Op Optimal Joint Partitioning and Lice censi sing of Sp Spect ctrum Bands s in in Tie iered d Spe pectr trum um Access unde under Stochas hastic tic Mar arket t Mo Model els Alhussein Abouzeid Professor, Electrical Computer and Systems Engineering Rensselaer Polytechnic Institute Joint work with Mr. Gourav Saha, PhD Candidate, RPI, NY, USA
Motivation CBRS Model § CBRS band is 150 MHZ band 150 MHz Spectrum Band § Spectrum sharing with 3-Tiers of priority. Divided into 15 channels each of 10 MHz − Tier-1: Federal users 7 PAL channels 8 channels for GAA users − Tier-2: PAL users (licensed channel access) − Tier-3: GAA users (opportunistic channel Decreasing Priority Federal Users Federal Users access) PAL users GAA users § Par titioned into 15 , 10 MHz channel. − 7 PAL channels; primarily for PAL users. GAA users − 8 reserved channels only for GAA users. Does partitioning the CBRS Band in 15 channels and allocating 7 channels for PAL licenses maximize spectrum utilization? 2
Related work Optimal Licensing Optimal Partitioning § [9] : Effect of the ratio between licensed and § [4] : Maximizing spatial density of unlicensed channel for CBRS band on market transmission subject to a fixed link competition in presence of Environmental transmission rate and packet error rate. Sensing Capability operators. § Works similar to licensed and unlicensed § [5] : Game theoretic approach towards band: partitioning of bandwidth in presence of - [10] : macro cells and small cells. guard bands. - [12] : long-term leasing market and short- term rental - [13] : 4G cellular and Super Wifi services Our work: joint partitioning and licensing problem in tiered spectrum sharing 3
Channel Model Generalized Channel Model § A spectrum band 𝑋 𝑁𝐼𝑨 𝑋 MHz Spectrum Band § Partitioned into 𝑁 , ! " MHz channels. Divided into M channels of uniform bandwidth − 𝑄 licensed channels → PAL channels P licensed channels M-P unlicensed channels − 𝑁 − 𝑄 unlicensed channels → Channels reserved for GAA users Decreasing Priority Tier-2 operators Tier-1 operators § Tier-1 operators → PAL users Tier-2 operators − Leases licensed channels. − Allocated through auctions. § Tier-2 operators → GAA users − Uses unlicensed channels opportunistically. − Uses a licensed channel opportunistically if a Tier-1 operator is not using the channel. − Allocation algorithm should be fair. 4
Channel Model § 𝑋 𝑁𝐼𝑨 bandwidth can serve a maximum of 𝐸 units Generalized Channel Model of customer demand. 𝑋 MHz Spectrum Band § Tier-1 operators using licensed channels: Divided into M channels of uniform bandwidth P licensed channels M-P unlicensed channels ! Channel capacity = " Decreasing § Tier-2 operators using licensed channels: Priority Tier-2 operators Tier-1 operators # ! ! Channel capacity = Tier-2 operators " § Tier-2 operators using unlicensed channels: Channel capacity = # " ! " 𝛽 ! , 𝛽 " → Efficiency of licensed and unlicensed channels for opportunistic use. We have, 𝛽 ! , 𝛽 " ≤ 1 . Typically, T2 operators don’t get a lot of a licensed channel, compared to an unlicensed channel, hence typically 𝛽 ! ≤ 𝛽 " 5
Types of Wireless Operators # . § Set of candidate licensed operators 𝒯 " − Primarily interested in licensed channel access. − If they are not allocated a licensed channel, then they access channels opportunistically. # . § Set of candidate unlicensed operators 𝒯 $ − O nly interested in opportunistic channel access. § Only a subset of candidate operators joins the market. Decision to join the market is based on an operator’s preferences. − Set of interested licensed operators 𝒯 $ . − Set of interested unlicensed operators 𝒯 % . 6
Example: Sequence of Events Increasing time 𝒖 = 𝟏 s 𝑫 = {𝟐, 𝟑, 𝟒, 𝟓, 𝟔} Stage 2 game: Operators in sets Stage 1 game: Regulator 𝓣 𝑴 % and 𝒯 & % decides whether to 𝒯 $ decides the value of 𝑫 = {𝟕, 𝟖, 𝟗} enter the market or not based number of channels 𝑁 𝓣 𝑽 on their preferences. Let’s say, and number of licensed 𝓣 𝑴 = {𝟐, 𝟑, 𝟒, 𝟓} channels 𝑄 . Let’s say, 𝓣 𝑽 = {𝟕, 𝟖} 𝑵 = 𝟓, 𝑸 = 𝟑 . Increasing time 𝒖 = 𝟐 𝒖 = 𝟑𝑼 + 𝟐 𝒖 = 𝑼 + 𝟐 Epoch 1 Epoch 2 3 -, auction 2 +, auction 1 )* auction Operators 1 and 4 wins the auction. Operators 3 and 4 wins the auction. Tier-1 Operators: Tier-1 Operators: 𝓤 𝟐 = 𝟐, 𝟓 𝓤 𝟐 = 𝟒, 𝟓 Tier-2 Operators: Tier-2 Operators: 𝓤 𝟑 = 𝟑, 𝟒 ∪ 𝟕, 𝟖 = 𝟑, 𝟒, 𝟕, 𝟖 𝓤 𝟑 = 𝟐, 𝟑 ∪ 𝟕, 𝟖 = 𝟐, 𝟑, 𝟕, 𝟖 7
Demand and Revenue Model § The 𝑙 %& interested licensed operators is associated with five gaussian random variables. Tier-1 operator Tier-2 operator 𝜍 / 𝜕 / 𝜍 / 𝑌 ',) ⟷ 𝑆 ',) ⟷ 𝐶 ' 𝑌 ',* ⟷ 𝑆 ',* Net demand served Net revenue earned Net demand served Net revenue earned Bid of a licensed by 𝑙 #$ operator in by 𝑙 #$ operator in by 𝑙 #$ operator in by 𝑙 #$ operator in channel for 𝑙 #$ an epoch if it is a an epoch if it is a an epoch if it is a an epoch if it is a operator. Tier-2 operator. Tier-2 operator. Tier-1 operator. Tier-1 operator. § The 𝑙 *. interested unlicensed operators is associated with two gaussian random variables. 8
Revenue and Objective Function § Revenue function ℛ ' 𝑁, 𝑄, 𝒯 " , 𝒯 $ : Net expected revenue of the 𝑙 %& operator in an epoch. − Decides which operators are interested in entering the market. − It is a function of the set of interested licensed and unlicensed operators. − Monotonic property: It decreases if the set of interested licensed and unlicensed operators increases. § Objective function U 𝑁, 𝑄, 𝒯 " , 𝒯 $ : A measure of the net customer demand served by all the interested operators. § We built a Monte-Carlo integrator to evaluate these two functions. § 𝒯 " and 𝒯 $ are themselves functions of 𝑁 and 𝑄 , and in general not independent 9
Stackelberg Game Stage-1 game § The regulator decides the value of M and P to maximize the objective function: U 𝑁, 𝑄, 𝒯 " 𝑁, 𝑄 , 𝒯 $ 𝑁, 𝑄 Output of Stage-2 game § We do this by performing a grid-search over 𝑁 and 𝑄 . − This possible because for any practical setup, the possible values of 𝑁 and 𝑄 are not too large. 10
Stackelberg Game Stage-2 game § Wireless operators decides whether to join the market or not based on the value of 𝑁 and 𝑄 set by the regulator in Stage-1 game. − Output of Stage-2 game: 𝒯 $ 𝑁, 𝑄 and 𝒯 & 𝑁, 𝑄 § The 𝑙 !" operator enters the market only if the expected revenue it can earn in an epoch is greater than 𝜇 # , i.e. ℛ ' 𝑁, 𝑄, 𝒯 " , 𝒯 $ ≥ 𝜇 ' . (minimum revenue requirement) § Operators are pessimistic in nature, i.e. they will enter the market only if the minimum expected revenue in an epoch with respect to 𝒯 " and 𝒯 $ is greater than 𝜇 ' . − An operator joins the market only if the dominant strategy is to join the market. Due to monotonic nature of revenue function, joining the market is dominant strategy if 𝑫 , 𝓣 𝑽 𝑫 𝓢 𝒍 𝑵, 𝑸, 𝓣 𝑴 ≥ 𝝁 𝒍 11
Numerical Result 1 § We study the variation of optimal value of 𝑁 , 𝑄 and the objective function with change in interference parameter for opportunistic access 𝛽 " and 𝛽 $ . We set 𝛽 " = 𝛽 $ = 𝛽 . § 8 licensed operators, NO unlicensed operators and 𝜇 ' = 0 ; ∀𝑙 . − No unlicensed operators implies no unlicensed channel, i.e. 𝑁 ∗ = 𝑄 ∗ . § As 𝛽 increases, 𝑉 ∗ increases. − Opportunistic access becomes more efficient. § As 𝛽 increases, 𝑁 ∗ decreases. − Lower 𝑁 implies more Tier-2 operators who uses channels opportunistically. − Efficiency of opportunistic access increases with increase in 𝛽 . − Therefore, lower 𝑁 is preferred when 𝛽 is high. 12
Numerical Result 2 § We study the variation of optimal value of the objective function and optimal ratio of unlicensed band, - ∗ ./ ∗ - ∗ , with change in 𝛽 " . 𝛽 " and 𝛽 $ are NOT equal; 𝛽 $ is a constant. § 4 licensed operators, 4 unlicensed operators and 𝜇 ' = 0 ; ∀𝑙 . § As 𝛽 " increases, 𝑉 ∗ increases. − Opportunistic access becomes more efficient. § As 𝛽 " increases, - ∗ ./ ∗ decreases. - ∗ − As 𝛽 $ increases, efficiency of opportunistic access for licensed channels increases. − Therefore, it is better to have more licensed channels than unlicensed channels. 13
Conclusion § We consider the joint problem of Channel Model partitioning a band into channels, and 𝑋 MHz Spectrum Band allocating channels to licensed tiered Divided into M channels of uniform bandwidth access or unlicensed access P licensed channels M-P unlicensed channels § Modeled as a two-stage Stackelberg Decreasing game Priority Tier-2 operators Tier-1 operators § Takes into account minimum revenue Tier-2 operators requirement of operators as well as the difference in channel capacity between opportunistic versus licensed access 14
Thank you for listening! Please email abouzeid@ecse.rpi.edu or sahag@rpi.edu for questions/ comments 15
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