A Large-Scale MIMO Precoding Algorithm Based on Iterative Interference Alignment

Transcription

1 BUGARAN ACADEMY OF SCENCES CYBERNETCS AND NFORMATON TECNOOGES Volume 14, No 3 Sofia 014 Print SSN: ; Online SSN: DO: 10478/cait A arge-scale MMO Precoding Algorithm Based on terative nterference Alignment Jing Jiang, Wei v Xi an University of Posts & Telecommunications, Xi an, CO China s: ianging18@gmailcom longeiba3000@sinacom Abstract: The performance of arge-scale MMO system is degraded by Pilot Contamination n order to reduce Pilot Contamination, a donlink precoding algorithm is put forard, based on nterference Alignment (A) The main idea of this algorithm is aligning the pilot contamination and inter-cell interference to the same null space in order to acquire the maximal degrees of freedom Then the donlink receiving precoding matrix is solved ith respect to a maximal SNR (Signal nterference Noise Ratio) criterion Exploiting the channel reciprocity and an iterative process, Base station and User Equipment sitch transmitting and receiving roles in the uplink and donlink, the precoding matrices of the Base station and User Equipment is gradually updated until convergence Finally, the simulation results have shon that the algorithm proposed can efficiently mitigate the impact of pilot contamination and outperform some popular precoding algorithms, eg, MF precoding algorithm and MMSE precoding algorithm When the number of antennas increases, the performance of the proposed algorithm ill be greatly improved Keyords: Massive MMO, large-scale MMO, precoding, pilot contamination, interference alignment 1 ntroduction arge-scale MMO or Massive MMO is an emerging research topic of the fifth generation broadband ireless systems, hich scales up MMO to possible orders of magnitude compared to current systems [1] Antenna arrays ith hundreds of antenna elements provide enormous large-scale array gains and interference suppression gains [-3] But the performance gain of the arge-scale MMO relies on good enough channel knoledge of the donlink and uplink channel 61

2 n the current system, the transmitter transmits pilots, and then the receiver estimates the channel impulse responses from the received pilots and feedbacks the channel information to the transmitter n the arge-scale MMO system, the amount of channel information is greatly increased ith antennas increasing, the channel state information needs vast physical resources to feedback To avoid mass feedback overhead, arge-scale MMO system calculates the donlink precoding matrix, utilizing the channel reciprocity in a TDD orking mode n it the user equipment transmits the uplink pilots, the base station estimates the uplink channel information and calculates the precoding matrix, based on the estimated uplink channel information instead of the donlink channel information feedback This scheme reduces the signaling overhead and simplifies the feedback process, but the channel estimation of the local cell may be interfered by non-orthogonal uplink pilots of adacent cells in an undesirable manner and result in inaccurate calculating of the donlink precoding matrix The performance of the arge-scale MMO is evenly degraded due to the impact of Pilot Contamination caused by the uplink interference from non-orthogonal pilots of other cells [4-5] Thus the key issue for a arge-scale MMO system is ho to reduce the pilot contamination [6-10] The authors in [6] considered that the uplink channel estimation as contaminated by non-orthogonal pilots from different cells and analyzed the performance degradation caused by the pilot contamination A multicell MMSE precoding as proposed to mitigate the pilot contamination hich minimized the interference from uplink pilots of other cells Reference [7] studied the effects of shifting the time location of pilots in neighboring cells and proved that it could obtain a better channel estimation because of the inter-cell interference reduction [8] considered a donlink Pilot Contamination Precoding (PCP) designing in the finite antenna regime t formulated the donlink PCP design as a source optimization problem to maximize the minimum SNR among all users subect to netork sum poer constraints The simulation results shoed that in a practical scenario, the proposed optimal and suboptimal PCP give very large gains over conventional SASs ith 100 transmitting antennas n [9] Pilot Contamination Precoding (PCP) is designed, in hich each base station linearly combines slo-fading coefficients beteen the terminals and the base stations to a slo-fading coefficients matrix The precoding matrix is the product of the slofading coefficients matrix and a ell knon single-cell precoding matrix t can achieve the capacity loer bound of PCP hich can efficiently eliminate the intercell interference in arge-scale MMO systems n [10] appropriate poer allocation algorithms are proposed under the circumstance of avoiding simultaneous non-orthogonal transmissions from adacent cells The techniques proposed are especially beneficial to users in unfavorable locations that ould otherise suffer of lo SNR nterference Alignment (A) is a promising technique to efficiently mitigate interference and achieve the maximum spatial degrees of freedom in ireless communication systems [11-14] n [11] the authors have proved that linear schemes of interference alignment sufficed to achieve all the degrees of freedom and deduced the basic principles of interference alignments in conditions of multi- 6

3 cell and single-user in every cell n [1] examples of iterative algorithms that utilized the reciprocity of ireless channel to achieve interference alignment ith only local channel knoledge at each node are provided The algorithm can acquire the minimal leakage of transmitting signals and the maximum degree of freedom of desired receiving signals The numerical results proved that this algorithm could achieve theoretically optimal performance To efficiently mitigate multi-cell interferences, a simple coordinated Zero-Forcing (ZF) scheme as proposed in [13] t reduced both C (nter Carrier nterference) and U (nter Users nterference) simultaneously and achieved the optimal Degrees of Freedom (DoF) in the multiple-input single-output interfering broadcast channels Since this scheme considered a user ith a single antenna, it only designed the transmitting beam forming vectors n [14] the authors have developed an nterference Alignment (A) technique for a donlink cellular system The proposed scheme could be implemented ith minimal changes to an existing cellular system here the feedback mechanism (ithin a cell) is already being considered for supporting multi-user MMO Moreover, it could provide a substantial gain especially hen the interference from a dominant interferer is significantly stronger than the remaining interference n this paper the interference alignment ill be applied to arge-scale MMO for the first time Based on the basic theory of interference alignment [1], the goal is designing the receiving precoding matrix to minimize pilot contamination in addition to the interferences from other cells, meanhile maximizing the degrees of space freedom for the desired receiving signals Then exploiting the channel reciprocity, the transmitter and receiver iteratively sitch roles to solve the receiving precoding matrix until the precoding matrices are updated to convergence t is theoretically proved that the maximal SNR in the donlink is equal to achieving a maximal SNR in the uplink Another idea of this paper is to replace the estimated channel and the pilot contamination channel as the true channel in the solving process, so that it can more efficiently mitigate the impact of pilot contamination on arge-scale MMO precoding Numerical results have proved that the proposed algorithm could outperform some of the popular techniques, eg, MF algorithm and multi-cell MMSE precoding algorithm System model n arge-scale MMO system, cells compose the cellular netork, each cell consists of a base station ith M antennas and K users ith N receiving antennas To analyze the pilot contamination, it is assumed that there are cells reused by the same pilots n addition, OFDM symbol t and subcarriers ω of the uplink training resource ill all be assigned to user k of per cell As previously mentioned, arge-scale MMO system orks in TDD mode The reciprocity for uplink and donlink exists, ie,, is the conugate transpose of matrix The donlink channel is equal to the transposition of uplink channel training in the coherence time 63

4 As shon in Fig 1, the receiving signal y of the base station of cell for OFDM symbol t and subcarriers ω is (1) y pτ x + pτ x + pτ x + n, r r l r i i i 1, i l l 64 Fig 1 Uplink system model of arge-scale MMO here p r is the transmitting poer of base station and τ is the length of pilot sequence; of dimension M N is the channel matrix from user k of cell to the base station of cell ; β h and β are indicated as real coefficients of the large scale fading and shado fading hich are assumed to be constant and knon to all base stations; h of dimension M N is the fast fading channel matrix hose elements are independent and identically distributed (iid) ith CN(0, 1); x denotes the training pilots transmitted by the k-th user of cells; x i denotes pilots used by cell i and orthogonal ith x hich can be indicated as xx i δi, δ i denotes the zero matrix; n is the additive hite Gaussian noise of cell hose elements are independent and n CN(0,1) From (1) the S (east Square) estimate ˆ of the channel, given y is () ˆ y x p τ + + n, r l nx M here n, n CN(0, ) t is shon in equation () that the estimated p p rτ rτ channel ˆ contains the desired channel, the pilot pollution channel l and the additive hite noise ' n f the donlink precoding directly applies the estimated channel ˆ to calculate precoding vectors, it ould greatly degrade the performance gains of arge-scale MMO by inaccurate precoding

5 3 A large-scale MMO precoding algorithm by interference alignment nterference Alignment (A) mitigates the impact of interference by aligning multiple interference signals in a signal subspace ith a dimension smaller than the number of interferers The transmitting precoding and the receiving precoding is solved in this algorithm v is the transmitting precoding matrix of user k of cell For the donlink OFDM symbol t+ Δ t and subcarrier ω, the received signal y of the user k of cell can be ritten as (3) y v x + v x + n, i i i i 1, i here: the first item vx is the desired signal from the base station of cell to the user k of cell, the second item lvlx l is the interference signal from adacent cells to the user k of cell l; l is the N M channel matrix from the base station of cell l to user k of cell l, each element of the matrix is independent and identically distributed ith CN(0, 1); n is the additive hite Gaussian noise vector ith zero mean unit variance per entry The user k of cell decodes the desired signals coming from their corresponding base station by multiplying the receiving precoding matrix u and the signal at user k of cell after the receiver combining is given by (4) %y u y u v x u v x u n + i i i + i 1, i According to the interference alignment theory, in (4), rank(u v ) is the rank of the matrix of desired signals and considered as the spatial freedom degree of desired signals, rank u lvi is the rank of the matrix of the interference i 1, i signal from adacent cells and considered as an interference signal space There rank() denotes the rank of the matrix For the receiving signal in (4), the ideal interference alignment requires that the interference signals and desired signals must satisfy the folloing conditions: (5) rank u v l i 0 i, i 1, i (6) rank( u v) d Considering that there is alays some interference in the actual situation of a ireless netork, (5) and (6) are difficult to be met in general n order to maximize the system capacity and minimize the interference, the actual scene to achieve interference alignment must satisfy the folloing conditions in the donlink: 65

6 (7) 66 i i i 1, i u v min[rank( u v )] i, max[rank ] n the same ay, the uplink interference alignment requirements of the interference signal and useful signal space satisfies the folloing conditions: (9) min rank( u lvl) l, (10) rank( u v ) (8) ( ) d According to the reciprocity of the channel, if the receiver aligns the desired signal to the space hich can achieve the maximal space freedom and the least interference at the corresponding transmitter, the transmitting signal acquires similar gains in the same space [1] n the system model (4), the donlink SNR of user k in cell is expressed as follos: u v SNR (11) 1+ u ivi i 1, i Formula (11) takes into account only the adacent cell interference to user k, not considering the impact of the pilot contamination on the performance of the system n a real system, e only acquire the estimated channel matrix ˆ n the previous analysis, the estimated channel state information contains the desired channel information and the pilot pollution from other reused pilot cells as denoted in () To evaluate the impact of pilot contamination, the desired channel information can be reritten as follos: (1) ˆ n After the donlink channel l is replaced by ( n ), ˆ l the poer of the desired signals is calculated by the folloing expression: ( ˆ u v u n ) v (13) here ˆ u v l u v + u lv + r ˆ, p τ is the poer of the desired signal, u l v is the poer of the channel pollution in the donlink because the estimated channel state information is polluted by uplink reused pilots So SNR in (11) is reritten as

7 follos: (14) Since (15) SNR 1+ + u v u ivi u lv i 1, i VV M, SNR 1+ + u u i u l i 1, i According to (15), the receiving precoding matrix u must achieve the maximal gain of desired signals, but also minimize the poer of pilot pollution and the interference poer The total interference at the receiver due to all undesired transmitters and pilot contamination from other non-orthogonal pilot cells, are given by (16) Tr[ u B u ], ( ) Tr denotes the trace of the matrix, here (17) B + l i l 1, i i 1, i l B is the interference and pilot contamination covariance at user k of cell The obective function is designing a receiving precoding matrix u to reduce the pilot contamination and interference So the unit matrix SNR is given by ( B) v u ( B) v (18) ( l + i ) v l 1, i i 1, i l ( + ) v l i l 1, i i 1, i l, u that maximizes N M emma 1 f x, y C are to independent matrices ith distribution CN (0,c N M), then (referring to [9]) x y x x (19) lim 0 and lim c M M M M M According to emma1, (1) is reritten as follos: 67

8 (0) u ˆ ( β ln + β in) ( l n ) v l 1, i i 1, i l ( ) ( ˆ β ln + β in l n ) v l 1, i i 1, i l As to the reciprocity netork, the uplink receiving precoding vectors sitch to the donlink transmitting precoding vectors: v u ; similarly the donlink receiving precoding vectors sitch to the uplink: v uthis iterative process is accomplished by the sitching process of donlink and uplink Finally, hen the iterative results meet the convergence, e meet the requirements of the precoding matrices of interference alignment 4 Numerical results n this section, the algorithm proposed (referred to as an terative A algorithm) is evaluated by the performance gain ith different numbers of antennas (from 0 up to 60 antennas) The simulation parameters are shon in Table 1 t is assumed that there are 3 cells in a arge-scale MMO system We consider the performance evaluation ith severe pilot contamination and ithout pilot contamination n the situation ith severe pilot contamination, Cell 1 and cell use the same pilot sequences, orthogonal ith cell 3 The large scale fading coefficient of cell 1 is β 1 0, the large scale fading coefficient of cell is β 0, and the large scale fading coefficient of cell 3 is β 3 0 n the situation ithout pilot contamination, the three cells respectively use orthogonal pilot sequences, so that there does not exist pilot contamination among the three cells t as compared ith a matched-filter algorithm (refer to []) and multi-cell MMSE precoding (refer to [8]) The matched-filter algorithm used at the base station in the -th cell is given by v /, and the multi-cell MMSE precoding matrix is calculated based on formula () in [8] Table 1 Simulation parameters Simulation parameters Multi-cell arge-scale fading coefficient Antennas configuration Transmission poer Uplink 10 db, r Channel model Modulation and coding scheme Channel estimation Simulation frames Values Three cells ith severe pilot contamination; ithout pilot contamination Base station: UA (Uniform inear Array), spacing 05λ UE 4 antenna UA, Antenna spacing 4λ p Donlink p 0 db Complex Gaussian channel Adaptive modulation and coding S channel estimation 5000 Frames f 68

9 We simulate the donlink spectrum efficiency of MF, Multi-cell MMSE precoding and terative A algorithm ith different numbers of antenn (Fig ) Without pilot contamination, the performance of the proposed algorithm is close to Multi-cell MMSE precoding The performance of MF algorithm is orse than the above algorithms because it cannot handle the donlink interference to the users of the other to cells n Fig a, the spectrum efficiency of multi-cell MMSE precoding algorithm and terative A algorithm is almost % higher than MF algorithm, hen the number of antennas is 40 With severe pilot contamination, it is obvious that multi-cell MMSE precoding and terative A algorithm is better than MF algorithm ith the pilot contamination reducing The performance of MF precoding remains almost unchanged ith the number of antennas increasing t is more obvious in Fig b because MF precoding is influenced by the severe pilot contamination The simulation trend is consistent ith the references, that the performance of a arge-scale MMO is limited by the pilot contamination [-6] 8 8 Spectrum Efficiency bps/z Single-cell MF 4 Multi-cell MMSE terative nterference allignment M a Spectrum Efficiency bps/z Single-cell MF Multi-cell MMSE terative nterference allignment M Fig Simulation results of a arge-scale MMO precoding algorithm: ithout pilot contamination (a); ith severe pilot contamination (b) n Fig a, the spectrum efficiency of the multi-cell MMSE precoding algorithm is 50 % higher than MF algorithm, and terative A algorithm is 65 % higher than MF algorithm t as proved that the precoding algorithm reducing pilot contamination could acquire about 15 times performance gain than the single-cell MF algorithm in case of severe pilot contamination Moreover, the terative A can leak the least interference and achieve the biggest space freedom degrees and acquire about 10 % performance gains compared to multi-cell MMSE precoding b 5 Conclusions n this algorithm, nterference alignment is firstly applied for reducing the pilot contamination of a arge-scale MMO system The goal of the proposed algorithm is aligning the pilot contamination and inter-cell interference to the same null space in order to acquire the maximal gains in the channel of desired signals Through several iterations in donlink and uplink transmission, the receiving and 69

10 transmitting precoding vectors are continually optimized based on A criterion The simulation results sho significant performance gains compared to popular MF algorithm Moreover, the proposed algorithm improves the performance of the arge-scale MMO system approximately linearly ith the increase of the number of antennas Acknoledgment: This paper is sponsored by the National Natural Science Foundation of China ( ) and the Natural Science Foundation of Shanxi Province (014JM830) R e f e r e n c e s 1 M a r z e t t a, T Noncooperative Cellular Wireless ith Unlimited Numbers of Base Station Antennas EEE Transactions on Wireless Communications, Vol 9, 010, No 11, R u s e k, F, D P e r s s o n, B u o n K i o n g a u Scaling Up MMO: Opportunities and Challenges ith Very arge Arrays EEE Signal Processing Magazine, Vol 30, 013, No 1, i e n, Q u o c N g o, E G a r s s o n, T M a r z e t t Energy and Spectral Efficiency of Very arge Multiuser MMO Systems EEE Transactions on Communications, Vol 61, 013, No 4, J o s e, J, A A s h i k h m i n, T M a r z e t t a Pilot Contamination and Precoding in Multi-Cell TDD Systems EEE Transactions on Wireless Communications, Vol 10, 011, No 8, i e n, Q u o c N g o, E G a r s s o n, T M a r z e t t Analysis of the Pilot Contamination Effect in Very arge Multicell Multiuser MMO Systems for Physical Channel Models n: Proc of EEE nternational Conference on Acoustics, Speech and Signal Processing, 011, J o s e, J, A A s h i k h m i n, T M a r z e t t a Pilot Contamination Problem in Multi-Cell TDD Systems n: Proc of EEE nternational Symposium on nformation Theory, 009, A p p a i a h, K, A A s h i k h m i n, T M a r z e t t a Pilot Contamination Reduction in Multi- User TDD Systems n: Proc of EEE nternational Conference on Communications, 010, iangbin, i, A Ashikhmin, T Marzetta Pilot Contamination Precoding for nterference Reduction in arge-scale Antenna Systems n: Proc of 51st Annual Allerton Conference on Communication, Control and Computing, 013, A s h i k h m i n, A, T M a r z e t t a Pilot Contamination Precoding in Multi-Cell arge-scale Antenna Systems n: Proc of 01 EEE nternational Symposium on nformation Theory, 01, F e r n a n d e s, F, A A s h i k h m i n, T M a r z e t t a nter-cell nterference in Noncooperative TDD arge-scale Antenna Systems EEE Journal on Communications, Vol 31, 013, No, C a d a m b e, V R, S A J a f a r nterference Alignment and Degrees of Freedom of the K User nterference Channel EEE Transaction on nformation Theory, Vol 54, 008, No 8, Gomadam, K, V R Cadambe, S A Jafar A Distributed Numerical Approach to nterference Alignment and Applications to Wireless nterference Netorks EEE Transactions on nformation Theory, Vol 57, 008, No 6, S e o k- a n, P a r k, n k y e e e Degrees of Freedom and Sum Rate Maximization for To Mutually nterfering Broadcast Channels n: Proc of EEE nternational Conference on Communications, 009, C h a n g h o, S u h, M o, D T s e Donlink nterference Alignment Proc of EEE Transactions on Communications, Vol 59, 011, No 9,