Formula For Symbol Error Probability Research Articles

Asymptotic SEP Analysis of Two-Way Relaying Networks With Distributed Alamouti Codes

Asymptotic symbol error probability (SEP) performance with an optimal maximum likelihood (ML) receiver and square quadrature amplitude modulation (QAM) constellations is investigated for two-way amplify-and-forward (AF) half-duplex relaying networks employing distributed Alamouti space-time block codes (DASTCs) recently proposed by Duong By developing a novel strategy to particularly deal with some specific Gaussian integrals, two asymptotic SEP formulas are derived for both fixed- and variable-gain AF protocols. These analytic results reveal that, when the signal-to-noise ratio (SNR) is large, the diversity gain for the variable-gain AF is 2, whereas the diversity gain function for the fixed-gain AF is proportional to SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> ln SNR.

On The Symbol Error Probability of Distributed-Alamouti Scheme

Taking into account the relay’s location, we analyze the maximum likelihood (ML) decoding performance of dualhop relay network, in which two amplify-and-forward (AF) relays employ the Alamouti code in a distributed fashion. In particular, using the well-known moment generating function (MGF) approach we derive the closed-form expressions of the average symbol error probability (SEP) for M-ary phase-shift keying (M-PSK) when the relays are located nearby either the source or destination. The analytical result is obtained as a single integral with finite limits and the integrand composed solely of trigonometric functions. Assessing the asymptotic characteristic of SEP formulas in the high signal-to-noise ratio regime, we show that the distributed-Alamouti protocol achieves a full diversity order. We also perform the Monte-Carlo simulations to validate our analysis. In addition, based on the upper bound of SEP we propose an optimal power allocation between the first-hop (the source-to-relay link) and second-hop (the relay-to-destination link) transmission. We further show that as the two relays are located nearby the destination most of the total power should be allocated to the broadcasting phase (the first-hop transmission). When the two relays are placed close to the source, we propose an optimal transmission scheme which is a non-realtime processing, hence, can be applied for practical applications. It is shown that the optimal power allocation scheme outperforms the equal power scheme with a SEP performance improvement by 2-3 dB.

Exact method for the error probability calculation of three-dimensional signal constellations

The contribution of this letter is the computation of exact symbol error probability (SEP) of three-dimensional (3-D) signal constellations over an additive white Gaussian noise (AWGN) channel. The originality of the proposed method is that it can be applied to any arbitrary 3-D constellation whose decision regions may not meet at right angles. We express the SEP in a triple integral form which is further simplified. The simplified form requires a single integral evaluation of standard erf function. Using the derived exact SEP formula, we plot SEP for a number of selected 3-D constellations. The SEP obtained using the proposed formula is validated by simulation results. It is also compared with the union bound approximation, an upper bound for SEP.

A new formula for MDPSK symbol error probability

This article presents an extremely compact new formula for the symbol error probability in M-ary differential phase shift keying (MDPSK) that is extraordinarily similar to its counterpart for M-ary phase shift keying (MPSK). This result follows from a new form for a generic error probability associated with the phase angle between two vectors perturbed by Gaussian noise. The new form also leads to a new expression for the Marcum Q-function. As special cases, the generic error probability is noted to also contain MPSK, CPFSK, and digital FM. Finally, it is pointed out that the generic error probability simplifies the error probability expressions in other situations such as nonorthogonal signaling, maximum-likelihood differential detection of DPSK with block-by-block detection, and Gray coding of MDPSK.