Simple Semi-Grant-Free Transmission Strategies Assisted by Non-Orthogonal Multiple Access

• SGF combines grant-based admission for one user with opportunistic grant-free admission for other users on the same channel.This arrangement allows grant-free users to share channels reserved by grant-based users.Source: §I · p. 2
• Two SGF mechanisms retain base-station control of access while using less signaling overhead than conventional grant-based transmission.The mechanisms aim to control how many users share a channel and limit grant-free interference to grant-based users.Source: §I · p. 3
• In open-loop SGF, the base station broadcasts a threshold and a qualification criterion, but the admitted user count remains random and may exceed channel capacity.The scheme does not require the base station to know users’ channel state information before transmission.Source: §I · p. 3
• Distributed contention control grants access to a fixed number of users with favorable channel conditions, with its contention criterion adapted to the SIC order.Unlike the open-loop approach, this mechanism ensures a fixed admitted-user count.Source: §I · pp. 3–4
• The open-loop threshold and user qualification criterion are designed for the selected SIC order; the grant-based user's decoding stage determines which grant-free channel conditions are suitable.Weak grant-free users are preferred when the grant-based signal is decoded first, while strong grant-free users are preferred when it is decoded last.Source: §I · pp. 3–4
• With the grant-based signal decoded first, SGF suits a near-base-station grant-based user and cell-edge grant-free users; decoding it last suits the reverse user placement.The paper reports analytical results comparing the suitability of the two SIC orders across these network scenarios.Source: §I · p. 4

II. SYSTEM MODEL

• A high-priority user U0 receives a dedicated resource block, while M grant-free users compete opportunistically to share it.The scenario combines grant-based and grant-free access on the same channel.Source: §II · p. 4

A. Assumptions for SGF Protocol Design

• The protocols admit grant-free users only when U0’s target rate can still be achieved with high probability.A sufficient number of orthogonal preambles is assumed for the base station to acquire transmitting grant-free users’ CSI for multi-user detection.Source: A. Assumptions for SGF Protocol Design · p. 5
• The design assumes quasi-static i.i.d. Rayleigh fading, known CSI at each user, and error-free sharing of U0’s CSI and transmit power.The base station does not acquire grant-free users’ CSI, reducing signalling overhead.Source: A. Assumptions for SGF Protocol Design · pp. 4–5

1) Open-loop contention control:

• Open-loop control broadcasts a channel-quality threshold, and users decide whether to join by comparing their channel gains with it.The admission direction depends on the SIC decoding order.Source: 1) Open-loop contention control · p. 5

2) Distributed contention control:

• Distributed control can select the strongest or weakest channel user through channel-dependent backoff times and beacon transmission.A user’s backoff is strictly decreasing or increasing with channel gain, so the best or worst channel waits least and identifies itself first.Source: 2) Distributed contention control · p. 5

III. SEMI-GRANT-FREE PROTOCOL - TYPE I

• Type I places U0’s message in the first SIC decoding stage, and its open-loop analysis gives a closed-form outage expression for U0.The expression is for the proposed open-loop Type I SGF protocol.Source: §III · p. 6, A. Open-Loop Contention Control · pp. 6–7

A. Open-Loop Contention Control

• With fixed grant-free-user SNR and τ∼1/P0 as P0→∞, Type I’s outage penalty tends to zero while SGF can connect more users than grant-based access.The paper identifies this as a scenario where the grant-based user is close to the base station and grant-free users are at the cell edge.Source: A. Open-Loop Contention Control · p. 7
• With fixed τ and grant-free-user SNR as P0 grows, the outage gap also approaches zero, but outage is worse than with τ∼1/P0 while more grant-free users can be supported..Source: A. Open-Loop Contention Control · p. 8

3) Impact of SGF transmission on grant-free users:

• Adapting a grant-free user’s rate according to the protocol requires access to other users’ CSI, obtainable through beacon-based distributed contention control.If that CSI is unavailable, the cited outage probability can be viewed as a lower bound.Source: 3) Impact of SGF transmission on… · p. 9
• The analysis treats the selected channel gain as an order statistic among N users and accounts for its dependence on the other selected users’ gains.The channel gain is the i-th smallest among N i.i.d. variables, and its density is obtained using order statistics.Source: 3) Impact of SGF transmission on… · p. 9
• The outage probability can be evaluated numerically, but a closed-form expression is difficult because the calculation contains a step function..Source: 3) Impact of SGF transmission on… · p. 10

B. Distributed Contention Control

• The method admits only users whose channel gains are below τ to contend, with a fixed number of qualified users considered in the analysis..Source: B. Distributed Contention Control · pp. 10–11
• As M grows, the outage-probability difference between admitting and not admitting a grant-free user approaches zero, helping preserve U0’s performance even with many grant-free users.Distributed contention control has higher system overhead than the open-loop scheme.Source: B. Distributed Contention Control · p. 11
• The selected grant-free user has an outage probability, and the analysis identifies an error floor for that probability.The error-floor discussion distinguishes the effects of increasing U0’s transmit power from increasing grant-free-user power.Source: B. Distributed Contention Control · pp. 12–13
• When the target SNR is at least τ, the selected grant-free user’s target rate cannot be met..Source: B. Distributed Contention Control · p. 12

IV. SEMI-GRANT-FREE PROTOCOL - TYPE II

• Type II assumes that U0’s message is decoded in the last stage of SIC..Source: §IV · p. 13
• The section introduces the corresponding design of two proposed SGF transmission schemes..Source: §IV · p. 13
• The two schemes’ designs are described in the following two subsections..Source: §IV · p. 13

A. Open-Loop Contention Control

• U0's outage depends on successful decoding of the grant-free users because U0's message is decoded last in the SIC sequence.Theorem 2 gives a closed-form outage expression for U0 under open-loop Type II SGF.Source: A. Open-Loop Contention Control · pp. 13–14
• For fixed P0 and τ, the outage-probability difference between admitting and not admitting grant-free users approaches zero as grant-free transmit power increases.This differs from Type I, where the difference approaches zero as P0 increases while grant-free transmit power is fixed.Source: A. Open-Loop Contention Control · p. 15
• Type II is suited to a cell-edge grant-based user and nearby grant-free users, supporting massive connectivity while strictly guaranteeing the grant-based user's QoS.This is the small-P0, large-grant-free-power uplink scenario described in the paper.Source: A. Open-Loop Contention Control · p. 15
• Increasing τ can reduce the stated outage probability to zero.The passage contrasts this threshold adjustment with reducing τ in the preceding case.Source: A. Open-Loop Contention Control · p. 15

2) Impact of SGF transmission on grant-free users:

• The analysis assumes N selected grant-free users and evaluates each user's probability of successfully sending L bits within B0.Each user is assumed to adapt its transmit data rate.Source: 2) Impact of SGF transmission on… · p. 15
• The resulting probability is harder to evaluate than (11) because it involves three random variables.The passage points to computer simulations in Section V for performance analysis.Source: 2) Impact of SGF transmission on… · p. 16

B. Distributed Contention Control

• Only grant-free users with channel gains above the broadcast threshold participate in distributed contention control.The analysis conditions on N users exceeding that threshold.Source: B. Distributed Contention Control · pp. 16–17
• Type II selects the strongest grant-free user, unlike Type I, which selects the weakest.The outage probability is formulated for the strongest selected user.Source: B. Distributed Contention Control · p. 16
• Unlike Type I's distributed-control error floor, Type II's selected-user outage approaches zero as grant-free transmit power grows, even when τ approaches zero and all grant-free users contend.The result is stated for fixed P0 and τ as grant-free transmit power grows, with the τ→0 case also noted.Source: B. Distributed Contention Control · pp. 17–18

V. NUMERICAL STUDIES

• With low grant-free transmit power, SGF's impact on U0 is insignificant; at high power, reducing τ can keep its outage similar to grant-based performance, while unrestricted grant-free transmission performs worst.The analytical results match simulations.Source: §V · p. 18, Figure 1 · p. 19
• Type I grant-free users exhibit transmission-error floors, which are lower for smaller user indices because those users experience less interference from earlier-decoded users.The figure studies N = 5 selected users.Source: §V · pp. 18–19, Figure 2 · p. 19
• At large M, Type I distributed contention control keeps U0 near grant-based performance while scheduling fewer grant-free users than open-loop control; grant-free transmission performs worst.For M = 1, the two contention-control protocols coincide.Source: §V · pp. 19–20, Figure 3 · p. 20
• The Type I distributed-control grant-free-user outage floor can be reduced by increasing N or lowering users' rate requirements.The passage attributes the floor to an SINR that becomes constant as both transmit powers approach infinity.Source: Figure 4 · p. 20, §V · pp. 20–21
• Type II open-loop SGF gives U0 the same outage performance as grant-based transmission, while the grant-free scheme performs worst and the SGF-to-grant-based gap narrows as grant-free power increases.The SGF outage has an error floor bounded below by the grant-based user's outage probability.Source: Figure 5 · p. 21, §V · pp. 21–22
• As M increases, Type II open-loop control admits more grant-free users but has worse outage performance than distributed control; both match grant-based performance for large grant-free power.The mechanisms coincide when there is only one grant-free user.Source: Figure 6 · p. 21, §V · p. 22
• Type II distributed control's selected grant-free-user outage approaches zero as grant-free transmit power grows.The simulations confirm this behavior.Source: Figure 7 · p. 22, §V · p. 22

VI. CONCLUSIONS

• The proposed SGF arrangement grants one user access through a grant-based protocol and admits other users to the same channel through grant-free access.The paper frames this as a combination of grant-based and grant-free protocols on a shared channel.Source: §VI · p. 23
• Two contention-control mechanisms regulate how many grant-free users share a grant-based user's channel, addressing the risk that excessive admissions cause multi-user detection failure.The paper provides analytical results and asymptotic analysis of the proposed schemes and SIC decoding orders.Source: §VI · p. 23
• Type I SGF schemes suit a nearby grant-based user sharing with cell-edge grant-free users, while Type II suits a cell-edge grant-based user with nearby grant-free users.The paper assumes each user knows its CSI perfectly and identifies the impact of imperfect CSI as future research.Source: §VI · p. 23

APPENDIX A

• Appendix A obtains P(N = n) using order statistics and treats the sum of the n smallest channel gains as a sum of n i.i.d. variables.The channel gains in that sum are below the threshold τ.Source: Appendix A · pp. 23–24
• The derivation obtains the density of the transformed channel gains through Laplace transforms and inverse transformation, then verifies a property of the resulting density in a lemma.Source: Appendix A · p. 24
• Appendix A simplifies Q1 using the incomplete Gamma function and series expansions, then applies the result to obtain the outage probability of U0.Source: Appendix A · pp. 25–26

APPENDIX B

• Appendix B proves the density lemma by rewriting the density and treating y ≥ nτ separately, with the simplification stated for l < n.Source: Appendix B · p. 27

APPENDIX C

• Appendix C starts by expressing P(N = n) for its derivation.Source: Appendix C · p. 27
• Appendix C derives the density of y_n from the n largest order statistics, alternatively treating y_n as a sum of n i.i.d. gains conditioned to be at least τ.Source: Appendix C · p. 28
• Appendix C calculates Q3 and substitutes its result to obtain a closed-form expression for PII,OL_0.Source: Appendix C · pp. 28–29