Bit and power loading for MIMO systems with statistical channel knowledge at the transmitter
- Autores: Hong Li
- Directores de la Tesis: Ana García Armada (dir. tes.)
- Lectura: En la Universidad Carlos III de Madrid ( España ) en 2011
- Idioma: inglés
- Tribunal Calificador de la Tesis: Antonio Artés Rodríguez (presid.), Victor Pedro Gil Jiménez (secret.), Santiago Zazo Bello (voc.), Ana Isabel Pérez Neira (voc.), Juan José Murillo Fuentes (voc.)
- Materias:
- Enlaces
- Tesis en acceso abierto en: e-Archivo
- Resumen
In MIMO (multiple input-multiple output) communication, the adaptation of the modulation and coding at the transmitter side according to the channel characteristics allows reducing the transmission power and/or enhancing the data rates. However, it is not always feasible to have instantaneous knowledge of the channel at the transmitter. This Thesis focuses on the case that the receiver has (perfect) instantaneous Channel State Information (CSIR) but the transmitter has only access to its distribution (CDIT). This is a practical case that applies, particularly, to situations where the channel varies rapidly. Under CDIT, the input cannot be adapted to the instantaneous state of the channel and thus SVD (singular value decomposition) cannot be used to diagonalize the channel. Achieving capacity requires a complex Gaussian input vector with a covariance that depends on the channel distribution. In practice, however, discrete constellations are used instead of Gaussian signals. Determining the optimum signalling strategy with discrete constellations is difficult in general, and thus a pragmatic approach is using the spatial signalling directions indicated by the capacityachieving covariance. Several classical practical bit and power loading algorithms are available for parallel-channel settings. To guarantee the quality of service, a certain average bit error probability (BER) is required at the receiver side. Different types of receiver correspond to differente relationships between the BER and the SINR. With the feedback of the parameters of the SINR (Signal-to-Interference-plus-Noise Ratio) distribution, two optimization problems for single user MIMO systems with correlation at the transmitter side can be solved, namely rate maximization with a total power constraint and power minimization with a target bit rate. The goal of this Thesis is to devise practical bit and power loading schemes for MIMO that can operate on the basis of CDIT only. For practical reasons, three typical receivers are considered, namely zero-forcing (ZF), minimum mean squared error (MMSE) and zero-forcing with successive interference cancellation (ZF-SIC). The following problems are addressed: • Maximization of the bit rates with discrete constellations, using the transmit directions given by the capacity achieving input covariance, at a certain average bit error probability (BER) and a constraint of total transmit power. • Minimization of the transmit power with discrete constellations, using the transmit directions given by the capacity achieving input covariance, at a certain average bit error probability (BER) and a target transmit bit rate. • Evaluation and comparison of the power gain when optimizing the transmission with the three mentioned types of receivers relative to a non-optimized transmission. In order to address these items, in this work it is essential to establish a relationship between the average BER corresponding to each of the three receivers and the powers allocated at the transmitter under the premise of CDIT. By utilizing these BER approximations, two dual optimization problems, bit maximization and power minimization, are solved for the practical case of statistical channel knowledge at the transmitter side and discrete constellations. Using a Gamma or a generalized Gamma distribution of the SINR, BER approximations can be obtained through integration. For a single user MIMO system with correlated channel, to accomplish the optimization process the mathematical methods used are a Levin-Campello algorithm for ZF, exhaustive search with additional constraints for MMSE and tree search with bit rate boundary for ZF-SIC. The accuracy of the developed expressions is verified with Monte Carlo simulations. The transmission environment is specified to be a Rayleigh flat-fading channel with correlation at the transmitter side. The Thesis is structured as follows. An introduction is presented at the first chapter, explaining the contents of this Thesis. Following a description of the basic process which takes place at the transmitter side, the second chapter presents the characteristics of the MIMO channel. Moreover, the system models of three typical receivers are described, namely ZF, MMSE and ZF-SIC. The third chapter starts with a review of capacity, and leads to the so-called waterfilling distribution. The dual optimization problems, bit rate maximization and power minimization, are defined with the objective of enhancing the performance via processing at the transmitter side. In some practical systems, Levin-Campello develops a solution for the dual optimization problems for discrete constellations that is described. Also, in order to further understand the power minimization problem for discrete constellations considering the loss of mutual information due to a given modulation, Mercury/Waterfilling is reviewed. In chapter IV, the BER of a ZF receiver is computed by using its SINR distribution, which is a Gamma distribution. For convenience, it is further accurately approximated at the high SNR regime. From the relationship between BER and power for different constellations, the two dual problems can be solved by a Levin-Campello algorithm, as the streams are independent with each other. To facilitate using the Levin-Campello algorithm, BER approximations are simplified to be established in convenient closedform equations. In chapter V, the BER of an MMSE receiver is also computed by using its SINR distribution, which can be modeled as a Gamma distribution or a generalized Gamma distribution. Some accurate closed-formed approximations are proposed and compared. In chapter VI, from these relationships between BER and power for different constellations, the two dual problems are solved by exhaustive search, as the streams are coupled with each other in the case of the MMSE receiver. In order to reduce the computational complexity, some additional constrains are added. For the two dual optimization problems, the total number of transmitted bits with an MMSE receiver cannot be less than those with a ZF receiver. Therefore, the starting point for the search is always the solution derived for ZF receivers, and the search progresses from that point towards higher loads until the constraints set in. The BER of MMSE can be approximated by the moment generating function (MGF), which includes the first three moments of SINR. Comparing two randomly selected antennas, when an increment of the number of bits is added to one of them, placing the increment in the antenna with better channel condition requires less total power to accomplish the transmission. Thus, it can be concluded that the better channel should be loaded with more bits. With this additional constraint, the computational complexity of the exhaustive search can be reduced even more reasonably. In chapter VII, taking into account the error propagation, a closed-form BER approximation can be derived for the ZF-SIC receiver by using the total probability theorem. Moreover, since the ordering of the decoding process can dramatically impact the system performance when using this receiver, a precoder is proposed to determine the decoder ordering to minimize the total power. Moreover, a boundary of possible bit rates for ZF-SIC is presented, considering the bit rate of ZF and ZF-PSIC (perfect SIC), for the two dual optimization problems. To make the search converge more efficiently, a tree search is implemented making use of this boundary. In the final chapter, the results obtained for the different receivers are compared to conclude the core of this Thesis. Then, some future work is outlined. ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
