can be efficiently mitigated! Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

36 What about FDD? Channel estimation for the uplink is essentially the same as for TDD. Estimating the downlink channel at the BS requires downlink training and feedback from the UEs which is proportional to N. Antenna correlation can be exploited to reduce this overhead! Let the received signal at a UE be y = h H wx + n where w C N 1 is a precoding vector, h CN (0, R), rank(r) = L, with SVD R = UDU H and U C N L. Assuming that R is known, the BS can apply an outer -precoder U which reduces the N-dimensional channel h to the L-dimensional effective channel U H h, i.e., w = U w, w C L 1. The UE only estimates and feeds back the coefficients of the effective channel. This overhead is proportional to L. This idea can be extended to multiple UEs [8]: Group users with similar covariance matrices together, use MU-MIMO on the effective channel to separate the UEs of a group, simultaneously schedule groups with almost orthogonal covariance matrices. The number of UEs per group is limited by the rank of the covariance matrix. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

37 Joint Space-Division and Multiplexing (JSDM) An idea from [8]: UEs in different circles of the same color have covariance matrices which span (nearly) orthogonal sub-spaces. They are simultaneously served by a combination of a deterministic pre-beamforming matrix and MU-MIMO schemes based on the reduced-dimensional effective channel. The BS is elevated from the ground and has a 2-dimensional array which makes it possible to separate UE-clusters in the azimuth and elevation angular domain. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

38 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

39 Hardware impairments Any transceiver suffers from hardware impairments which create a mismatch between the intended and emitted signal distort the received signal The distortions depend in general on the transmitted or received power. Sources of impairments are: oscillator phase noise amplifier non-linearity (especially for OFDM with high PAPR) IQ imbalance due to imperfections in the quadrature mixer quantization noise Hardware impairments are known to limit the performance in the high-snr regime but much less is known for the large-n regime [19]. For massive MIMO cheap, low-power, and low-cost transceivers are desirable. What are the impacts of hardware imperfections? Can the hardware quality be reduced by increasing N? All of the results in this part are taken from [20, 21]. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

40 Uplink system and channel model Downlink: Pilots & Data Uplink Pilot & Control Signals Uplink Data Transmission Downlink Pilot & Control Signals Downlink Data Transmission Uplink: Pilots & Data T UL pilot T UL data T DL pilot T DL data Coherence Period Tcoher Base station User equipment ( Uplink : y BS = h x UE + η UE t ) + η BS r + n BS Additive distortion where E [ x UE 2] = p UE, n BS CN (0, S), and h CN (0, R). UE transmit distortion: η UE t BS receive distortion: η BS r CN ( 0, κ UE t p UE) CN (0, κ BS r p UE diag( h 1 2,..., h N 2 )) The parameters κ UE t and κ BS r are usually in the range [0, 0.03]. The smaller these values, the more accurate and expensive is the corresponding transceiver hardware component. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

41 Channel estimation with hardware imperfections The BSs computes the linear MMSE estimate of h based on a single uplink pilot x UE = d, d 2 = p UE : ĥ = d RZ 1 y BS where R ii is the ith diagonal element of R and [ Z = E y BS (y BS ) H] ( ) = p UE 1 + κ UE t R + p UE κ BS r diag(r 11,..., R NN ) + S. We can decompose the channel as h = ĥ + h, where E [ĥĥ H] = R C E [ h hh ] = C C = R p UE RZ 1 R. Remarks Due to the distortion noise, the MMSE estimator is very complicated to derive and not identical to the LMMSE estimator. ĥ and h are neither independent nor jointly complex Gaussian, but only uncorrelated with zero mean. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

42 Channel estimation with hardware imperfections: Insights Impact of pilot power For R = S = I N, we have ( ) 1 C = 1 I 1 + κ UE t + κ BS r + 1 N, p UE ( ) 1 lim C = 1 I p UE 1 + κ UE t + κ BS N. r Thus, even with infinite pilot power, perfect estimation accuracy cannot be achieved and the performance is limited by the sum of the hardware impairments at the UE and BS. Impact of pilot length If the UE sends B pilot tones, the estimation accuracy can be improved by averaging B separate LMMSE estimates ĥ = 1 B B ĥ i = h 1 B i=1 B h i. i=1 If the errors h i are uncorrelated, they average out as B increases. However, the distortion might be correlated and increasing B decreases the time for data transmission. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

43 Channel estimation with hardware imperfections: Numerical results 10 0 Relative Estimation Error per Antenna κ UE t = κ BS r = κ UE t = κ BS r = κ UE t = κ BS r = κ UE t = κ BS r = LMMSE Estimator Error Floors Average SNR [db] Relative estimation error tr tr C for N = 50 over SNR = tr R pue R tr. The matrix R is generated S by the exponential model [22] with correlation coefficient ρ = 0.7 and S = I N. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

44 Channel estimation with hardware imperfections: Numerical results Relative Estimation Error per Antenna db 30 db Fully Correlated Distortion Noise Uncorrelated Distortion Noise Ideal Hardware Pilot Length (B) Relative estimation error tr tr C over the pilot length B for for N = 50 and R = κ BS r = κ UE t Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

45 Channel estimation with hardware imperfections: Numerical results 10 0 Relative Estimation Error per Antenna Case 1: Uncorrelated Case 2: Exp.Mod., r = 0.7 Case 3: One-Ring, 20 deg Case 4: One-Ring, 10 deg 5 db 30 db Number of Base Station Antennas (N) Relative estimation error tr tr C over N for κue R t = κ BS r = Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

46 Channel estimation with hardware imperfections: Discussion Perfect channel estimation with hardware imperfections is impossible. The estimation accuracy is fundamentally limited by Distortions for high SNR Coherence time and correlation of distortion noise for long pilot sequences Hardware qualities of the UE and the BS are equally important. The channel model largely impacts the estimation accuracy: Correlated channels are easier to estimate [23]. For large N, accurate estimates of R and S are difficult to obtain. The impact on the estimation performance is unclear. In practice [24], one would expect additive and multiplicative distortions. The latter are more difficult to analyze and can make things only worse. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

47 Downlink channel model with hardware imperfections Downlink: Pilots & Data Uplink Pilot & Control Signals Uplink Data Transmission Downlink Pilot & Control Signals Downlink Data Transmission Uplink: Pilots & Data T UL pilot T UL data T DL pilot T DL data Coherence Period Tcoher Base station User equipment ( ) Downlink : y UE = h H wx BS + η BS t + ηr UE + n UE Additive distortion Remark where E [ x BS 2] = p UE, w = 1, and n UE CN (0, σ 2 UE). BS transmit distortion: η BS t UE receive distortion: η UE r CN (0, κ BS t p BS diag( w 1 2,..., w N 2 )) CN (0, κ UE r p BS h H w ) Despite channel reciprocity, the UE needs to estimate the effective SISO channel h H w. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

48 Capacity upper bounds Assuming perfect CSI at the BS and UE and Gaussian signaling, one can show that the ergodic UL and DL capacities are bounded from above by ) 1 C UL T data UL h (κ H BS r D h + 1 p S h E log T UE ( ) 1 coher 1 + κ UE t h H κ BS r D h + 1 p S h UE Cupper UL = T data UL ( G UL ) log T coher 1 + κ UE t G UL C DL T data DL E T coher log Cupper DL = T data DL T coher log 2 ) 1 h (κ H BS t D h + σ2 UE p I h BS ( 1 + κ UE r h H ( 1 + G DL κ BS t 1 + κ UE r G DL ) 1 D h + σ2 UE p I BS ) h ( ) ] ( ) ] 1 1 where G UL = E [h H κ BS r D h + 1 p S h, G DL = E [h H κ BS UE t D h + σ2 UE p I h, and BS D h = diag( h 1 2,..., h N 2 ). Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

49 Asymptotic behavior of the upper bounds High-SNR regime data lim C p UE upper UL = T UL lim C p BS upper DL = T DL T coher log 2 data T coher log 2 ( 1 + ( 1 + κ BS r κ BS t ) N + Nκ UE t ) N + Nκ UE r Large-N regime lim C upper UL = T data UL N T coher log 2 ( ), lim κ C UE upper DL = T data DL t N T coher log 2 ( ) κ UE r Observations The UL/DL capacities have finite ceilings which depend on the hardware quality. The UE impairments are N times more influential than the BS impairments. As N, only the UE hardware limits the performance; the BS distortion averages out. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

50 Capacity lower bounds One can show that the ergodic UL/DL capacities are bounded from below by ([25, 13]) where v UL, v DL are functions of ĥ and C UL Clower UL = T data UL ( ) log T SINR UL lower coher C DL Clower DL = T data DL ( ) log T SINR DL lower coher [ E h SINR UL H lower = v UL] 2 [ h (1 + κ UE t )E H v UL 2] [ E h H v UL] 2 + κ BS N r i=1 E [ h i 2 vi UL 2] + E[(vUL ) H Sv UL ] p UE SINR DL lower = E [ h H v DL] 2 [ (1 + κ UE r )E h H v DL 2] E [ h H v DL] 2 + κ BS N t i=1 E [ h i 2 vi DL 2]. + σ2 UE p BS Remarks The bounds hold for any v UL, v DL ; especially for v UL = v DL = C UL lower ĥ ĥ. depends only on κue t, κ BS r while Clower DL depends on all κ-parameters. The impact of κ BS t vanishes as N. One can show that, if κ UE t = 0, lim N Cupper DL Clower DL = 0. This does not happen for κ BS r = 0. Thus, the capacity limit is mainly determined by the impairments at the UE. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

51 Capacity bounds: Numerical results 8 Spectral Efficiency [bits/channel use] κ BS = κ UT = 0 κ BS = κ UT = κ BS = κ UT = Capacity: Upper Bounds 1 Capacity: Lower Bounds Asymptotic Limits (Upper & Lower) Number of Base Station Antennas (N) Lower and upper bounds on the capacity for R = S = I Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

52 Capacity bounds: Numerical results 4 Spectral Efficiency [bits/channel use] Decreasing with Increasing impairments: κ BS {0, , } 2.5 Capacity: Upper Bounds Capacity: Lower Bounds Asymptotic Limits (Upper & Lower) Number of Base Station Antennas (N) Lower and upper bounds on the capacity for R = S = I and κ UE t = κ UE r = The impact of the hardware impairments at the BS vanishes asymptotically. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

53 Scaling down the power or hardware quality Uplink: Let p UE 1, 0 < t < 1 or κ BS N t 2 r lim N C UL log 2 ( 1 + N t, 0 < t < 1. Then, 4 ) 1 2κ UE t + (κ UE t ) 2 Downlink: Let p BS 1 N t BS, pue 1 κ BS r Remark N t 1, κ BS t, t N t UE BS + t UE < 1, t BS 0, 0 < t UE < 1 or 2 N t 2, 0 < t 1 + t 2 < 1. Then, 2 ( ) lim C DL 1 log N The transmit powers can be roughly reduced as transceiver can be reduced as 1 N κ UE r 1 N + κ UE t + κ UE r κ UE t or the hardware quality of the BS while still a non-zero capacity is achieved. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

54 Lessons learned II With TDD, the pilot overhead is independent of N. The effects of imperfect CSI vanish as N. The transmit power can be made proportional to 1/ N when channel estimation is taken into account (in contrast to 1/N with perfect CSI). This holds even with hardware impairments. Pilot contamination can be a performance bottleneck, but it is not a fundamental limitation. It can be mitigated by blind channel estimation schemes, scheduling, or precoding. Hardware imperfections seem to be a fundamental limitation. The quality of the UE-transceiver is more important than that of the BS-transceiver. The quality of the BS-transceivers can be decreased as N grows (roughly proportional to N 1 4 ). Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

55 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

56 Some interesting areas for future research Channel modeling: Measurements, ray-tracing, new statistical models [26, 10] New deployment models: Distributed massive MIMO, antennas in building facades or windows [27], massive MIMO in HetNets [28, 29, 30] New applications for massive MIMO: Wireless backhaul [31], sensor networks Estimation of covariance matrices: Impact for channel estimation, precoding/detection Hardware impairments: Fundamental limits and ways to mitigate them [20] Cost and impacts of TDD reciprocity calibration Combination of massive MIMO and stochastic geometry [32, 33] Total energy efficiency of massive MIMO systems [34, 28, 20, 21] Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

57 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

58 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

59 Massive MIMO versus Small Cells From a coverage as well as area spectral efficiency point of view, it is preferable to distribute the available antennas as much as possible [35]. However, with small cells deployed below the roof tops, it is difficult to ensure coverage support highly mobile UEs (due to frequent handovers) But, massive MIMO is particularly suited to provide coverage of large areas support highly mobile UEs (TDD reduces the turnaround time) Can we integrate the complementary benefits of both? Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

60 A two-tier network architecture Massive MIMO BSs overlaid with many small cells (SCs) BSs ensure coverage and serve highly mobile UEs SCs drive the capacity (hot spots, indoor, etc.) There is a large number of excess antennas in the network, which should be exploited. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

61 The role of TDD A network-wide synchronized TDD protocol has the following advantages: The downlink channels can be estimated from uplink pilots. Enable massive MIMO Channel reciprocity holds for the desired and interfering channels. Knowledge about the interfering channels can be acquired for free at every device (BS, SC, UE). Idea: Sacrifice excess antennas to reduce intra- and inter-tier interference. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

62 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

63 A simple idea from cognitive radio [36] 1 The secondary BS listens to the transmission from the primary UE: y = hx + n 2...and computes the covariance matrix of the receive signal: [ E yy H] = hh H + SNR 1 I Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

64 A simple idea from cognitive radio [36] 3 With the knowledge of the SNR, the secondary BS designs a precoder w which is orthogonal to the sub-space spanned by hh H. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

65 A simple idea from cognitive radio [36] 3 With the knowledge of the SNR, the secondary BS designs a precoder w which is orthogonal to the sub-space spanned by hh H. 4 The interference to the primary UE can be entirely eliminated without explicit knowledge of h. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

66 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

67 Translate this idea to HetNets Every device estimates its received interference covariance matrix and precodes (partially) orthogonal to the dominating interference subspace. Advantages Interference to the directions from which a device received most interference is reduced. No feedback or data exchange between the devices is needed. Every device relies on locally available information alone. The scheme is fully distributed an scalable. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

68 Baseline scenarios: FDD, TDD, RTDD, and co-channel deployment FDD TDD frequency SC DL SC UL BS DL BS UL frequency SC UL BS UL SC DL BS DL time time co-channel TDD co-channel reverse TDD frequency SC UL SC DL frequency SC DL SC UL BS UL BS DL BS UL BS DL time time FDD: Channel reciprocity does not hold TDD: Only intra-tier interference can be reduced co-channel TDD: Inter and intra-tier interference can be reduced reverse (R) TDD: Order of UL/DL is reversed in one of the tiers Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

69 TDD versus reverse TDD (RTDD) Order of UL/DL periods decides which devices interfere with each other: TDD BS and small cell UEs (SUEs) SCs and macro UEs (MUEs) Intra-tier interference (SC-SUE, BS-MUE) RTDD BS and SCs MUEs and SUEs Intra-tier interference (SC-SUE, BS-MUE) The BS-SC channels change very slowly (quasi-static). Thus, covariance estimation becomes easier for RTDD. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

70 Co-channel TDD: Uplink signaling F antennas N antennas single antenna B BSs with N antennas SC j,s BS j SUE j,s MUE j,k MUE i,k K single-ant. MUEs per BS S SCs per BS with F antennas 1 single-ant. SUE per SC BS i SUE i,s SC i,s Received signals at the ith BS and jth SC in cell i: ( B K S yi BS = PMUE h BS-MUE ibk xbk MUE + PSUE h BS-SUE ibs xbs SUE y SC ij = b=1 k=1 ( B K PMUE h SC-MUE ijbk xbk MUE + b=1 k=1 s=1 S s=1 PSUE h SC-SUE ijbs xbs SUE ) ) + n BS i + n SC ij Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

71 Co-channel TDD: Uplink rates BSs and SCs have perfect knowledge of the direct channels and the individual receive covariance matrices: [ Q BS i = E yi BS (yi BS ) H] [, Q SC ij = E yij SC (yij SC ) H] Achievable rates of the MUE k and SUE s in cell i with MMSE detection: R UL,MUE ik = T ( ( UL T log P MUE (h BS-MUE iik ) H Q BS i P MUE h BS-MUE iik (h BS-MUE iik ) H) ) 1 h BS-MUE iik R UL,SUE is = T ( ( UL T log P SUE (h SC-SUE isis ) H Q SC is P SUE h SC-SUE isis (h SC-SUE isis ) H) ) 1 h SC-SUE isis where T is the channel coherence time and T UL is the duration of the uplink cycle. On the CSI assumption In practice, the direct channels must be estimated by uplink pilots. For a sufficiently long coherence time, the covariance matrices can be estimated by simple time averages. It is implicitly assumed that the transmit powers and noise variances are perfectly known. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

72 Co-channel TDD: Downlink signaling Received signals at the jth MUE and jth SUE in cell i: ( B K yij MUE PBS S = K (hbs-mue bij ) H wbk BS xbs bk + y SUE ij = b=1 k=1 ( B K PBS b=1 k=1 K (hbs-sue bij ) H w BS s=1 S bk xbs bk + s=1 PSC (hbsij SC-MUE ) H wbs SC xsc bs PSC (hbsij SC-SUE ) H wbs SC xsc bs The BSs and SCs apply linear beamforming to serve their UEs: wbk BS = κbs bk (1 α)p MUE h BS-MUE bbj (h BS-MUE bbj ) H + αq BS b (1 α)noi N w SC bs ( = κsc bs (1 β)p SUE h SC-SUE bsbs j ) 1 ) 1 (h SC-SUE bsbs ) H + βq SC bs + (1 β)noi F h SC-SUE bsbs ) + n MUE ij + n SUE ij h BS-MUE bbk where α, β are regularization parameters and κ BS bk, κ SC bs normalize the vector norms to one. About the regularization parameters For α, β = 0, the BSs and SCs transmit as if they were in an isolated cell, i.e., MMSE precoding (BSs) and maximum-ratio transmissions. By increasing α, β, the precoding vectors become increasingly orthogonal to the interference subspace. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

73 Co-channel TDD: Downlink rates Achievable downlink rates of the MUE k and SUE s in cell i: where SINR DL,MUE ik = SINR DL,SUE is = ( R DL,MUE ik = 1 T UL T R DL,SUE is = N o + P BS K N o + P BS K ( 1 T UL T ) log 2 ( ) log 2 ( ) 1 + SINR DL,MUE ik ) 1 + SINR DL,SUE is P BS K (h BS-MUE iik ) H wik BS 2 (b,j) (i,k) (h BS-MUE bik ) H wbj BS 2 + P SC b,s (h SC-MUE bsik ) H wbs SC 2 P SC (h SC-SUE isis ) H wis SC 2 (b,j) (h BS-SUE bis ) H wbj BS 2 + P SC (b,s) (i,s) (h SC-SUE bjis ) H wbj SC 2 Other duplexing schemes The other duplexing schemes work similarly, by adapting the covariance matrices and interference terms. In FDD, covariance knowledge cannot be exploited as channel reciprocity does not hold. Without co-channel deployment, there is only intra-tier interference. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

74 Numerical results 3 3 grid of BSs with wrap around BS 1000 m 40 m 111 m SC MUE SUE S = 81 SCs per cells on a regular grid K = 20 MUEs randomly distributed in each cell 1 SUE per SC randomly distributed on a disc around each SC channel model with path loss, shadowing and fast fading, N/LOS links from [37] TX powers: 46 dbm (BS), 24 dbm (SC), 23 dbm (MUE/SUE) 20 MHz bandwidth, 2 GHz center frequency no user scheduling, power control averages over channel realizations and UE locations T UL = 0.5T Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

75 Downlink rate regions SC DL area spectral efficiency ( b/s/hz/km 2) Macro DL area spectral efficiency ( b/s/hz/km 2) FDD (N = 20, F = 1) Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

76 Downlink rate regions SC DL area spectral efficiency ( b/s/hz/km 2) F = 1 4 FDD region more antennas N = FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) Macro DL area spectral efficiency ( b/s/hz/km 2) Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

77 Downlink rate regions SC DL area spectral efficiency ( b/s/hz/km 2) F = 1 4 β = 0 1 FDD region more antennas N = TDD region FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1) less intra-tier interf. α = Macro DL area spectral efficiency ( b/s/hz/km 2) Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

78 Downlink rate regions SC DL area spectral efficiency ( b/s/hz/km 2) F = 1 4 β = 0 1 CoTDD region FDD region β more antennas N = α TDD region FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1) less intra-tier interf. α = 0 1 Macro DL area spectral efficiency ( b/s/hz/km 2) Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

79 Downlink rate regions SC DL area spectral efficiency ( b/s/hz/km 2) F = 1 4 β = 0 1 β α CoTDD region FDD region CoRTDD region β more antennas N = α TDD region FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1) less intra-tier interf. α = 0 1 Macro DL area spectral efficiency ( b/s/hz/km 2) Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

80 Uplink rate regions Small cell UL sum-rate ( b/s/hz/km 2) F = 1 4 α more antennas N = FDD/TDD (N = 20, F = 1) Macro UL sum-rate ( b/s/hz/km 2) FDD/TDD (N = 100, F = 4) co-channel TDD co-channel reverse TDD Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

81 Observations Increasing the number of antennas at each device leads to tremendous performance improvements for all duplexing schemes (N = , F = 1 4, FDD): +200 % BS UL, +150 % BS DL, +100 % SC UL, +50 % SC DL TDD channel reciprocity allows for intra-tier interference reduction (α, β : 0 1): +50 % BS DL, +30 % SC DL Even a few excess antennas at the SCs leads to significant gains. With RTDD, the SCs cannot reduce interference towards the BS (since F N). With the proposed precoding scheme, a co-channel deployment of BSs and SCs leads to the highest area spectral efficiency (α = β = 1, 20 MHz bandwidth): UL DL Area throughput 7.63 Gb/s/km Gb/s/km 2 Rate per MUE 38.2 Mb/s 25.4 Mb/s Rate per SUE 84.8 Mb/s 104 Mb/s As the scheme is fully distributed and requires not data exchange between the devices, the rates can be simply increased by adding more antennas to the BSs/SCs or increasing the SC-density. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

82 Discussion Channel reciprocity requires: Hardware calibration [38, 39, 40, 12] Scheduling of UEs on the same resource blocks in subsequent UL/DL cycles. The network-wide TDD protocol requires tight synchronization of all devices: GPS (outdoor) NTP/PTP (indoor) BS reference signals Channel estimation will suffer from pilot contamination. Covariance matrix estimation becomes difficult for large N, F [41, 42]. We have considered a worst case model with fixed cell association, no power control or scheduling. Location-dependent user scheduling and interference-temperature power control could further enhance the performance [43]. Band switching duplexing could be used to reduce duplexing delays [44]. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

83 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

84 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

85 Massive MIMO for wireless backhaul The unrestrained SC-deployment where needed rather than where possible requires a high-capacity and easily accessible backhaul network. Already for most WiFi deployments, the backhaul capacity ( Mbit/s) and not the air interface ( Mbit/s) is the bottleneck. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

86 Massive MIMO for wireless backhaul small cell wireless backhaul wireless data wired backhaul Core network massive MIMO base station user equipment The unrestrained SC-deployment where needed rather than where possible requires a high-capacity and easily accessible backhaul network. Already for most WiFi deployments, the backhaul capacity ( Mbit/s) and not the air interface ( Mbit/s) is the bottleneck. Why not provide wireless backhaul with massive MIMO [31]? Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

87 Massive MIMO wireless backhaul: Advantages No standardization or backward-compatibility required BS-SC channels change very slowly over time: Complex transmission/detection schemes (e.g., CoMP) can be easily implemented FDD might be possible due to reduced CSI overhead Provide backhaul where needed: Adapt backhaul capacity to the load Statistical multiplexing opportunity to avoid over-provisioning of backhaul SCs require only a power connection to be operational Line-of-sight not necessary if operated at low frequencies Remark Interestingly, the backhaul load is highest in lightly loaded cells where a single UE with a very good channel achieves the maximum possible data rate on the wireless link [45]. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

88 Massive MIMO wireless backhaul: Is it feasible? How many antennas are needed to satisfy the desired backhaul rates with a given transmit power budget? Assumptions: Every BS knows the channels to all SCs. The BSs can exchange some control information. Full user data sharing between the BSs is not possible. Single-antenna SCs, BSs with N antennas TDD with channel reciprocity Check if the power minimization problem with target SINR constraints for the multi-cell multi-antenna wireless system is feasible [46]. Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96

89 Outline 1 Massive MIMO Benefits Favorable propagation conditions Channel estimation and pilot contamination Hardware impairments Research topics 2 Massive MIMO and HetNets Small cells, a two-tier network architecture, and the role of TDD An idea from cognitive radio Translate this idea to HetNets 3 Massive MIMO for wireless backhaul Motivation and advantages Power and antenna minimization problem Jakob Hoydis (Bell Labs) Massive MIMO and HetNets IMSS / 96