Precoding and Massive MIMO
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1 Precoding and Massive MIMO Jinho Choi School of Information and Communications GIST October / 64
2 1. Introduction 2. Overview of Beamforming Techniques 3. Cooperative (Network) MIMO 3.1 Multicell with a common group of users 3.2 Multicell with different groups of users 4. Massive MIMO 4.1 Partial cooperation 4.2 Pilot contamination in massive MIMO 4.3 Pilot contamination precoding 5. Conclusions 2 / 64
3 1. Introduction 1. Introduction Beamforming with antenna arrays has been studied for wireless communications since early 90s. Transmit and receive beamforming have been considered for cellular systems to improve the signal-to-noise ratio (SNR) or extend the coverage. A better beamforming gain can be achieved if the number of antennas in an array is large. In cellular systems, as base stations (BSs) can have a number of antennas, beamforming can be easily employed at BSs. In this case, transmit beamforming becomes downlink beamforming and receive beamforming becomes uplink beamforming. 3 / 64
4 44/60 / 64 Precoding Beamforming and and Massive Massive MIMO MIMO 1. Introduction Downlink beamforming = transmit beamforming at BS Beamformer w 1 Data symbols w 2 Dynamic or static Beampattern w L
5 1. Introduction Unfortunately, due to various problems, the number of antenna elements in an array for downlink beamforming is limited. However, in 5G, transmit (or downlink) beamforming has been considered seriously to extend the coverage. In this tutorial, we review existing downlink beamforming approaches and focus on cooperative and noncooperative approaches in multi-cell MIMO systems. In the end, we wil attempt to highlight the differences between network MIMO and massive MIMO in multi-cell systems. 5 / 64
6 1. Introduction How transmit beamforming works: TX 1 h 1 TX 2 h 2 Let h 1 and h 2 denote the channel coefficients from TX antennas 1 and 2, respectively. If TX antenna k transmits w k s, where w k is the weight and s is the signal to be transmitted, the received signal becomes r = h 1 w 1 s + h 2 w 2 s + n = (h 1 w 1 + h 2 w 2 )s + n, where n is the background noise. 6 / 64
7 1. Introduction The SNR at the receiver becomes SNR = h 1w 1 + h 2 w 2 2 E s N 0 h 2 w 2 E s N 0, where the equality holds if w k h k. A full diversity order is equal to the number of antennas. The more transmit antennas, the better performance. However, the channel state information (CSI) is required for transmit beamforming to achieve the maximum SNR. If the transmitter does not know the CSI, the receiver has to feed back it to the transmitter. With limited feedback, the number of antennas cannot be large, which has been one of the major drawbacks of transmit beamforming, which may not be a drawback in TDD mode (using the channel reciprocity). 7 / 64
8 2. Overview of Beamforming Techniques 2. Overview of Beamforming Techniques There are three different systems where beamforming can be employed: A. Point-to-point MIMO (single-user beamforming) B. Multiuser (point-to-multipoint) MIMO (multiuser beamforming) C. Multipoint-to-multipoint (or network) MIMO (cooperative beamforming) We can also consider a different system in which beamforming plays a crucial role: D. Massive MIMO: this is the case where single-user beamforming is employed in a multi-cell system For cellular systems, single-cell: point-to-point or multiuser MIMO multi-cell: network MIMO (there is inter-cell interference problem), massive MIMO 8 / 64
9 2. Overview of Beamforming Techniques A. Point-to-point MIMO To achieve diversity gain: beamforming with CSI at transmitter space-time coding (STC) without CSI at transmitter To achieve multiplexing gain: SVD with CSI at transmitter BLAST techniques without CSI at transmitter There are also other techniques that enjoy the trade-off between diversity and multiplexing gains Ref. Zheng and Tse, Diversity and Multiplexing: A Fundamental Tradeoff in Multiple Antenna Channels, IEEE TIT, May / 64
10 2. Overview of Beamforming Techniques Beamforming for point-to-point MIMO It is often known as single-user beamforming To maximize the SNR, the principle of matched filtering (MF) can be employed when CSI is available, which is known as maximal ratio transmission (MRT) scheme in the context of MIMO. There are also other approaches without CSI or partial CSI: Blind beamforming (or long-term transmit beamforming) with statistical properties of channels Semi-blind beamforming (with partial CSI) Diversity beamforming (with channel coding): compared to blind beamforming, it can achieve a diversity gain Ref. J. Choi, Diversity eigenbeamforming for coded signals, IEEE TCOM, June / 64
11 2. Overview of Beamforming Techniques 10 1 Coded D eigen Eigen 1 Optimized 10 2 BER SNR (db) Performance of blind beamforming (Eigen-1), diversity beamforming (D-eigen and Optimized) 11 / 64
12 2. Overview of Beamforming Techniques B. Multiuser MIMO There exists interference due to the presence of multiple signals to be transmitted to multiple users. Dirty paper coding (DPC) can achieve the channel capacity by suppresing known interference. However, its implementation is not easy. Multiuser beamforming can provide a reasonable performance with low-complexity. A better performance can be achieved with multiuser diversity & user selection CSI at BS is required to mitigate the (intra-cell) interference: No feedback in TDD: channel reciprocity can be used Feedback in FDD: excessive overhead Resource allocation (including power control) becomes a crucial. 12 / 64
13 2. Overview of Beamforming Techniques Capacity of multiuser MIMO Dirty paper coding: it can achieve the capacity, but difficult to implement C sum = E max P k log det(i + HPH H ) E log det(i + P total K HHH )(equal power) Multiuser diversity: it is simple, but overall throughput is low C md = E log(1 + P total max h k 2 ) k Multiuser beamforming: if user selection is combined, it its upper bound is proportional to the number of selected users (scaling law is applied): C mb E log(1 + P k h k 2 ) k U orthogonal 13 / 64
14 2. Overview of Beamforming Techniques 30 C sum (equal power) C md 25 C mbeam (approx.) Achievable Rate 60 users, 4 users are selected in multiuser downlink beamforming 14 / 64
15 2. Overview of Beamforming Techniques Conventional Multiuser Beamforming Problem (without user selection) Base station Mobile terminal Mobile terminal Mobile terminal w k : beamforming vector to user k; h k : channel vector to user k, P k = E[ s k 2 ]: TX power to user k multiuser beamforming, where s k is the signal to user k TX signal: K k=1 w ks k 15 / 64
16 2. Overview of Beamforming Techniques Multiuser joint beamforming and power control: { ˆP k, ŵ k } = arg min { k P k P q h H q w q 2 subject to k q P γ k h H q w k 2 +σq 2 q w q 2 = 1 This is an optimization problem to minimize the total transmission power subject to SINR constraints. Based on the uplink-downlink duality, this problem has been solved. 16 / 64
17 2. Overview of Beamforming Techniques C. Network (or Cooperative) MIMO Highly sophisticated systems to deal with intra-cell as well as inter-cell interference (ICI) Known techniques Cooperative transmissions (e.g., CoMP) Interference alignment Distributed nature Backhaul transmissions Interference channel models There should be the trade-off between performance and complexity (or overhead) 17 / 64
18 2. Overview of Beamforming Techniques TX RX TX RX TX RX 18 / 64
19 2. Overview of Beamforming Techniques Remarks on beamforming in network MIMO: Advantages Easy to implement Optimal solutions to most beamforming optimization problems are known (QoS can be guaranteed) Spatial multiplexing gain with reasonable performances Disadvantages Not capacity-achieving schemes Most (downlink) beamforming methods require CSI at BS. Furthermore, in network MIMO, BSs in cooperation need to share their CSI. Dilemma in FDD mode Due to limited CSI feedback, it is prohibitive to use large antenna arrays. However, with arrays of a few antenna elements, a significant performance improvement may not be achieved. 19 / 64
20 2. Overview of Beamforming Techniques D. Massive MIMO TDD mode to exploit the channel reciprocity for the CSI at BS and make use of large antenna arrays Multi-cell, but noncooperative systems Due to noncooperative transmissions, no backhaul communications between BSs are required. But, systems can suffer from ICI. Using massive antenna arrays, ICI can be mitigated. Key issues: pilot contamination, array calibration, etc. There are other advantages. One of them is that the short-term fading disappears by the law of large numbers. This makes resource allocation easy and reduces the burden of channel coding. 20 / 64
21 3. Cooperative (Network) MIMO 3. Cooperative (Network) MIMO Network MIMO is to fully exploit the spatial gain in a multi-cell system In network MIMO, intercell interference can be mitigated by cooperation between BSs through backhaul links: Ref. 1 Karakayali, et al., Network coordination for spectrally efficient communications in cellular systems, IEEE Comm. Mag., Ref. 2 Gesbert, et al., Multi-cell MIMO cooperative networks: a new look at interference, IEEE JSAC, Provided that each BS in cooperation is equipped with an antenna array, cooperative beamforming can mitigate intercell as well as intracell interference in downlink transmissions. Regardless of its implementability, it may provide performance bounds. 21 / 64
22 3. Cooperative (Network) MIMO BS BS BS BSs in cooperation need to share users data and/or CSI to their users through a backhaul network. 22 / 64
23 3. Cooperative (Network) MIMO Levels of cooperation between BSs through backhaul links: full cooperation: BSs share all CSI and signals (this is equivalent to the case of a big BS with distributed arrays or a single big cell) partial cooperation 1: BSs share all CSI, but not signals partial cooperation 2: BSs share all signals, but not CSI partial cooperation 3: each BS has its local CSI and signals (but limited information can be exchanged between BSs for such as user allocation) The cooperation would be limited by backhaul overhead. Thus, effective partial cooperation, not full cooperation, is desirable in practice. 23 / 64
24 3. Cooperative (Network) MIMO 3.1 Multicell with a common group of users 3.1 Multicell with a common group of users 1. All BSs in cooperation support a common group of users (these users would be cell-edge users). 2. The cooperation between BSs is limited (if there is no limitation, this scenario is equivalent to a single-cell). 3. Each BS has local CSI, which is the channel vectors from the BS to all users in a common group, while other BSs CSI is unknown. 4. There could be some cooperation between BSs such as user allocation. 24 / 64
25 3. Cooperative (Network) MIMO 3.1 Multicell with a common group of users ZF-DPC precoding in a multicell system Ref. Ho, et al., Decentralized precoding for multicell MIMO downlink, IEEE TWC, Assumptions: There are Q BSs in cooperation and N users per cell (there are K = QN users in total). Each BS is equipped with an antenna array of L elements. The CSI from each BS to all K users (not just N in the cell) is known by each BS, while the CSI from the other BSs to users is not known. That is, at BS q, the CSI to K users are known, but not the CSI from BS q q to K users. This partial CSI can allow block diagonalization to suppress intercell interference Within a cell, then DPC is used to suppress intracell interference 25 / 64
26 3. Cooperative (Network) MIMO 3.1 Multicell with a common group of users Key variables: H q : L K downlink channel matrix from BS q to all K users G q : L N submatrix of H q (channel vectors to users in cell q from B W q : L N beamforming matrix at BS q s q : N 1 signal vector at BS q r q : N 1 signal vector received by users in cell q n q : N 1 noise vector received by users in cell q Let H q = [G q H q ]. The received signal vector at users in cell q is given by Q r q = G H q W p s p + n q p=1 Block diagonalization to avoid intercell interference: H H qw q = / 64
27 3. Cooperative (Network) MIMO 3.1 Multicell with a common group of users For block diagonalization, orthogonal projection matrix can be used: P q = I H q ( H H q H q ) 1 H H q. The beamforming matrix can be W q = ζ q P q G q, where ζ q is the normalization factor that is given by ζ q = N P q G q F The average power per beamforming vector is unity. 27 / 64
28 3. Cooperative (Network) MIMO 3.1 Multicell with a common group of users BS1 W1 G1 H 1 user 1 H 2 BS2 user 2 W2 G2 Then, the received signal vector becomes Q r q = G H q ζ q P p G p s p + n q p=1 = ζ q G H q P q G q s q + n q. 28 / 64
29 3. Cooperative (Network) MIMO 3.1 Multicell with a common group of users Within r q, there exists intracell interference. Thus, s q has to be DPCed signals. The sum rate becomes C = Q E [ log 2 det ( I + Ω ζ q 2 Ψ q Ψ H )] q q=1 where E[n q n H q ] = I, E[s q s H q ] = ΩI, and Ψ q = G H q P q G q. 29 / 64
30 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users 3.2 Multicell with different groups of users Each BS has its own group of users. There are Q BSs and each BS has N users. Each BS is equipped with L antennas for beamforming. In this case, local CSI at BS is not sufficient to suppress the intercell interference. In order to migitate both intercell and intracell interference by beamforming, SINR could be considered. 30 / 64
31 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Key variables: H q,k : W q : s q : the L N channel matrix from BS k to the users in cell q the L N beamforming matrix the N 1 signal vector from BS q Local CSI at BS k is {H 1,k, H 2,k,..., H Q,k }. W q = [w 1;q... w N;q ] decides the transmission power if E[s q s H q ] = I, i.e., P i;q = w i;q / 64
32 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users The received signal at cell q is given by Q r q = H H q,k W ks k + n q. k=1 At user i in cell q, the received signal becomes Q N r i;q = w u;k s u;k + n i;q h H i;q,k k=1 u=1 = h H i;q,qw i;q s i;q + u i h H i;q,qw u;q s u;q } {{ } =intracell + N h H i;q,k w u;ks u;k +n i;q k q u=1 }{{} =intercell 32 / 64
33 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users The SINR becomes SINR i;q = h H i;q,q w i;q 2 u i hh i;q,q w u;q 2 + N k q u=1 hh i;q,k w u;k 2 + σi;q 2 In general, any beamforming algorithm that minimizes the SINR requires full CSI, which requires significant backhaul transmissions. Define the intercell interference at cell q as Z i;q = k q N h H i;q,k w u;k 2. u=1 Note that this interference is not a function of W q. 33 / 64
34 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Well-known multiuser beamforming problems: Maximization of SINR with power constraints max Wq SINR i;q subject to W q 2 F P q Minimization of power with SINR constraints min q W q 2 F subject to SINR i;q Γ i;q See SINR-based Joint Power Control and Beamforming to solve the above problem 34 / 64
35 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Interference leakage based approaches are also popular: Define the interference leakage from BS q to cell k as I k (W q ) = H H k,q W q 2 F. To minimize the leakage to the other cells, we can have the following constraint: I k (W q ) = tr W q H H k,q H H k,q W q I q,leak. k q k q 35 / 64
36 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Distributed optimization approaches: Forming a global optimization problem Decompose it into local optimization problems Each local optimization problem is solved at a BS and update variables through backhaul links Do iterations until a satisfactory performance is achieved Key references: Palomar and Chiang, A tutorial on decomposition methods for network utility maximization, IEEE JSAC, Chiang, et al., Layering as optimization decomposition: a mathematical theory of network architectures, Proc. IEEE, / 64
37 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Example: Dual decomposition The minimization of power with SINR constraints: where C q (W q ) = W q 2 F. Using Lagrangian multipliers, min = min Q q=1 C q(w q ) subject to SINR i;q (W q ) Γ i;q Q C q (W q ) q=1 Q q=1 ( Q q=1 i=1 N λ i;q (SINR i;q (W q ) Γ i;q ) N min C q (W q ) λ i;q (SINR i;q (W q ) Γ i;q ) W q i=1 }{{} =local optimization ) 37 / 64
38 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users At each BS, the local optimiztion is carried out as follows: Ŵ q = arg min C q (W q ) W q N λ i;q SINR i;q (W q ) i=1 At a higher level (i.e., at a central unit), the master dual problem is to update λ s: where min λ Q g q (λ) q=1 N λ i;q Γ i;q, λ 0, i=1 g q (λ) = N λ i;q SINR i;q (Ŵq) C q (Ŵq). i=1 38 / 64
39 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users To update λ s at a higher level, the following gradient method can be used: [ ( )] + λ i;q (t + 1) = λ i;q (t) α SINR i;q (Ŵq) Γ i;q, where [x] + = max{0, x} and α > 0 is the step-size. Thus, BSs need to send their SINRs to a central unit and this central unit sends λ s to BSs. This approach would have a slow convergence rate, but it does not require excessive backhaul transmissions between BSs and a central unit. 39 / 64
40 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Example Minimization interference leakage problem with SINR min Q q=1 Q k=1 I k(w q ) subject to SINR i;q (W q ) Γ i;q A direct decomposition can be considered. At each BS, min i wh i Xw i h subject to H i w i 2 Γ q i hh i wq 2 +Z i i X k q H k,qh H k,q w i w i;q h i h i;q Z i Z i;q + σi;q 2 Γ i Γ i;q 40 / 64
41 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Since the ICI Z i;q (W q ) in the SINR depends on the other beamforming matrices, an iterative algorithm is required to solve the NML beamforming problem, which consists of the following two key steps. Solving the local minimization problem (at BS q): subject to W q (l) = arg min C q (W q ) h H i;q,q w i;q 2 u i hh i;q,q wu;q 2 +Z i;q (W (l 1) q )+σi;q 2 Γ i;q updating the ICI: Z i;q (W (l) q ) = N h H i;q,k w(l) u;k 2, k q u=1 which is fed back by the users (not by other BSs) to BS q. 41 / 64
42 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Low-Dimensional Beamforming Consider the following eigendecomposition: X = k q H k,q H H k,q + αi = EΛEH, where E = [e 1... e L ] and Λ = diag(λ 1,..., λ L ). The local cost function becomes C q (W) = I k (W) = tr ( W H XW ) k q The complexity can be reduced if a subspace of E used as w i w i = Ẽ Λ 1/2 v i, where Ẽ = [e 1... e M ] and M < L. 42 / 64
43 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users With v i of size M 1, we have C q (W) N v i 2 The local optimization at BS q is carried out to minimize C q (W) through v i of size M 1. The subspace beamforming with optimized v i (not w i ) can reduce the complexity by a factor of ( L M ) 2. For highly correlated channels, this approximation may not result in a significant loss. The complexity of the eigendecomposition of X may not be significant if second order statistics are used: i=1 X E[X] = k q E[H k,q H H k,q ] + αi = EΛEH. 43 / 64
44 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Simulation Results Three different approaches are used: Approach A: The cooperative min-power beamforming with target SINR Approach B: The NML beamforming with target SINR Approach C: The noncooprative minimum total power (NMP) beamforming with the following cost function: C q (W q ) = W q 2 F, which is to reduce the transmission power rather than interference leakage (an egoistic approach). Approach A is cooperative, while Approaches B and C are noncooperative (i.e., no backhaul communications between BSs) The elements of channel matrices are independent Gaussian (no spatial correlation is considered) 44 / 64
45 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Feasibility results: The NMP beamforming (Approach C) cannot achieve target SINR, but both cooperative min-power beamforming and NML beamforming (Approaches A and B) can achieve target SINR Cooperative Noncoop. (min power) Noncoop. (min leakage) Achieved SINR (db) Target SINR (db) L = 30, Q = 3, N = 5, and M = L = / 64
46 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Approach A performs better than Approaches B and C, but requires backhaul communications between BSs Cooperative Noncoop. (min power) Noncoop. (min leakage) 60 Total transmission power (db) Target SINR (db) L = 30, Q = 3, N = 5, and M = L = / 64
47 3. Cooperative (Network) MIMO 3.2 Multicell with different groups of users Low-complexity versions of Approach B (NML): tradeoff between complexity and performance If M 20, no performance degradation is observed (note that uncorrelated channels are used in simulations) Total transmission power (db) M L = 30, Q = 3, N = 5, and Γ = 10 db 47 / 64
48 4. Massive MIMO 4. Massive MIMO Proposed by Marzetta in 2010 to effectively mitigate ICI without any cooperation between BSs A massive MIMO system consists of BSs with large antenna arrays. The number of antenna elements is about 100. Frequency reuse factor is 1 and orthogonal channels within a cell (no intra-cell interference) TDD to exploit the channel reciprocity. The channel vector, h, from a BS to a user can be factorized as h = βu, where β is a parameter for large-scale fading and u CN ( 0, 1 L I) is a random vector for small-scale fading, where L / 64
49 4. Massive MIMO Base Station Large Array narrow beam user user In each cell, each user has an orthogonal channel (i.e., no intra-cell interference) and h k,q denotes the channel vector from BS q to the user in cell k. 49 / 64
50 4. Massive MIMO For a large L, the matched-filter (MF) beamforming can be used. The beamforming vector is given by w k = h k,k h k,k. Since the received signal at the user in cell k is r k = h H k,k w ks k + q k h H k,q w qs q + n k, the SINR becomes SINR k = P k h k,k 2 q k P q h H k,q w q 2 + σk / 64
51 4. Massive MIMO ICI can be mitigated as L as the inner product of two random vectors, x = h k,k and y = h k,q, k q, approaches <x,y> L: number of antennas This is the key idea of massive MIMO. That is, without any cooperation between BSs, it is possible to mitigate ICI by increasing L (similar to CDMA). 51 / 64
52 4. Massive MIMO Approximation for a large L: h k,q 2 β k,q u H k,q w q CN (0, 1/L) P q h H k,q w q 2 +σk 2 = q k q k The approximate SINR is P q β k u H k,q w q 2 +σk 2 1 P q β k,q +σk 2 L. q k SINR k = LP k β k,k q k P qβ k,q + Lσk 2 In SINR, small-scale fading terms disappear the SINR is much less fluctuated over time. 52 / 64
53 4. Massive MIMO 4.1 Partial cooperation 4.1 Partial cooperation Since the frequency reuse factor is 1, there exists ICI although it may not be significant for a large L (as shown in the SINR expression). ICI can be further mitigated if ZF or MMSE beamforming can be used in cooperation with adjacent BSs as in network MIMO. However, it requires massive CSI exchange, which would provide a marginal gain at the expense of excessive backhaul communications. There might be a tradeoff between ICI mitigation (high ICI for a small L) performance and the backhaul overhead (a large overhead for a large L) in the case of cooperation. 53 / 64
54 4. Massive MIMO 4.1 Partial cooperation In order to improve the performance further, partial cooperation can be considered. Not exchange the CSI of fast-fading, but the CSI of slow-fading, which is β k for large-scale fading. Then, the joint power control is carried out to minimize the total power of BSs in cooperation with SINR constraints. This partial cooperation can guarantee target SINR in massive MIMO. 54 / 64
55 4. Massive MIMO 4.1 Partial cooperation average/minimum SINR (db) Average SINR (equal power) Average SINR (opt. power) Minimum SINR (equal power) Minimum SINR (opt. power) target SINR (db) Arrays of L = 100 elements, 3-cell, 4 users per cell 55 / 64
56 4. Massive MIMO 4.2 Pilot contamination in massive MIMO 4.2 Pilot contamination in massive MIMO A main issue of massive MIMO is pilot contamination. As the coherence time is limited and the number of users per cell can be large, the same set of orthogonal pilot sequences can be used in all cells, which results in interference from adjacent cell during the uplink training. The estimated uplink channel can be contaminated by the interference and the performance of beamforming can be degraded. This problem is called the pilot contamination. To mitigate this problem, we can take into account interfering pilot signals from adjacent cells in estimating uplink channels; adjust precoding vectors to reduce the interference. 56 / 64
57 4. Massive MIMO 4.2 Pilot contamination in massive MIMO Two-cell example (TDD: channel reciprocity) Assume that MRT precoding vectors are used from estimated channels. 57 / 64
58 4. Massive MIMO 4.3 Pilot contamination precoding 4.3 Pilot contamination precoding For a large L, statistical precoding can be used to mitigate the intercell interference resulting from pilot contamination. This scheme is called the pilot contamination precoding (PCP). Assume that there are K cells. The estimated channel vector at the BS in cell k is ĥ k = K h q,k + n k. q=1 The MF beamforming vector is used as: ĥk w k = ĥk. 58 / 64
59 4. Massive MIMO 4.3 Pilot contamination precoding Received signal at the user in cell k: x k = = K h H k,q w qs q + v k q=1 K q=1 s q ˆα q K h H k,q h t,q + v k, t=1 where ˆα k = ĥk. Since h k,q = β k,q u k,q and u k,q are iid, we have Thus, as L, we have K x k = u H k,q u t,q δ k,q as L w.p. 1 q=1 s q ˆα q β k,q + v k. 59 / 64
60 4. Massive MIMO 4.3 Pilot contamination precoding Staking x k s: x = [x 1... x K ] T [ ] βk,q = [s 1... s K ] T + [v 1... v K ] T α q = As + v, where [A] k,q = β k,q α q. To avoid the interference, s can be replaced with s Bs, where B = A 1. This means that the BSs need to exchange the channel information (elements in A) for precoding. The resulting received signal is x = s + v. 60 / 64
61 4. Massive MIMO 4.3 Pilot contamination precoding Since each BS needs to estimate β k,q and ˆα q = ĥq, which are related to slow fading coefficients only, their estimation can be done precisely, and their exchange through a backhaul network may not result in a heavy overhead. Note that the transmission power depends on B = A 1. DPC or VP technique can help reduce the total transmission power when precoding is used. 61 / 64
62 4. Massive MIMO 4.3 Pilot contamination precoding Improvement by partial cooperation against pilot contamination without PCP with PCP 62 / 64
63 As a remedy, partial cooperation could be considered. 63 / 64 Precoding and Massive MIMO 5. Conclusions 5. Conclusions Beamforming is a simple and effective means to increase SNR or coverage, which can be employed in more complicated systems as follows: Network MIMO Cooperation between BSs with not too big arrays More controls (for better performance) Backhaul overhead for cooperation might be a critical issue Distributed optimization will play a key role in reducing backhaul overhead Massive MIMO Noncooperation, each BS with a big array might be robust enough against ICI Less controls (for implementation) There exists ICI, and due to it, there is difficulty to guarantee certain performance in terms of SINR.
64 5. Conclusions Network MIMO versus Massive MIMO: Network MIMO is to reduce cooperation (full to partial cooperation) Massive MIMO is to introduce cooperation (no cooperation to partial cooperation) In the end, network MIMO meets massive MIMO. 64 / 64
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