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SUMMARYWe consider the physical layer error performance parameters and design criteria for digital satellite systems established by ITU-R Recommendation S.1062, where the performance objectives are given in terms of the bit error rate (BER) divided by the average number of errors within a cluster. It is well known that errors on satellite links employing forward error correction (FEC) schemes tend to occur in clusters. The resulting block error rate is the same as if it was caused by randomly occurring bit errors with an error-event ratio of BER/a, where a is the average number of errors within a cluster. The factor, a, accounts for the burstiness of the errors and also represents the ratio between the BER and the error-event ratio. This paper proposes theoretical methods to estimate the factor, a. Using the weight distributions of the FEC codes, we derive a set of expressions for the factor, a, as well as their compact lower bounds. We present lower bounds for various FEC schemes including binary BCH codes, block turbo codes, convolutional codes, and turbo codes. The simulation results show that the proposed lower bounds are good estimates in the high signalto-noise ratio region.

The Cholesky decomposition-block diagonalization (CD-BD) interference alignment (IA) for a multiuser multiple input multiple output (MU-MIMO) relay system is proposed, which designs precoders for the multiple access channel (MAC) by employing the singular value decomposition (SVD) as well as the mean square error (MSE) detector for the broadcast Hermitian channel (BHC) taken advantage of in our design. Also, in our proposed CD-BD IA algorithm, the relaying function is made use to restructure the quasieigenvalue decomposition (quasi-EVD) equivalent channel. This approach used for the design of BD precoding matrix can significantly reduce the computational complexity and proposed algorithm can address several optimization criteria, which is achieved by designing the precoding matrices in two steps. In the first step, we use Cholesky decomposition to maximize the sum-of-rate (SR) with the minimum mean square error (MMSE) detection. In the next step, we optimize the system BER performance with the overlap of the row spaces spanned by the effective channel matrices of different users. By iterating the closed form of the solution, we are able not only to maximize the achievable sum-of-rate (ASR), but also to minimize the BER performance at a high signal-to-noise ratio (SNR) region.

In this paper, we investigate a joint source and relay precoding design scheme for an amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system with absence of the direct link. The joint optimization problem, which is to minimize an objective function based on the mean square error (MSE), is formulated as a nonconvex optimization problem in the AF MIMO relay system. Instead of the conventional iterative method, we use an inequality to derive a lower bound of the MSE under the power constraint for obtaining a suboptimal solution of the objective function, which makes the optimization problem convex and also approaches the existing upper bound of the MSE, especially at the high signal-to-noise ratio (SNR). Numerical results show that this scheme outperforms the previous schemes in terms of either MSE or bit error rate (BER).

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