Energy Efficient Design for OFDM-Based Underlay Cognitive Radio Networks

Algorithm 2

Exact power allocation algorithm (EPAA) for Problem P4.

Step  1. Initialization, 𝜇←0, 𝒜←{𝑔₁,𝑔₂,...,𝑔_𝑁},

𝑅←0, 𝑃_𝑡←0.

Step  2. Using the similar way to (15), we can obtain the

optimal unconstrained water level as

𝜇_un←2^{−𝑅/𝑚𝐵}𝑒𝐺exp𝑊₀𝛼𝑃_𝑡+𝑃_𝑠𝐺𝛼𝑚−𝑔𝑒2^{𝑅/𝑚𝐵}, where

𝐺←∏^𝑚_𝑛=1𝒜_𝑛^1/𝑚, 1𝑔←𝑚^𝑚_𝑛∑₌₁1𝒜_𝑛, 𝒮←𝑛∣𝜇_un>1𝒜_𝑛

and 𝑚←|𝒮|.

Step  3. Select, 𝑛←argmax_𝑛{𝒜_𝑛}.

Step  4. Remove and update, if 𝜇−1/𝒜_𝑛>𝑝_𝑜, then

𝒜←𝒜⧵{𝒜_𝑛}, 𝑅←𝑅+𝐵log₂(1+𝑝_𝑜𝒜_𝑛),

𝑃_𝑡←𝑃_𝑡+𝑝_𝑜 and goto Step  2; else goto Step  5.

Step  5. Optimal power allocation for each subchannel,

𝑝_𝑛←𝜇_opt−1𝑔_𝑛^𝑝𝑜₀, where

𝜇_opt←min(𝜇_max,max(𝜇_un,𝜇_min)).