How many users are needed for non-trivial performance of random beamforming in highly-directional mm-wave MIMO downlink? Gilwon Lee School of Electrical Engineering KAIST Oct. 14, 2015 Joint work with Prof. Youngchul Sung and Junyeong Seo Information Theory Workshop 2015, Jeju island, Korea

5G Key Technologies Average rate (bits/s/active user) 10~100x 5G Requirements Average rate (bits/s/active user) 10~100x Average area rate (bits/s/km2) 1000x Active devices (per km2) 10-100x Energy efficiency (bits/Joule) 1000x Key Technologies Focus of this talk Cellular band Mm-wave band 3 GHz 30 GHz 300 GHz (Prof. Heath’s Fig) (argos ant.) Mm-wave MIMO Massive MIMO

Mm-wave Channel Characteristics Quasi-optical nature of propagation Very few multi-path components Channel sparsity Channels are sparse Many literatures use geometric channel model Ex) cf. S. Sun, T. S. Rappaport, “Wideband mmWave Channels: Implications for Design and Implementation of Adaptive Beam Antennas ,” IEEE 2014 Intl. Microwave Symp. (IMS), June 2014, Tampa, Fl

Mm-wave Channel Characteristics Large path-loss High noise power due to large-bandwidth (Friis’ law) Mm-wave noise BW microwave noise BW G. R. MacCartney, M. K. Samimi, and T. S. Rappaport, "Omnidirectional Path Loss Models in New York City at 28 GHz and 73 GHz,“ IEEE 2014 PIMRC. Massive antennas Exploiting large-array antenna gain

A Challenging Issue: Channel Estimation Channel sounding also requires highly-directional training beams due to large path-loss and high noise power. Furthermore, there are few multi-path components in channels Full-training method Long training period is required!

A Challenging Issue: Channel Estimation An efficient method: Multi-resolution Hierarchical approach Divide full-range of the BS into two regions and transmit training beams to each of them After feedback, the BS chooses the better region 1st stage feedback A. Alkhateeb, O. E. Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for millimeter wave cellular systems,” IEEE JSTSP, Oct. 2014.

A Challenging Issue: Channel Estimation An efficient method: Multi-resolution Hierarchical approach Divide full-range of the BS into two regions and transmit training beams to each of them After feedback, the BS chooses the better region and further divides the chosen region into two sub-regions. 2nd stage A. Alkhateeb, O. E. Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for millimeter wave cellular systems,” IEEE JSTSP, Oct. 2014.

A Challenging Issue: Channel Estimation An efficient method: Multi-resolution Hierarchical approach Divide full-range of the BS into two regions and transmit training beams to each of them After feedback, the BS chooses the better region and further divides the chosen region into two sub-regions. 3rd stage Properties of the method Training period can be significantly reduced. However, power consumption for training is very large at early stages. This approach is useful for single-user case. A. Alkhateeb, O. E. Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for millimeter wave cellular systems,” IEEE JSTSP, Oct. 2014.

A Fundamental Question We have seen some results of singe-user systems. Then, what about multi-user systems? Is long training period still needed to obtain reasonable performance for multi-user systems?

Some Insights Let’s assume the BS transmits a highly directional training beam to a random angle direction. Now we ask what happens if there are many users in the cell. Intuitively, we can expect the single random beam performs well when the number of users is large. Then how many users are needed? Specify the # of users!

Multi-User Diversity In fact, many works on the multi-user diversity (opportunistic beamforming) have been conducted in the Rayleigh fading channel model which is usually suitable for the cellular band. i.i.d. Ex. Random beamforming (RBF), Semi-orthogonal user selection (SUS) However, there are no any analysis results on multi-user diversity in the mm-wave band. M. Sharif and B. Hassibi, “On the capacity of MIMO broadcast channels with partial side information,” IEEE Trans. Inf. Theory, vol. 51, pp. 506–522, Feb. 2005. T. Yoo and A. Goldsmith, “On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming,” IEEE J. Sel. Areas Commun., vol. 24, pp. 528–541, Mar. 2006

Exploring Multi-User Diversity in Mm-wave System Model MU-MISO downlink BS with ULA of antennas single-antenna users Channel Model Uniform-Random Single-Path (UR-SP) Channel vector of user k AoD Path gain Steering vector

UR-SP Channel Model UR-SP Channel Model When LoS exists Considering not only LoS environment but also one dominant path in NLoS environment When LoS exists When LoS does not exist One dominant NLOS path The different path gain between LoS and NLoS components can be captured by the assumption

Singe Beam Case The BS transmits a randomly directional training beam to receivers in the direction of a random angle .

Singe Beam Case The BS transmits a randomly directional training beam to receivers in the direction of a random angle . Then, each user feeds back the signal power to the BS. After the feedback is over, the BS selects the user that has the maximum signal power, and transmits a data stream with the beamforming vector . (single beam rate)

Fejer Kernel of Order M Since mm-wave systems use many antennas, we adopt asymptote. Beam pattern The value of beam pattern w.r.t. the difference btw and . Fejer kernel of order M

Fejer Kernel of Order M: Observation Order of 1/M

Singe Beam Rate Based on the above facts, we have the following observation. Observation When for all k, and for fixed , we have (trivial performance) If we can find a user k such that almost surely, we have (non-trivial performance) Q) How many users K as a function of M are needed to obtain non-trivial performance?

Lemma 1 To explicitly derive it, we assume for simple explanation and provide a lemma related to signal power as follows. (The effect of is fully considered in the paper, but is trivial so we omitted it in this presentation.) Lemma 1 For any constant and sufficiently large M, we have where signal power Proof of Lemma 1: omitted

Theorem 1 – Asymptotic Rate of Based on Lemma 1, we can show the following theorem. Theorem 1 Corollary 1 For and any given , we have where . For Rate when perfect CSI is available Proof of Theorem 1: omitted 𝒒= 𝟏 𝟐 is the performance transition point !

Theorem 1 – Asymptotic Rate of Corollary 1 For Rate when perfect CSI is available 𝒒= 𝟏 𝟐 is the performance transition point !

Theorem 1 – Asymptotic Rate of Need more training beams! 𝒒= 𝟏 𝟐 is the performance transition point !

Effect of Training Multiple Training Beams: Remark: where is an offset angle. Remark:

Theorem 2 – Asymptotic Rate of Corollary 2 For , and any such that , we have where . For Rate when perfect CSI is available Proof of Theorem 2: omitted ℓ+𝒒= 𝟏 𝟐 is the performance transition point !

Theorem 2 – Asymptotic Rate of Corollary 2 For Rate when perfect CSI is available ℓ+𝒒= 𝟏 𝟐 is the performance transition point !

Theorem 2 – Asymptotic Rate of ℓ+𝒒= 𝟏 𝟐 is the performance transition point !

Theorem 2 – Asymptotic Rate of When the number of users is too small to achieve non-trivial performance, Theorem 2 specify how much training is required to achieve it!

Simulation Results M=1000 Single beam case Multi-beam case

Extension to the Multi-User Selection Multi-user selection with multi-beam Random beamforming (RBF) Each user k feeds back the maximum SINR and the corresponding beam index. For each beam, the BS chooses the user that has the maximum SINR and transmits data streams to the chosen users through the corresponding beams at the same time. Rate of a selected user where G. Lee, Y. Sung, and J. Seo, “Randomly directional beamforming in millimeter wave multi-user MISO downlink,” to appear in IEEE Tran. Wireless Commun.

Theorem 3 – Asymptotic Rate of For , with and , we have where for . Sum Rate As , (the optimal rate) G. Lee, Y. Sung, and J. Seo, “Randomly directional beamforming in millimeter wave multi-user MISO downlink,” to appear in IEEE Tran. Wireless Commun.

Asymptotic Results of RBF in UR-SP Linear sum rate scaling w.r.t. M can be achieved, if K increases linearly w.r.t. M. Furthermore, the optimal sum rate can be achieved if K increases linearly w.r.t. M. This result is contrary to the existing result in the Rayleigh fading channel model where linear sum rate scaling w.r.t. M can be achieved, if K increases exponentially w.r.t. M. As , G. Lee, Y. Sung, and J. Seo, “Randomly directional beamforming in millimeter wave multi-user MISO downlink,” to appear in IEEE Tran. Wireless Commun.

Conclusion (Single beam case) There exists a performance transition point in the number of users (relative to the number of antennas) for non-trivial performance. (Single-user selection with multi-beam case) We specify how much training is required for obtaining non-trivial performance. (Multi-user selection with multi-beam case) Furthermore, the performance of random beamforming can achieve the optimal sum rate if K increases linearly w.r.t. M.