I need you to implement Matlab simulator followed by the paper I attached.
All you need to do is make a simulator to show same result described in the paper.
Here is an introduction.
M-aryPSK signaling represents a popular modulation technique because of its good spectral efficiency and energy efficiency (for peak-power-limited comparisons). Moreover, the (unfiltered) transmitted signal possesses constant envelope, allowing nonlinear amplification. The detection efficiency is best when a phase-coherent reference oscillator is present in the receiver, normally obtained by some form of suppressed-carrier phase tracking loop @-power loop or decision-aided PLL [l]). Such loops, however, have an M-fold phase ambiguity, requiring the use of differential phase encoding and post-detection differential decoding. This roughly doubles the symbol error probability (a minor penalty), but is easily imple-mented.
In many applications, such coherent detection is economically unattractive, or infeasible because of the need for fast camer phase acquisition (TDMA systems and frequency hopping are two situations where this applies), or because of channel fading (e.g.. cellular radio). In such cases, differentially-coherent demodulation of the differentially-encoded modulation is performed, Normally this is designated as DPSK. Only frequency synchronization is required for this method, and normally this is more readily provided.
While DPSK modulatioddetection solves the phase acquisition problem, the deficiency of DPSK is that the decisions are developed by comparison of two successive noisy phase measurements. For M=2, the energy penalty, relative to coherent detection with differential decoding, on the additive white Gaussian noise channel is about 0.6 dB at P, = but grows to about 2.5 dB for M=8. Asymptotically (for large M and SNR) the cost of differential detection is 3 dB, which
follows from the doubling of the variance of the decision statistic under the phase differencing operation.
The intent of this paper is to formulate and analyze multi-symbol detection algorithms which close much of the gap in performance. The algorithms are general for any M, and employ a detection window length of N+l symbols, to jointly decide N symbols. Normal DPSK will correspond to the case N=l. By making N > 1, we will gain the ability to progressively improve with respect to classical DPSK, and approach the performance of coherent detection (with differential decod-ing). The intuitive notion behind both algorithms is that a sequence of phase measurements contains an unknown phase offset which is a "nuisance parameter", assumed constant over the block of N+l symbols. Rather than taking direct phase differences to eliminate this unknown parameter, better performance is obtainable by a more general detection-theoretic approach. In fact, as the observation window becomes long, we expect the ability to completely mitigate this unknown phase angle.
Related work on this problem has been recently contributed by Divsalar and Simon , who independently have formulated the optimal detector. Also, - provide another related viewpoint on the problem, that of correcting errors in DPSK detection by use of sequence measurements. In a slightly different vein, other investigators have studied open-loop or feedback block phase estimators as a precursor to coherent detectioddifferential decoding. The recent paper by Leib and Pasupathy  is representative of this class.
In the following sections, we formulate the problem and establish notation. Section 3 presents a statement of the optimal detector, along with analysis and simulation results. In Section 4, we propose two suboptimal algorithms which greatly reduce complexity yet retain good performance relative to the optimal detector.