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Soft Pilot Reuse and Multi-Cell Block Diagonalization Precoding for Massive MIMO Systems

Xudong Zhu, Zhaocheng Wang, Chen Qian, Linglong Dai, Jinhui Chen, Sheng Chen, Lajos Hanzo

arXiv:1507.04213v1cs.ITmath.IT

TL;DR

Pilot contamination from adjacent-cell pilot reuse limits channel estimates and achievable performance in multi-cell massive MIMO. The paper combines soft pilot reuse with multi-cell block-diagonalization precoding to address edge-user contamination and interference. Its analysis and simulations report significantly improved edge-user uplink and downlink rates, with a slight center-user rate cost.

  • Problem

    Adjacent-cell pilot reuse causes pilot contamination, while downlink inter-cell interference also limits multi-cell massive MIMO performance.

    Source: §I · p. 1, §III · p. 4

  • Method

    The approach separates center and edge users, reuses center pilots across cells, assigns edge pilots to adjacent-cell edge users, and projects downlink signals into the null space of their inter-cell channels.

    Source: §I · p. 2

  • Results

    Both edge-user uplink and downlink rates improve significantly, and simulated average cell throughput approaches or exceeds the conventional system when a modest BS-antenna increase is affordable.

    Source: §I · p. 2

  • Takeaways & Limitations

    SPR slightly reduces the uplink rate of center users because of pilot overhead, alongside the reported edge-user gains.

    Source: §I · p. 2, B. Uplink Transmission · p. 7

Abstract

from arXiv · show

The users at cell edge of a massive multiple-input multiple-output (MIMO) system suffer from severe pilot contamination, which leads to poor quality of service (QoS). In order to enhance the QoS for these edge users, soft pilot reuse (SPR) combined with multi-cell block diagonalization (MBD) precoding are proposed. Specifically, the users are divided into two groups according to their large-scale fading coefficients, referred to as the center users, who only suffer from modest pilot contamination and the edge users, who suffer from severe pilot contamination. Based on this distinction, the SPR scheme is proposed for improving the QoS for the edge users, whereby a cell-center pilot group is reused for all cell-center users in all cells, while a cell-edge pilot group is applied for the edge users in the adjacent cells. By extending the classical block diagonalization precoding to a multi-cell scenario, the MBD precoding scheme projects the downlink transmit signal onto the null space of the subspace spanned by the inter-cell channels of the edge users in adjacent cells. Thus, the inter-cell interference contaminating the edge users' signals in the adjacent cells can be efficiently mitigated and hence the QoS of these edge users can be further enhanced. Our theoretical analysis and simulation results demonstrate that both the uplink and downlink rates of the edge users are significantly improved, albeit at the cost of the slightly decreased rate of center users.

I. INTRODUCTION

The introduction targets pilot contamination and downlink inter-cell interference by separating users according to contamination severity and pairing soft pilot reuse with multi-cell precoding. The system model uses TDD reciprocity to obtain downlink channel estimates.

I. INTRODUCTION

  • Pilot reuse in adjacent cells contaminates channel estimates, while commonly used matched-filter and zero-forcing precoding impose downlink inter-cell interference that more BS antennas cannot reduce.Existing mitigation approaches also incur costs such as additional spectral resources or feedback and information-exchange overhead.Source: §I · p. 1
  • The proposal distinguishes center users with modest pilot contamination from edge users with more severe contamination, directing QoS efforts toward the latter.The grouping is based on users’ large-scale fading coefficients.Source: §I · p. 2
  • SPR reuses center pilots across cells and assigns an edge pilot group to edge users in adjacent cells, improving edge-channel estimation and uplink rate.The BS can also estimate adjacent-cell edge channels using slightly more pilot resources.Source: §I · p. 2
  • MBD projects downlink signals into the null space of partially known adjacent-cell edge channels to mitigate inter-cell interference.This extends classical block diagonalization to a multi-cell scenario.Source: §I · p. 2
  • Both edge-user uplink and downlink rates improve significantly; simulated average cell throughput approaches or exceeds the conventional system when a modest increase in BS antennas is affordable.The analysis also reports a slightly increased pilot requirement.Source: §I · p. 2

II. SYSTEM MODEL

  • The system model has L cells, each with an M-antenna BS serving K single-antenna users, and assumes TDD reciprocity for sufficiently narrow bandwidth.Channels include independent Gaussian small-scale fading and user-dependent large-scale fading coefficients.Source: §II · pp. 2–3

III. PILOT CONTAMINATION

Reusing pilot sequences across adjacent cells contaminates channel estimates, limiting uplink rates and leaving downlink interference that does not vanish with more BS antennas. The section describes how this contamination arises during the TDD protocol.

III. PILOT CONTAMINATION

  • Each coherence interval has four stages: uplink data, uplink pilots, BS processing, and downlink data.The BS estimates its channel matrix by correlating the received pilot matrix with its local pilot matrix.Source: §III · p. 3
  • Reused pilots make a user’s channel estimate a linear combination of channels from users in other cells sharing that sequence, which is pilot contamination.Pilots are orthogonal within a cell but typically reused in adjacent cells because orthogonal sequences are limited.Source: §III · p. 3
  • The uplink achievable rate remains limited by pilot contamination and cannot be increased simply by raising data or pilot transmission power.The section derives the uplink SINR and rate after channel estimation and matched-filter detection.Source: §III · pp. 3–4
  • Pilot contamination limits downlink performance because reuse-induced interference cannot be reduced by increasing the number of BS antennas.The downlink discussion derives SINR and achievable rate under matched-filter precoding.Source: §III · p. 4

IV. MOTIVATION OF OUR PROPOSAL

Because users experience different levels of pilot contamination, the paper divides each cell’s users into center and edge groups. The proposed division uses locally available large-scale fading coefficients, while accurately assessing contamination from other cells is difficult without cooperation.

IV. MOTIVATION OF OUR PROPOSAL

  • Users differ in pilot-contamination severity because their large-scale fading coefficients—and thus attainable SINR—vary within each cell.The paper distinguishes center users with modest contamination from edge users with severe contamination.Source: §IV · p. 4
  • Accurately estimating other-cell large-scale fading coefficients is difficult for a base station without cooperation, which can require substantial side-information overhead.The paper notes that a base station can readily obtain its own-cell coefficients, unlike those from other cells.Source: §IV · p. 4
  • The proposed division uses a configurable threshold on users’ large-scale fading coefficients, not their geographic locations, to distinguish center from edge users.Center users are associated with slight pilot contamination; edge users are subjected to severe contamination and are expected to perform poorly under the conventional scheme.Source: §IV · p. 4

V. THE PROPOSED SOFT PILOT-REUSE SCHEME AND MULTI-CELL BLOCK DIAGONALIZATION PRECODING

The proposed approach pairs soft pilot reuse (SPR) with multi-cell block diagonalization (MBD) to improve service for edge users. SPR reuses center pilots across cells while assigning orthogonal pilot subgroups to adjacent-cell edge users, at a modest increase in pilot resources.

A. Proposed Soft Pilot Reuse Scheme

  • SPR assigns orthogonal pilot subgroups to edge users in adjacent cells while reusing a center pilot group across cells.This separates the edge-user pilot assignments while retaining reuse for center users.Source: A. Proposed Soft Pilot Reuse Scheme · p. 5
  • Users are divided by large-scale fading coefficients into center and edge groups, with respective counts K_i,c and K_i,e.The threshold is adjustable for the system configuration.Source: A. Proposed Soft Pilot Reuse Scheme · p. 5
  • SPR uses K_c = max_i K_i,c center pilots and K_e = Σ_i K_i,e edge pilots, with L cooperating cells and a moderate L assumed.Center pilots are reused across cells, whereas edge pilots are dedicated to edge users in adjacent cells.Source: A. Proposed Soft Pilot Reuse Scheme · p. 5
  • In the three-cell example, SPR requires 8 pilot sequences versus 6 for conventional reuse and 15 for complete pilot orthogonality.The passage reports that SPR uses slightly more pilot resources than the conventional scheme while improving edge-user QoS.Source: A. Proposed Soft Pilot Reuse Scheme · p. 5

B. Channel Estimation Based on Soft Pilot Reuse

SPR enables cleaner channel estimates for edge users and gives base stations partial inter-cell channel information for adjacent-cell edge users. These estimates support more accurate uplink detection and provide channel information for downlink precoding.

B. Channel Estimation Based on Soft Pilot Reuse

  • SPR lets a base station estimate its edge users’ channels without pilot contamination because edge-user pilots are orthogonal.The scheme also provides partial knowledge of adjacent-cell edge-user inter-cell channels, a dominant source of interference to those users during downlink transmission.Source: B. Channel Estimation Based on Soft… · p. 5
  • Center users continue to reuse the center pilot group, with only minor pilot contamination in their channel estimates.The passage contrasts this with the orthogonal pilot assignment used for edge users.Source: B. Channel Estimation Based on Soft… · pp. 5–6
  • SPR substantially improves edge-user channel-estimation accuracy over the conventional scheme, enabling a significantly increased uplink achievable rate.The passage attributes the cleaner estimate to elimination of pilot contamination for edge users.Source: B. Channel Estimation Based on Soft… · p. 6
  • A base station can estimate partial inter-cell channels from adjacent-cell edge users without pilot contamination using their orthogonal edge pilots.These estimates can become arbitrarily accurate as the number of base-station antennas increases.Source: B. Channel Estimation Based on Soft… · p. 6

C. Multi-Cell Block Diagonalization Precoding

MBD extends block diagonalization across cells by projecting downlink signals into the null space of adjacent-cell edge-user channels, thereby mitigating inter-cell interference. The scheme uses estimated partial inter-cell channels and relies on the base station having many more antennas than edge users.

C. Multi-Cell Block Diagonalization Precoding

VI. PERFORMANCE ANALYSIS

The performance analysis examines pilot-resource requirements, derives uplink and downlink achievable rates, and considers computational complexity.

VI. PERFORMANCE ANALYSIS

  • The analysis first considers the amount of pilot resources required by the proposed schemes.Source: §VI · p. 7
  • It then derives achievable rates for both uplink and downlink transmission.Source: §VI · p. 7
  • The analysis also considers the computational complexity imposed by the schemes.Source: §VI · p. 7

A. Pilot Resource Consumption

Soft pilot reuse trades additional pilot resources for improved edge-user performance, with the threshold controlling the number of users classified as edge users. In uplink transmission, edge-user pilot contamination is eliminated, while center-user rates are slightly reduced.

A. Pilot Resource Consumption

  • Eliminating pilot contamination by using orthogonal pilots for all users would require more sequences and substantially reduce spectral efficiency.Source: A. Pilot Resource Consumption · p. 7
  • The additional SPR pilot sequences are close in number to the total edge users, and threshold λ flexibly adjusts that edge-user count.The orthogonal-pilot extreme uses KOS sequences, while the conventional-reuse extreme uses KCS sequences.Source: A. Pilot Resource Consumption · p. 7

B. Uplink Transmission

  • SPR uplink SINR for center users is almost the same as under conventional reuse, but their achievable rate is slightly reduced by pilot overhead.Source: B. Uplink Transmission · p. 7
  • For edge users, uplink SINR increases with the number of base-station antennas and tends to infinity asymptotically, eliminating pilot contamination and significantly improving achievable rate.The paper also states that ZF detection outperforms MF detection.Source: B. Uplink Transmission · p. 8

C. Downlink Transmission

MBD projects downlink transmissions to mitigate interference affecting edge users. The analysis reports improved edge-user downlink rates at the cost of slightly reduced center-user rates.

C. Downlink Transmission

  • The MBD precoding matrix projects downlink transmission into a null space so adjacent-cell edge-user channels receive no inter-cell signal from the projected transmission.Source: C. Downlink Transmission · p. 8
  • For edge users, the proposed scheme eliminates pilot contamination in downlink transmission and reduces both inter-cell and intra-cell interference.The reported edge-user SINR increases with the number of base-station antennas and tends to infinity asymptotically.Source: C. Downlink Transmission · p. 8
  • Edge users’ downlink rates are significantly improved, while center users’ rates are slightly reduced when the extra pilot resource is included.Source: C. Downlink Transmission · p. 8

D. Computational Complexity

The MBD implementation’s stated complexity is comparable to the conventional scheme and within the computational capability of a typical state-of-the-art base station.

D. Computational Complexity

  • The complexity analysis identifies SVD and matrix pseudo-inverse operations as the two main contributions.The passage associates the pseudo-inverse with generating the ZF-based MBD precoding matrix using the Gram–Schmidt algorithm.Source: D. Computational Complexity · p. 9
  • The SVD contribution is quantified in terms of complex-valued multiplications, but its stated order is incomplete in the supplied passage.The accompanying pseudo-inverse complexity expression is likewise incomplete.Source: D. Computational Complexity · p. 9
  • The MBD scheme’s total computational complexity is comparable to the conventional scheme and within the capability of a typical state-of-the-art BS.The complexity accounting includes SVD and matrix pseudo-inverse operations.Source: D. Computational Complexity · p. 9

VII. SIMULATION STUDY

Simulations compare conventional reuse with SPR and, for downlink, SPR combined with MBD. SPR improves edge-user channel estimation and rates, while its pilot overhead can reduce center-user rates; MBD further improves downlink edge-user performance and cell throughput at sufficiently large antenna counts.

Simulation setup

  • Users are classified by a threshold ρ_i associated with λ, not by distance from the serving BS.The simulation uses randomly generated user positions in a hexagonal cellular network.Source: §VII · p. 9

Channel estimation

  • SPR significantly improves edge-user channel-estimation accuracy by using orthogonal pilots in adjacent cells; center-user accuracy remains similarly excellent.Increasing λ classifies more users as edge users.Source: §VII · pp. 9–10

Uplink SINR

  • With M = 128 and λ = 0.1, SPR yields significantly higher UL SINR for edge users, while center-user SINR remains similar to conventional reuse.ZF is about 2 dB better than MF for both center and edge users.Source: §VII · p. 10, Figure 8 · p. 10

Uplink achievable rate

  • SPR significantly improves edge-user UL achievable rates, while center-user rates decrease because of increased pilot overhead.The ZF detector outperforms MF by about 0.3 bps/Hz per user.Source: §VII · p. 10, Figure 9 · p. 10

Uplink cell throughput

  • For λ ≤ 0.2, SPR improves edge-user performance while preserving cell throughput; for λ > 0.5, excessive pilot overhead outweighs its gain.ZF provides about 5 bps/Hz more average cell throughput than MF.Source: §VII · pp. 10–11, Figure 10 · p. 10
  • At M = 32, SPR’s average UL cell throughput is about 5 bps/Hz below conventional reuse with MF; at M = 256, it approaches conventional throughput.The throughput reduction at lower antenna counts reflects the increased pilot overhead; the ZF–MF gap shrinks as M increases.Source: §VII · p. 11, Figure 11 · p. 11

Downlink achievable rate

  • With M = 128 and λ = 0.1, MBD significantly improves edge-user DL achievable rates, while center-user rates decrease slightly.ZFMBD gains about 0.4 bps/Hz over MFMBD for edge users.Source: §VII · p. 11

Downlink throughput

  • At M = 256, SPR with MBD achieves the best average DL cell throughput among the three systems, while SPR alone approaches conventional throughput.At M = 32, the SPR-and-MBD system performs worst; as M increases further, its throughput gap over conventional grows.Source: §VII · p. 11, Figure 13 · p. 11

VIII. CONCLUSIONS

The paper combines SPR and MBD to improve edge-user rates in LS-MIMO systems. Simulations and analysis report gains in both uplink and downlink, with average cell throughput only slightly reduced by SPR and further improved in downlink by MBD.

VIII. CONCLUSIONS

  • SPR and MBD significantly enhance edge-user achievable rates in both uplink and downlink.SPR separates center and edge users and assigns adjacent-cell edge users orthogonal pilots, reducing their pilot contamination; MBD extends block diagonalization to mitigate downlink inter-cell interference.Source: §VIII · p. 11, Figure 12 · p. 12
  • SPR requires slightly more pilot sequences and can slightly reduce average cell throughput relative to the conventional system.The conclusion describes the average uplink and downlink throughput reduction as slight and negligible.Source: §VIII · p. 11
  • MBD further improves edge-user downlink performance and average downlink cell throughput beyond the gain from SPR.The BS can estimate adjacent-cell edge-user channels with SPR without the detrimental effects of pilot contamination.Source: §VIII · p. 11
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