Partial Preamble Transmission in NB-IoT

• Partial Preamble Transmission (PPT) is a method that divides NB-IoT preambles into multiple shorter Partial Preamble Sequences (PPS) to balance collision probability with detection performance.
• PPT reduces preamble collisions and expands contention opportunities by controlling the repetition count, thereby optimizing ARP success under varying device loads.
• Analytical modeling of PPT supports parameter optimization based on system load, SNR, and false alarm targets, enabling robust performance without major hardware changes.

Partial Preamble Transmission (PPT) is a contention resolution and detection strategy introduced in NB-IoT random access protocols to expand contention opportunities and reduce preamble collisions. The mechanism punctures each full preamble into multiple, shorter partial units—Partial Preamble Sequences (PPS)—in order to provide a trade-off between collision probability and mis-detection probability by controlling the number and length of repetitions transmitted. The PPT mechanism is designed to maximize Access Reservation Protocol (ARP) success under varying system load, with analytical guarantees provided for its performance in terms of false alarm, mis-detection, and collision probabilities (Kim et al., 2017).

1. NB-IoT Access Reservation and Motivation for PPT

The ARP in NB-IoT systems is a contention-based protocol where each device initiates access by selecting one of $N_\mathrm{P}$ orthogonal preamble sequences and transmitting it over the Narrowband Physical Random Access Channel (NPRACH). ARP performance is challenged by:

• Frequent preamble collisions at high device density, reducing the probability that a random access attempt will succeed.
• Stringent coverage requirements, which mandate long repetition of preambles, lowering the probability of mis-detection but aggravating contention.

PPT is introduced to directly address these challenges. Each conventional preamble sequence is divided into $G$ non-overlapping PPS, and devices transmit a randomly selected PPS rather than the full preamble. This construction effectively multiplies the number of available contention resources, at the cost of reduced detection gain due to shorter sequence length.

2. Preamble Structure and PPT Transmission Procedure

The baseline preamble consists of:

• Symbol group: One cyclic prefix (CP) and $\xi$ data symbols.
• A set of $\nu$ symbol groups making a basic unit, repeated $M_b = 2^{q_b}$ times, for a full preamble of length $L_b = \nu M_b$.
• Each symbol group hops over one of 48 subcarriers according to a predetermined hopping pattern $\Omega(i)$.

In the PPT configuration:

• The repetition count is shortened to $M_p=2^{q_p}\le M_b$ per PPS, so $L_p = \nu M_p$.
• The full preamble is divided into $G = M_b / M_p$ PPS (partial units).
• Each device randomly selects a preamble index $G$0 and a partial unit and transmits only the corresponding PPS of length $G$1.

At the eNodeB:

• Correlation and energy accumulation are performed independently over each PPS-sized window, totaling $G$2 detection events per preamble.
• A detection threshold $G$3 is applied, and a Random Access Response (RAR) message, containing both the preamble and partial-unit index, is sent for each detected access.

3. Analytical Performance Modeling

A flat Rayleigh block-fading channel model is considered, with open-loop power control providing an average received power $G$4 per symbol and noise variance $G$5.

Received Power Characterization

• For $G$6 devices transmitting on a PPS, the normalized received power is

$G$7

Key Error Probabilities

• False alarm ($G$8):

$G$9

where $\xi$0 denotes the cumulative distribution function (CDF) of the gamma distribution.

• Mis-detection ($\xi$1):

$\xi$2

where $\xi$3 and $\xi$4.

• Collision ($\xi$5):

$\xi$6

• ARP success ($\xi$7):

$\xi$8

4. Trade-offs and Parameter Optimization

PPT introduces a controllable trade-off governed by $\xi$9:

• Reducing $\nu$0: Increases the number of PPS slots $\nu$1, thus reducing $\nu$2 (collision probability) but raising $\nu$3 (mis-detection) due to shorter PPS lengths and reduced energy accumulation.
• Increasing $\nu$4: Lowers $\nu$5 (better detection) but decreases $\nu$6, making collisions more likely.

The optimal repetition count $\nu$7 is computed by solving:

$\nu$8

subject to $\nu$9, for given expected device number $M_b = 2^{q_b}$0, power $M_b = 2^{q_b}$1, and a target false-alarm level $M_b = 2^{q_b}$2. The search is typically performed numerically.

Selected performance results are summarized in the table below for sample system settings found in Table III (Kim et al., 2017):

$M_b = 2^{q_b}$3	SNR	Baseline $M_b = 2^{q_b}$4 (%)	$M_b = 2^{q_b}$5	PPT $M_b = 2^{q_b}$6 (%)
5	–5 dB	70.6	8	94.5
10	–10 dB	45.7	16	72.3

At higher loads, PPT yields notable gains, more than doubling ARP success probability by reducing contention, with only a modest increase in detection failures.

5. Implementation Considerations and System Compatibility

PPT is implemented without modification to the NB-IoT NPRACH physical layer waveform or subcarrier hopping scheme. The eNodeB adapts detection to treat a full NPRACH preamble period as $M_b = 2^{q_b}$7 partial detection windows. Only minor protocol enhancements are required:

• RAR messages are extended to encode the identified partial-unit index.
• The computational cost of slot-wise correlation is multiplied by $M_b = 2^{q_b}$8 due to the increased number of windows, but each detection uses shorter sequences ($M_b = 2^{q_b}$9), keeping per-event cost constant.
• All NB-IoT coverage classes, each corresponding to different $L_b = \nu M_b$0, are supported by selecting $L_b = \nu M_b$1.

PPT may require slightly increased UE transmit power per PPS to counteract the diversity loss from shorter lengths. This change is directly accommodated within existing NB-IoT power control mechanisms.

6. Deployment Guidelines and Operational Insights

The key operational principle underlying PPT is the balanced exploitation of contention resource expansion (reducing collision probability) against the detection gain of longer preambles (reducing mis-detection):

• Light system load: Full-length preambles ($L_b = \nu M_b$2) are preferred to minimize mis-detections.
• High system load: Shorter repetitions ($L_b = \nu M_b$3 lower, $L_b = \nu M_b$4 higher) are recommended to expand the contention space and reduce collisions; select $L_b = \nu M_b$5 via offline numerical optimization based on expected $L_b = \nu M_b$6 and SNR.
• Detection thresholds $L_b = \nu M_b$7 should be adapted to maintain a target false-alarm probability across different $L_b = \nu M_b$8.

PPT is fully compatible with 3GPP NB-IoT standards and requires only minor enhancements at both the eNodeB and UE. Following these guidelines enables significant gains in ARP success rates in dense NB-IoT scenarios, supporting robust large-scale device access without hardware changes (Kim et al., 2017).