An Efficient Precoder Design for Multiuser MIMO Cognitive Radio Networks with Interference Constraints

We consider a linear precoder design for an underlay cognitive radio multiple-input multiple-output broadcast channel, where the secondary system consisting of a secondary base-station (BS) and a group of secondary users (SUs) is allowed to share the same spectrum with the primary system. All the transceivers are equipped with multiple antennas, each of which has its own maximum power constraint. Assuming zero-forcing method to eliminate the multiuser interference, we study the sum rate maximization problem for the secondary system subject to both per-antenna power constraints at the secondary BS and the interference power constraints at the primary users. The problem of interest differs from the ones studied previously that often assumed a sum power constraint and/or single antenna employed at either both the primary and secondary receivers or the primary receivers. To develop an efficient numerical algorithm, we first invoke the rank relaxation method to transform the considered problem into a convex-concave problem based on a downlink-uplink result. We then propose a barrier interior-point method to solve the resulting saddle point problem. In particular, in each iteration of the proposed method we find the Newton step by solving a system of discrete-time Sylvester equations, which help reduce the complexity significantly, compared to the conventional method. Simulation results are provided to demonstrate fast convergence and effectiveness of the proposed algorithm. 

Precoder Detection for Cooperative Decode-and-Forward Relaying in OFDMA Systems

We consider an LTE network where a secondary user acts as a relay, transmitting data to the primary user using a decode-and-forward mechanism, transparent to the base-station (eNodeB). Clearly, the relay can decode symbols more reliably if the employed precoder matrix indicators (PMIs) are known. However, for closed loop spatial multiplexing (CLSM) transmit mode, this information is not always embedded in the downlink signal, leading to a need for effective methods to determine the PMI. In this thesis, we consider 2x2 MIMO and 4x4 MIMO downlink channels corresponding to CLSM and formulate two techniques to estimate the PMI at the relay using a hypothesis testing framework. We evaluate their performance via simulations for various ITU channel models over a range of SNR and for different channel quality indicators (CQIs). We compare them to the case when the true PMI is known at the relay and show that the performance of the proposed schemes are within 2 dB at 10% block error rate (BLER) in almost all scenarios. Furthermore, the techniques add minimal computational overhead over existent receiver structure. Finally, we also identify scenarios when using the proposed precoder detection algorithms in conjunction with the cooperative decode-and-forward relaying mechanism benefits the PUE and improves the BLER performance for the PUE. Therefore, we conclude from this that the proposed algorithms as well as the cooperative relaying mechanism at the CMR can be gainfully employed in a variety of real-life scenarios in LTE networks.

On the diversity analysis of the sequential slotted amplify-decode-and-forward protocol

In this paper, we review the sequential slotted amplify-decode-and-forward (SADF) protocol with half-duplex single-antenna and evaluate its performance in terms of pairwise error probability (PEP). We obtain the PEP upper bound of the protocol and find out that the achievable diversity order of the protocol is two with arbitrary number of relay terminals. To achieve the maximum achievable diversity order, we propose a simple precoder that is easy to implement with any number of relay terminals and transmission slots. Simulation results show that the proposed precoder achieves the maximum achievable diversity order and has similar BER performance compared to some of the existing precoders.

Slotted cooperative communication in half duplex relay networks

In cooperative communication systems, several wireless communication terminals collaborate to form a virtual-multiple antenna array system and exploit the spatial diversity to achieve a better performance. This thesis proposes a practical slotted protocol for cooperative communication systems with half-duplex single antennas. The performance of the proposed slotted cooperative communication protocol is evaluated in terms of the pairwise error probability and the bit error rate. The proposed protocol achieves the multiple-input single-output performance bound with a novel relay ordering and scheduling strategy.

A rate-one full-diversity low-complexity space-time-frequency block code (STFBC) for 4-Tx MIMO-OFDM

It is known that by employing space-time-frequency codes (STFCs) to frequency selective MIMO-OFDM systems, all the three diversity viz spatial, temporal and multipath can be exploited. There exists space-time-frequency block codes (STFBCs) designed using orthogonal designs with constellation precoder to get full diversity (Z.Liu, Y.Xin and G.Giannakis IEEE Trans. Signal Processing, Oct. 2002). Since orthogonal designs of rate one exists only for two transmit antennas, for more than two transmit antennas STFBCs of rate-one and full-diversity cannot be constructed using orthogonal designs. This paper presents a STFBC scheme of rate one for four transmit antennas designed using quasi-orthogonal designs along with co-ordinate interleaved orthogonal designs (Zafar Ali Khan and B. Sundar Rajan Proc: ISIT 2002). Conditions on the signal sets that give full-diversity are identified. Simulation results are presented to show the superiority of our codes over the existing ones.

Robust Transceiver Design for Multiuser MIMO Downlink

In this paper, we consider robust joint linear precoder/receive filter design for multiuser multi-input multi-output (MIMO) downlink that minimizes the sum mean square error (SMSE) in the presence of imperfect channel state information (CSI). The base station is equipped with multiple transmit antennas, and each user terminal is equipped with multiple receive antennas. The CSI is assumed to be perturbed by estimation error. The proposed transceiver design is based on jointly minimizing a modified function of the MSE, taking into account the statistics of the estimation error under a total transmit power constraint. An alternating optimization algorithm, wherein the optimization is performed with respect to the transmit precoder and the receive filter in an alternating fashion, is proposed. The robustness of the proposed algorithm to imperfections in CSI is illustrated through simulations.

Jointly Optimal MMSE design for non-redundant FIR precoding and equalization

We provide a filterbank precoding framework (FBP) for frequency selective channels using the minimum mean squared error (MMSE) criterion. The design obviates the need for introducing a guard interval between successive blocks, and hence can achieve the maximum possible bandwidth efficiency. This is especially useful in cases where the channel is of a high order. We treat both the presence and the absence of channel knowledge at the transmitter. In the former case, we obtain the jointly optimal precoder-equalizer pair of the specified order. In the latter case, we use a zero padding precoder, and obtain the MMSE equalizer. No restriction on the dimension or nature of the channel matrix is imposed. Simulation results indicate that the filterbank approach outperforms block based methods like OFDM and eigenmode precoding.

Precoding with X-codes to increase capacity with discrete input alphabets

We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on X-Codes in to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using Singular Value Decomposition (SVD) and X-codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and the 2 × 2 real rotation matrices for each pair (parameterized with a single angle). This precoding structure enables to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is equivalent to i) optimizing the rotation angle and the power allocation within each pair and ii) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz et al., and significantly better than mercury/waterfilling strategy by Lozano et al.. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.

Precoding by Pairing Subchannels to Increase MIMO Capacity With Discrete Input Alphabets

We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on the X-Codes in 1] to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using singular value decomposition (SVD) and X-Codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and a 2 x 2 real rotation matrix for each pair (parameterized with a single angle). This precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is solved by: i) optimizing the rotation angle and the power allocation within each pair and ii) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz et al., and is significantly better than Mercury/waterfilling strategy by Lozano et al. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.

On Precoding for Constant K-User MIMO Gaussian Interference Channel With Finite Constellation Inputs

This paper considers linear precoding for the constant channel-coefficient K-user MIMO Gaussian interference channel (MIMO GIC) where each transmitter-i (Tx-i) requires the sending of d(i) independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution to receiver-i (Rx-i) for i = 1, 2, ..., K. We define the maximum rate achieved by Tx-i using any linear precoder as the signal-to-noise ratio (SNR) tends to infinity when the interference channel coefficients are zero to be the constellation constrained saturation capacity (CCSC) for Tx-i. We derive a high-SNR approximation for the rate achieved by Tx-i when interference is treated as noise and this rate is given by the mutual information between Tx-i and Rx-i, denoted as I(X) under bar (i); (Y) under bar (i)]. A set of necessary and sufficient conditions on the precoders under which I(X) under bar (i); (Y) under bar (i)] tends to CCSC for Tx-i is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Furthermore, we propose gradient-ascentbased algorithms to optimize the sum rate achieved by precoding with finite constellation inputs and treating interference as noise. A simulation study using the proposed algorithms for a three-user MIMO GIC with two antennas at each node with d(i) = 1 for all i and with BPSK and QPSK inputs shows more than 0.1-b/s/Hz gain in the ergodic sum rate over that yielded by precoders obtained from some known IA algorithms at moderate SNRs.

Transceiver designs and analysis for LTI, LTV and broadcast channels - new matrix decompositions and majorization theory

Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.

In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.

The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.

In the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.

The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.

Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.

Novel Z-Domain precoding method for blind separation of spatially correlated signals

In this paper, we address the problem of blind separation of spatially correlated signals, which is encountered in some emerging applications, e.g., distributed wireless sensor networks and wireless surveillance systems. We preprocess the source signals in transmitters prior to transmission. Specifically, the source signals are first filtered by a set of properly designed precoders and then the coded signals are transmitted. On the receiving side, the Z-domain features of the precoders are exploited to separate the coded signals, from which the source signals are recovered. Based on the proposed precoders, a closed-form algorithm is derived to estimate the coded signals and the source signals. Unlike traditional blind source separation approaches, the proposed method does not require the source signals to be uncorrelated, sparse, or nonnegative. Compared with the existing precoder-based approach, the new method uses precoders with much lower order, which reduces the delay in data transmission and is easier to implement in practice.

Separating spatially correlated signals using first-order precoders

This paper deals with blind separation of spatially correlated signals mixed by an instantaneous system. Taking advantage of the fact that the source signals are accessible in some man-made systems such as wireless communication systems, we preprocess the source signals in transmitters by a set of properly designed first-order precoders and then the coded signals are transmitted. At the receiving side, information about the precoders are utilized to perform signal separation. Compared with the existing precoder-based methods, the new method only employs the simplest first-order precoders, which reduces the delay in data transmission and is easier to implement in practical applications.