We develop a process for determining the signal constellation set for generalized space shift key-ing (GSSK) based on the linear minimum mean square error (MMSE) estimate of the transmitted vector and propose a compressed sensing (CS) based detector exploiting the MMSE estimate. The antenna activity probability (AAP) vector, whose element represents the probability that each antenna is switched on, plays an important role in designing both the constellation set and the detector. It is observed that the covariance ma-trix of the transmitted vector can be approximated as a diagonal matrix with the AAP vector on its diagonal. Based on this observation, a convex optimization problem is formulated and solved for finding the optimal constellation. The corresponding optimal AAP vector can be used for the CS-based detection. The proposed detector is an extended orthogonal matching pursuit (OMP) algorithm, called the minimum mean square error oblique matching pursuit (MMSE-ObMP), which uses the linear MMSE estimate of the transmitted binary vector in conjunction with the OMP. In this method, the MMSE estimate is represented in terms of the AAP vector. The proposed design for GSSK can be directly applied to closed loop frequency division duplexing (FDD) systems with a feedback path, providing the transmitter with the optimal AAP vector, as well as time division duplexing (TDD) systems where the channel state information (CSI) is available at the transmitter. Furthermore, our results provide a guideline on designing GSSK for open loop FDD systems where there is no feedback. The simulation results demonstrate the advantages of the proposed design over conventional de-sign methods for GSSK.
MMSE기반의 Generalized space shift keying(GSSK) 안테나 constellation set을 설계하고 MMSE estimate을 활용하는 압축센싱 기반의 수신기를 제안한다. 안테나가 활성화될 확률(Antenna Activity Probability, AAP) 벡터는 constellation set 설계와 수신기 모두에 중요한 역할을 한다. 송신 신호의 covariance 행렬은 AAP벡터를 대각 원소로 하는 행렬로 근사화 될 수 있다. 최적의 안테나 constellation set을 찾는 문제는 convex 최적화 문제로 formulation하고, 풀 수 있다. 해당 AAP벡터는 압축센싱 기반의 수신 알고리즘에 활용 된다. 제안 알고리즘은 MMSE-ObMP로 칭하였으며, 제안 디자인은 FDD 시스템에 피드백 채널을 이용해 AAP vector를 제공함으로써 적용가능하며 TDD시스템에서는 CSI가 송신단에 주어지므로 적용 가능하다. 컴퓨터 모의실험 결과를 통해 제안 알고리즘의 SER성능이 기존 수신 알고리즘보다 월등함을 보인다.
