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Directional Cell Discovery in Millimeter Wave Cellular Networks

C. Nicolas Barati, S. Amir Hosseini, Sundeep Rangan, Pei Liu, Thanasis Korakis, Shivendra S. Panwar, Theodore S. Rappaport

arXiv:1404.5068v3cs.IT

TL;DR

The paper addresses the difficulty of mmWave initial cell search, where directional transmission requires discovering both a base station and suitable spatial directions. It proposes periodic synchronization-signal transmission with GLRT-based detectors and evaluates alternative transmission and receiver architectures. Simulations show advantages for digital over analog beamforming and for omnidirectional over randomly scanned synchronization transmissions.

  • Problem

    Directional mmWave transmission complicates initial cell search because mobiles must detect both base stations and the spatial angles of arriving signals.

  • Method

    The paper models periodic PSS transmission using omnidirectional or randomly varying directions and derives GLRT detectors for analog and digital receiver beamforming.

  • Results

    Omnidirectional synchronization transmission generally outperforms random directional scanning, while digital beamforming exceeds analog beamforming by more than 20 dB in SNR for PMD = 0.01.

  • Takeaways & Limitations

    For mmWave cell search, constant-power omnidirectional synchronization and digital receiver processing are favored within the evaluated designs.

Abstract

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The acute disparity between increasing bandwidth demand and available spectrum, has brought millimeter wave (mmW) bands to the forefront of candidate solutions for the next-generation cellular networks. Highly directional transmissions are essential for cellular communication in these frequencies to compensate for high isotropic path loss. This reliance on directional beamforming, however, complicates initial cell search since the mobile and base station must jointly search over a potentially large angular directional space to locate a suitable path to initiate communication. To address this problem, this paper proposes a directional cell discovery procedure where base stations periodically transmit synchronization signals, potentially in time-varying random directions, to scan the angular space. Detectors for these signals are derived based on a Generalized Likelihood Ratio Test (GLRT) under various signal and receiver assumptions. The detectors are then simulated under realistic design parameters and channels based on actual experimental measurements at 28~GHz in New York City. The study reveals two key findings: (i) digital beamforming can significantly outperform analog beamforming even when the digital beamforming uses very low quantization to compensate for the additional power requirements; and (ii) omni-directional transmissions of the synchronization signals from the base station generally outperforms random directional scanning.

I. INTRODUCTION

Millimeter-wave systems offer abundant spectrum and potential beamforming gains, but directional transmission makes initial cell search difficult because mobiles must discover both base stations and transmission directions. The paper proposes periodic PSS-based directional discovery and compares omnidirectional and random directional transmission with analog and digital receiver beamforming.

  • Motivation: mmWave bands offer up to 200 times more spectrum than current cellular allocations, while high isotropic path loss challenges signal range.Dense antenna arrays can provide beamforming gains that theoretically compensate for the increased path loss.
  • Motivation: Directional transmission complicates initial cell search because mobiles must detect both base stations and the spatial angles of arriving synchronization signals.Without exploiting antenna gain during discovery, mobiles may reach high-data-rate regions yet remain unable to locate the base station.
  • Detection and receiver architectures: The study derives GLRT detectors for directional cell discovery under analog and digital mobile beamforming assumptions.Digital receivers access samples from all antenna elements, whereas analog receivers inspect one or a small number of directions at a time.
  • Results: Omnidirectional synchronization transmissions provide significant detection-time advantages over randomly varying base-station directions under GLRT detection.After detection, additional procedures are still required to estimate and track transmit and receive directions for directional communication.
  • Results: Digital beamforming can outperform analog beamforming substantially; in the reported 4×4 mobile-array simulations, the loss from analog beamforming reaches 18 dB.The paper reports that low-bit-rate digital front ends incur minimal synchronization-detection loss from quantization noise.
  • Proposed procedure: The proposed procedure periodically transmits PSS synchronization signals, either omnidirectionally or in randomly varying directions that scan the angular space.The PSS is sent once every Tper seconds during a brief interval of length Tsig.

III. PSS DETECTOR

The paper models periodic PSS detection as a delay-indexed binary hypothesis test and derives GLRT detectors from received multi-antenna signals under explicit channel assumptions. For digital reception, the GLRT reduces to matched filtering followed by spatial aggregation through the largest singular value.

  • Signal model: PSS sub-signals are transmitted periodically across indexed time slots, with each transmit waveform shaped by a beamforming vector.The k-th slot contains sub-signals indexed by J_k, while omnidirectional transmission uses a constant transmit vector.
  • Signal model: The detector assumes locally flat channels and derives a single-path rank-one model with fixed transmit and receive spatial signatures during detection.Simulations later consider higher-rank multipath channels despite the rank-one assumption used for detector derivation.
  • Digital GLRT: For each delay τ in [0, Tper], the receiver tests whether a PSS is present using H1 versus absent using H0.Because the PSS is periodic, only delay hypotheses within one PSS period need to be tested.
  • Digital GLRT: The GLRT maximizes likelihoods over unknown spatial direction, noise power, and complex sub-signal gains before comparing the resulting ratio with a threshold.The implementation avoids adding frequency offset as a GLRT parameter and instead repeats testing over discretized frequency hypotheses.
  • Digital GLRT: The digital detector correlates each sub-signal across receive vectors, forms V(τ), and uses its largest singular value to identify energy in the most likely spatial direction.A maximum singular vector can be computed, for example, with a power method, making the added processing potentially feasible.

C. GLRT for Analog Beamforming

For analog reception, the mobile selects one receive beam per PSS time slot and observes only the resulting scalar signal. The corresponding GLRT becomes a noncoherent energy detector over matched-filter outputs from the sub-signals.

  • Analog signal model: Analog reception selects a receive beamforming vector for each PSS time slot and applies it before observing the scalar output.The same receive and transmit beamforming gains are used for all sub-signals within a slot because analog hardware supports one beam direction at a time.
  • Analog signal model: The analog hypothesis model contains unknown noise variance and effective channel gains after transmit and receive beamforming.These parameters form the unknown vector used by the analog GLRT.
  • Analog GLRT: The analog detector applies a GLRT to the beamformed observations for each delay hypothesis using a thresholded correlation statistic.The beamformed observation set Z_τ is defined analogously to the digital observation set.
  • Analog GLRT: The resulting analog GLRT noncoherently adds matched-filter energy from the L sub-signals.The same detector can also support hybrid beamforming when outputs from multiple streams are treated as separate measurements.

IV. SIMULATION

The simulations evaluate analog, digital, and hybrid detectors using single-path and measured New York City multipath channels, with realistic antenna arrays and false-alarm thresholding. The figures compare misdetection against data SNR while varying transmission strategy and search time.

  • Simulation setup: Random-direction transmission selects horizontal and elevation angles randomly, requiring random antenna-element phases rather than random magnitudes.This implements the directional scanning case evaluated against omnidirectional transmission.
  • Thresholding: False-alarm thresholds account for signal, delay, and frequency-offset hypotheses, with delay hypotheses computed at twice the PSS bandwidth.The threshold procedure targets the maximum false-alarm rate per search period across all tested hypotheses.
  • Fig. 3: Fig. 3 plots misdetection probability against data SNR for omnidirectional and random-direction PSS transmission, comparing analog, digital, and 3-bit quantized digital reception.The red reference marks the target SNR for Rtgt = 10 Mbps.
  • Fig. 4: Fig. 4 plots misdetection probability against data SNR for omnidirectional transmission while increasing search time at fixed 2% overhead.The figure is intended to show the effect of longer search-time combining relative to the Rtgt = 10 Mbps target.

A. Detection Performance with Single Path Omnidirectional Transmissions

Under omnidirectional synchronization transmissions, digital beamforming substantially improves detection over analog beamforming, while analog operation requires higher SNR or additional search resources. Results are plotted against data SNR to relate detection performance to target-rate requirements.

  • Detection comparison: More than 20 dB separates digital and analog beamforming at PMD = 0.01 because digital processing determines spatial direction across sub-signals.Analog beamforming can look in only one direction at a time.
  • SNR interpretation: The simulations detect PSS at PSS SNR but plot misdetection against data SNR, the theoretical full-bandwidth SNR with optimal beamforming.This makes detection results interpretable relative to data-rate requirements.
  • Rate-target interpretation: At Rtgt=10 Mbps, Wtot = 1 GHz, and β = (0.5)(0.8), digital beamforming reliably detects the signal at the target data SNR.Analog beamforming requires a significantly larger SNR for the same rate target.
  • SNR interpretation: For a fixed data-SNR requirement, larger beamforming gain lowers the required PSS SNR; the simulations use Gtx,max = 64 and Grx,max = 16.In a single-path channel, beamforming gain equals the number of antennas.
  • Design implications: With 256 rather than 64 base-station antennas, data SNR must increase by 6 dB to maintain the same misdetection rate.Compensation requires longer detection times or more overhead.
  • Design implications: Non-coherent combining improves analog detection, but diminishing returns and delay overhead make longer searches costly.Increasing synchronization-signal frequency instead trades fixed search time for additional overhead.

B. Detection Performance with a Single Path Channel and Randomly Varying Transmission Angles

Randomly varying directional synchronization transmissions can miss the mobile, degrading detection relative to omnidirectional transmission. Digital beamforming substantially outperforms analog beamforming, while low-rate quantization can preserve digital performance with modest power consumption.

  • Directional transmission: 11 dB and 5 dB: directional PSS transmission degrades detector performance in analog and digital beamforming, respectively.Random beams often miss the UE, whereas omnidirectional transmission provides constant weak received power.
  • Directional transmission: Omnidirectional synchronization transmission generally outperforms randomly scanning angles, although realistic BS downtilt may reduce the relative benefit.The conclusion holds across other parameter settings, but the cited antenna pattern can narrow the advantage.
  • Multipath channels: 4 dB: multipath improves analog detector performance over a single-path channel, while digital performance gains are small.Multipath creates more opportunities to discover synchronization signals when analog beamforming searches one direction at a time.
  • Quantization effects: Less than 0.2 dB: three-bit quantization creates a small effective-SNR gap under the simulation assumptions.The low loss is attributed to already-low SNR at the target rate.
  • Quantization effects: 15 mW: a 16-ADC, three-bit digital beamforming architecture is estimated to require this power.The paper presents low-rate digital beamforming as a way to retain cell-search performance advantages over analog beamforming.
  • Hybrid beamforming: Hybrid beamforming performs between analog and digital beamforming because it offers more directional-search opportunities than analog but fewer than digital beamforming.The trade-off can reduce search time while using fewer digital streams than a fully digital architecture.

APPENDIX A DERIVATION OF THE GLRT FOR DIGITAL BEAMFORMING

The digital-beamforming appendix rewrites the GLRT in a finite-dimensional signal-space representation. By minimizing the likelihood expressions over unknown parameters, it shows that the GLRT is equivalent to a correlation test.

  • Signal-space representation: The derivation represents received signals and noise in finite-dimensional spaces for each PSS time slot.Matrices R_k and D_k contain coefficients of the received and noise signals in orthonormal signal bases.
  • Likelihood formulation: The digital GLRT is formulated from likelihoods under H0 and H1 with unknown noise, channel, and spatial-signature parameters.The likelihood factors across independent PSS time slots, and the received coefficients are modeled as complex Gaussian variables.
  • GLRT optimization: Orthogonality of the PSS subsignals simplifies the minimization over their coefficients and reduces the H1 optimization to a matrix singular-value problem.The minimum over the spatial parameter is given by the maximum singular value.
  • GLRT reduction: The resulting likelihood-ratio statistic is threshold-equivalent to a test based on the statistic T.The appendix obtains this form by substituting the minimized H0 and H1 expressions into the GLRT.
  • Correlation-test equivalence: The signal-space statistic equals the normalized correlation statistic because orthonormal coordinates preserve energy and inner products.This identifies the matrix V used in the derivation with the normalized received-signal correlations.

APPENDIX B DERIVATION OF THE GLRT FOR ANALOG BEAMFORMING

The analog-beamforming appendix derives a finite-dimensional GLRT for beamformed PSS observations. Its likelihood minimizations likewise reduce the detector to a correlation threshold test.

  • Signal-space representation: The analog derivation represents each delayed beamformed PSS signal, noise signal, and subsignal in a finite-dimensional signal space.The data across all time slots are collected into the matrix R.
  • Likelihood formulation: The analog GLRT is expressed through likelihoods for the received data under H0 and H1 with unknown noise and channel-gain parameters.The likelihood ratio factors over time slots because the noise vectors are independent.
  • GLRT optimization: Orthogonality of the PSS subsignals simplifies the coefficient minimization and supports the subsequent minimizations over noise variance and channel-related quantities.The appendix evaluates the two hypotheses separately before combining their minimized expressions.
  • GLRT reduction: The resulting analog likelihood ratio is threshold-equivalent to a test based on a statistic T.The equivalence follows because the likelihood ratio is an increasing function of T.
  • Correlation-test equivalence: The derived statistic is the correlation threshold test used for analog beamforming.The appendix identifies the statistic from the finite-dimensional derivation with T(τ).

APPENDIX C SIMULATION PARAMETER SELECTION DETAILS

The appendix specifies synchronization-signal, false-alarm, antenna, and initial-access search parameters used in the simulations.

  • Signal parameters: The simulations use Nsig = 4 narrow-band synchronization sub-signals, with Tsig = 100 µs for the PSS interval.The choice balances frequency diversity and coherent combining.
  • Signal parameters: 2% is the synchronization-signal overhead under the selected parameters, and any Tper greater than 5 ms keeps overhead below 2%.Overhead is defined as Tsig/Tper.
  • False alarm target: The initial-access simulations target at most 0.01 false alarm per search period, distributing this target across delay hypotheses.The per-delay constraint is PF A ≤ RF A/(Nhyp).
  • False alarm target: For initial access, the delay search uses Ndly = 10^4 hypotheses, based on twice the signal bandwidth over a 5 ms period.The calculation uses Ndly = 2WsigTper.
  • Antenna pattern: The antenna model uses 8 × 8 elements at the base station and 4 × 4 elements at the receiver, with λ/2 element spacing.These two-dimensional arrays were considered for small-cell urban deployments.

APPENDIX D QUANTIZATION EFFECTS

The appendix models quantization as additive noise and examines how quantizer resolution affects effective SNR and coding gain.

  • Signal model: The signal model defines r[n] = x[n] + w[n], with Es and N0 denoting signal and noise energy per sample.The corresponding SNR is derived from these signal and noise energies.
  • Quantization model: The quantized signal is modeled as the original signal plus uncorrelated quantization noise whose variance depends on relative quantization error α.The scalar quantizer is applied independently to each sample.
  • Quantizer resolution: The relative quantization error varies with bit count, quantizer levels, and the input distribution.Table II evaluates α for a scalar uniform quantizer using Gaussian input and an optimized step size.
  • Practical considerations: In practice, imperfect A/D signal-level matching may require a few more bits than the optimized scalar-quantizer values indicate.The tabulated values assume an optimized step size.
  • PSS detection: The PSS SNR is derived from received power P, noise spectral density N0, and the Nsig sub-signals, each with bandwidth Wsig.The derivation first obtains energy per orthogonal sample and then the resulting SNR.
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