Analysis of multiuser MIMO systems with MMSE receiver based on worst case noise

The capacity of a cellular MIMO system is limited by the additive white Gaussian noise, intracell interference from the other users within the cell and by intercell interference from users outside the considered cell. The receiver as well as the transmitter have perfect channel state information. We are interested in the limits of the MIMO channel capacity under the different types of noise plus interference. Therefore, we consider three scenarios in which the noise is subject to different constraints. In all scenarios the achievable capacity of the MIMO system with worst case noise is equal to the capacity of some MIMO system in which either the channels are orthogonal or the transmit antennas are not allowed to cooperate. Furthermore, the minimax expressions fulfill a saddle point property.

In this paper, a comprehensive comparison analysis in terms of outage probability and average symbol error ratio (SER) is presented for cooperative cognitive multiple-input and multiple-output (CC-MIMO) multiuser systems with amplify-and-forward (AF) protocol. Specially, we consider two scenarios where the CC-MIMO multiuser systems have the perfect and imperfect channel state information (CSI). The CC-MIMO multiuser systems consist of one multi-antenna source, one single-antenna relay, and multiple multi-antenna destinations. At the secondary source and destinations, the maximal ratio transmission (MRT) and maximal ratio combining (MRC) are employed, respectively. For such CC-MIMO multiuser systems, we first obtain the exact closed-form expressions of outage probability under the two cases where the CC-MIMO multiuser systems have the perfect and imperfect CSI. Then, to reduce the implementation complexity, the tight lower bounds of outage probability and average SER are derived. Finally, to obtain insight, by using the high signal-to-noise ratio (SNR) approximation, the asymptotic estimations of outage probability are achieved. The numerical results show that the derivations are agreed with the simulations, which validate our derivations. At the same time, the results show that, for the systems without perfect CSI, the achievable diversity order reduces to one, regardless of the number of antennas at the cognitive source and destinations as well as the number of the cognitive destinations. Nevertheless, these key parameters affect the coding gain of the CC-MIMO multiuser systems. When the systems have the perfect CSI (or without feedback delay), the achievable diversity gain is determined by the minimum between the number of source’s antennas and the product of the number of destinations and the number of destination’s antennas. For the effect of PU’s parameters, our results indicate that primary systems only affect the coding gain but not the diversity gain.

Massive MIMO is one of the technologies considered in 5G to provide a much higher capacity without requiring more wireless spectrum. Because of the congestion in the radio frequency spectrum below 6 GHz, the millimeter Wave (mmWave) band has increasingly become more attractive to researchers since it offers a much larger unused bandwidth. However, the higher path loss at mmWave frequencies and the poor scattering nature of the mmWave channel (fewer paths exist) represent a challenge for communications. A hybrid beamforming technique with large antenna arrays and the Alamouti coding scheme are used in this paper to improve the performance of a single-user mmWave massive MIMO system. When perfect Channel State Information (CSI) is not available at the Base Station (BS), computer simulations have shown that a gain of 20 dB or more can be achieved by using the Alamouti code compared to the system with hybrid beamforming only, and more importantly, the error probability does not level off.

In wireless communication systems, the intended receiver is able to obtain the perfect channel state information (CSI) as long as the training sequence is sufficiently long, and then through a quantized feedback channel (QFC), the transmitter gets imperfect CSI caused by the quantized noise. In general, the design of efficient coding schemes for wireless channels with imperfect CSI at the transmitter (I-CSIT) is difficult and challenging, and one possible method is to construct such a scheme by using channel feedback. In the literature, it has already been shown that the classical Schalkwijk-Kailath (SK) scheme for the additive white Gaussian noise (AWGN) channel with noiseless feedback is a highly efficient coding scheme since its coding complexity is extremely low and the decoding error doubly exponentially decays as the coding blocklength tends to infinity. Existing SK-type schemes mainly focus on the case that perfect CSI is known at the transceiver, and adopt modulo lattice function to eliminate the impact of feedback channel noise (often considered as AWGN) on the performance of SK-type schemes. However, for channels with I-CSIT and QFC, this does not work since the distribution of quantized noise is unknown and I-CSIT brings additional non-convergence estimation error to the transceiver, leading to the application of SK-type schemes to practical wireless scenarios becomes challenging. In this paper, first, for the quasi-static fading channel with I-CSIT and QFC, we design a modulo lattice based SK-type scheme where the receiver adopts an auxiliary signal to decode the message, and numerical results show that the rate of our scheme almost approaches that of the same model with perfect CSI at the transceiver and noise-free feedback for some cases. Next, we further extend the above scheme to the two-path fading scenario, which is modeled as the two-ray channel with I-CSIT and QFC. Treating the signal of the second path as a relay, our extended scheme combines the amplify-and-forward relay strategy and the previously proposed scheme for the same model without ISI. However, this extended scheme cannot be applied to multi-path fading scenario, to this end, we propose a new SK-type scheme for the multi-path fading case. The intuition behind this scheme is to transform the multi-path fading channel into a fading MIMO channel by discrete fourier transform (DFT), and then apply the SK-type scheme to the MIMO channel in frequency domain and use inverse DFT to obtain the codeword in time domain. The study of this paper may provide a way to design efficient coding scheme for fading channels in the presence of imperfect CSI and quantized feedback.

In this paper, we first address the effects of the feedback delay on a variable-rate variable-power adaptive modulation MIMO system that is designed under a perfect channel state information (CSI) assumption. Closed-form expressions for the average bit error rate (BER) and average spectral efficiency (ASE) are derived. Based on that, simple but effective adaptive modulation designs using the outdated instantaneous CSI and time correlation coefficient are proposed based on the signal-to-interference and noise ratio (SINK) and BER analysis. Analytical and simulation results show that these designs provide good trade-offs between the ASE and BER in an adaptive way, and make the adaptive MIMO system much more robust to the CSI imperfection

Block diagonalization (BD) as a low complexity MIMO technique has been considered for inter-cell interference mitigation based on the perfect channel state information (CSI) in many previous works. However, the imperfect CSI feedback is more practical and beneficial for lower complexity in real situation. Thus, in this paper, the performance of BD for inter-cell interference mitigation is investigated under the constraint of imperfect CSI feedback. Simulation results demonstrated that BD algorithm still can work efficiently with limited feedback for the inter-cell interference cancellation.

We study transmit power adaptation and capacity-approaching coding/decoding in multiple-input-multiple-output (MIMO) Rayleigh fading channels under the assumption that perfect channel state information (CSI) is known at both the transmitter and the receiver. The capacity in MIMO systems with transmitter CSI can be achieved via two schemes: 1) a multiple-coding scheme with temporal and spatial water filling and 2) a single-coding scheme with temporal and spatial water filling. The former requires an infinite number of different codes, and the latter one requires interblock coding and, therefore, a very long code. We propose three simple but powerful methods for transforming the MIMO fading channel into a set of additive white Gaussian noise channels to which standard codes for the Gaussian channel can then be applied. We show through a number of examples that these methods can closely approach channel capacity. As a by-product, the closed-form expressions of the marginal probability density function of the ordered and unordered eigenvalues of Wishart matrices are derived.

In this paper, we investigate the capacity performance of non-orthogonal transmission schemes under imperfect channel state information (CSI) caused by feedback delay and thermal noise for various values of the signal to noise ratio (SNRinput). We use orthogonal transmission, i.e. singular value decomposition (SVD), as a benchmark. With perfect CSI, the multiplexing schemes achieve higher capacity than single data stream transmission under high SNRinput (30dB). In terms of the delayed CSI, the capacity of all multiplexing schemes converges and multiplexing schemes are only beneficial for large antenna systems (4times2) and high SNRinput (20dB). When the CSI is corrupted by thermal noise, a 20dB SNR can be tolerated in the CSI estimation.

Nowadays, the majority of new GNSS applications targets dynamic users in urban environments; therefore the decoder input in GNSS receivers needs to be adapted to the urban propagation channel to avoid mismatched decoding when using soft input channel decoding. The aim of this paper consists thus in showing that the GNSS signals demodulation performance is significantly improved integrating an advanced soft detection function as decoder input in urban areas. This advanced detection function takes into account some a priori information on the available Channel State Information (CSI). If no CSI is available, one has to blindly adapt the detection function in order to operate close to the perfect CSI case. This will lead to avoid mismatched decoding due to, for example, the consideration by default of the Additive White Gaussian Noise (AWGN) channel for the derivation of soft inputs to be fed to soft input decoders. As a consequence the decoding performance will be improved in urban areas. The expressions of the soft decoder input function adapted for an urban environment is highly dependent on the available CSI at the receiver end. Based on different model of urban propagation channels, several CSI contexts will be considered namely perfect CSI, partial statistical CSI and no CSI. Simulation results will be given related to the GPS L1C demodulation performance with these different advanced detection function expressions in an urban environment. The results presented in this paper are valid for any kind of soft input decoders, such as Viterbi decoding for trellis based codes, the MAP/BCJR decoding for turbo-codes and the Belief Propagation decoding for LDPC codes.

The design of trellis coded modulation (TCM) schemes for QAM constellations to counteract simultaneous flat fading and additive white Gaussian noise (AWGN) is considered. Motivated by the results of Divsalar and Simon (see IEEE Trans. Commun., vol.36, p.1004, 1988), and incorporating some recent ideas from Boulle and Belfiore (1992), we develop novel 2-D TCM schemes that attain diversity of order two even for a trellis structure that includes parallel paths with one symbol per edge. An algorithm is described that transforms codes designed for the AWGN channel into codes that achieve significant gains over flat fading channel, while preserving their coding gain over AWGN channel. Their performance is assessed via computer simulation for some representative TCM-QAM schemes under the assumption of uncorrelated fading and perfect channel state information (CSI). Finally, the effects of finite interleaving as well as imperfect CSI on code performance are investigated. >

Detection in multiple-input-multiple-output (MIMO) wireless communication systems is a crucial procedure in receivers since the multiple access transmission schemes generate interference due to the simultaneous transmission along with the several antennas, unlike single-input-single-output (SISO) transmission schemes. Precoding is a technique in MIMO systems used to mitigate the effects of the channel over the received signal. Hence, it is possible to adjust continuously the transmitted information to reverse the effect of the wireless channel at the receiver side. In this work, linear sub-optimal detectors and precoders for massive MIMO (M-MIMO) systems are implemented, analyzed, and compared in terms of performance-complexity trade-off. It is also being considered numerical results in both channel scenarios: a) receiver and transmitter have perfect channel state information (CSI); b) complex channel coefficients are estimated with different levels of inaccuracy. Monte-Carlo simulations (MCS) reveal that linear zero-forcing (ZF) and minimum mean squared error (MMSE) massive MIMO detectors result in a certain robustness against multi-user interference when operating under low and medium system loading, L = K/M, thanks to the favourable propagation phenomenon arising in massive MIMO systems.

In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, the authors propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, the authors compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. The authors show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR.

In this paper, we consider the problem of Angle of Departure (AoD) based channel feedback in Frequency Division Duplex (FDD) massive Multiple-Input Multiple-Output (MIMO) systems with multiple antennas at the users. We consider the use of Zero-Forcing Block Diagonalization (BD) as the downlink precoding scheme. We consider two different cases; one in which the number of streams intended for a user equals the number of antennas at that user and the other case in which the number of streams is less than the number of user antennas. BD requires the feedback of the subspace spanned by the channel matrix at the user or a subspace of it in the case of having less number of streams than the number of antennas at a specific user. Based on our channel model, we propose a channel feedback scheme that requires less feedback overhead compared to feeding back the whole channel matrix. Then, we quantify the rate gap between the rate of the system with perfect Channel State Information (CSI) at the massive MIMO Basestation (BS) and our proposed channel feedback scheme for a given number of feedback bits. Finally, we design feedback codebooks based on optimal subspace packing in the Grassmannian manifold. We show that our proposed codes achieve performance that is very close to the performance of the system with perfect CSI at the BS.

In a wireless multi-user system using multiple antennas, full multiplexing gain can be achieved through perfect channel state information (CSI) at the base station (BS). However, because of the limitations on the feedback rate and of standard requirements, such as the 3GPP, it is difficult to obtain perfect CSI, or even partial CSI with the extremely large number of feedback bits needed at the region of high signal-to-noise ratios (SNR) in practical systems. Instead of a feedback channel resource, this paper considers another resource for the system, a cooperation channel, which can be used by users to participate in cooperation in a broadcast fading channel. The cooperation among users in a multi-user system has the effect of transforming it into a cooperative point-to-point MIMO system. This paper analyzes the cooperation channel gain and the mobile power used in a cooperation channel to maintain a constant rate gap against the zero-forcing beamforming scheme with full CSI at the BS. In addition, the performance results of this proposed cooperation strategy are provided by computer simulations.

Interference alignment (IA) is a multi-user wireless communication strategy that enables several transmitters simultaneous communicate with their paired receivers without interfering each other. IA is a multiplexing gain optimal strategy at the expense of requiring the global channel state information (CSI) at the transmitters. Most previous works assume the availability of perfect CSI which is not possible in practice. The performance of IA algorithms based on perfect CSI drop dramatically in circumstance where CSI errors exist. In this paper we propose a robust minimum mean square error (MMSE) IA algorithm with imperfect CSI. Based on a Gaussian statistic channel error model, we give the mean square error objective function with per transmitter power constraint. The objective function is not joint convex in precoders and decoders, but convex in precoders with fixed decoders and vice versa. We convert the problem to two convex sub problems and iteratively find the solutions. Numerical results are presented to validate the effectiveness of proposed algorithm when CSI errors exist.