Vector Perturbation Precoding (VPP) has gained recognition as a reduced-complexity method to achieve high-rates in multiuser multiple-input multiple-output (MIMO) downlink. Here we propose Space-Time VPP (STVPP), where the nonlinear lattice-based precoding operations of standard VPP are extended into the time domain. This is done by introducing temporal precoding lattices for each user, and performing the perturbation step at the transmitter for all users jointly. Although the transmitter complexity is increased, we show that by employing root lattices for the temporal precoding the computational complexity at each mobile receiver remains O(1). We provide new bounds on the required transmit energy scaling, as well as the sum rate. We show that the optimal sum rates are approached for moderate to high signal-to-noise ratio (SNR). Simulations show that significant gains can be achieved by precoding over even a few time instants, and that the proposed bounds are tight.

In this paper we propose a modification of the Hopfield neural networks for vector precoding, based on Lenstra, Lenstra, and Lovasz lattice basis reduction. This precoding algorithm controls the energy penalty for system loads α = K/N close to 1, with N and K denoting the number of transmit and receive antennas, respectively. Simulation results for the average transmit energy as a function of α show that our algorithm improves performance within the range 0.9 ≤ α ≤ 1, between 0.4 dB and 2.6 dB in comparison to standard HNN precoding. The proposed algorithm performs close to the sphere encoder (SE) while requiring much lower complexity, and thus, can be applied as an efficient suboptimal precoding method.

This paper considers the use of a sensor network to estimate the position of a transmitting radio based on the received signal strength at the sensors. A generic path loss model which includes the effects of spatially correlated shadowing is assumed. A weighted likelihood (WL) estimator is proposed, which can be seen as a simplified minimum mean square error (MMSE) estimator. This estimator can be used for localizing a source in a static scenario or it can provide the initial position estimate of a tracking algorithm. The performance of the WL estimator is simulated, and robustness to erroneous assumptions about path loss exponent, shadowing variance and correlation distance is demonstrated.

This paper considers the performance of the multiuser multi-antenna downlink where NTbase station antennas transmit to K non-collocated, single antenna users over correlated channels. A practical and near-capacity multi-user technique called vector perturbation precoding (VPP) is considered. For these scenarios, we derive a lower bound to the average energy of the precoded vector. We use this to approximate the effective noise gain at the receivers due to the presence of transmit side correlation. Furthermore, we obtain simple approximations for the noise gain for constant and exponential transmit correlation models. Simulation results show that our approximations predict the performance loss due to correlation remarkably well regardless of the correlation parameter.

This work considers the performance of multiple-input single-output (MISO) wireless systems employing beamforming over correlated wireless channels. More specifically, we examine the use of Random Vector Quantization (RVQ) as a limited feedback method of informing the transmitter of the appropriate beamforming vector. Using RVQ, we are able to derive the distribution functions of the beamforming gain in such a system in closed form. In addition, we derive the power offset in the delay-limited capacity for RVQ systems in closed form based on the approach of Au-Yeung and Love for i.i.d. channels [1]. This result is applicable to any channel model. For all of these results we derive simplifications for the case of two transmit antennas. Simulation results are provided that confirm our results and show a decrease in performance for the correlated channels.

This paper considers the multiuser multiple-input multiple-output (MIMO) broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via vector perturbation. We derive expressions for the sum rate in terms of the average energy of the precoded vector, and use this to derive a high signal-to-noise ratio (SNR) closed-form upper bound, which we show to be tight via simulation. We also propose a modification to vector perturbation where different rates can be allocated to different users. We conclude that for vector perturbation precoding most of the sum rate gains can be achieved by reducing the rate allocation problem to the user selection problem. We then propose a low-complexity user selection algorithm that attempts to maximize the high-SNR sum rate upper bound. Simulations show that the algorithm outperforms other user selection algorithms of similar complexity.

We propose a new algorithm for noncoherent sequence detection of M-ary phase-shift-keying (M-PSK) symbols transmitted over a block fading channel. The algorithm is of complexity O(T), where T is the sequence length, and is therefore computationally superior to existing maximum-likelihood (ML) detectors of complexity O(T logT). Our detector is based on a new approximation we propose to the noncoherent ML function. We show that by using this close approximation, the detection problem reduces to a nearest lattice point problem for the lattice An*, from which we derive our O(T) approach. Simulation results are provided that show the difference in bit error rate is negligibly small for a wide range of signal-to-noise ratios.

This paper considers the multiuser multiple-input multiple-output (MIMO) Rayleigh fading broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via a multi-user technique known as vector perturbation. We derive expressions for the capacity in terms of the average energy of the preceded vector, and use this to derive a closed-form high-SNR upper bound, which we show to be tight via simulation. We then turn to the practical issue of user selection. We propose a low-complexity user selection algorithm that attempts to maximize the high-SNR sum rate upper bound. Simulations show that the algorithm outperforms other user selection algorithms of similar complexity.

This paper proposes reflected simplex codebooks for limited feedback beamforming in multiple-input multiple-output (MIMO) wireless systems. The codebooks are a geometric construction based on simplices and the Anlattice. We propose a fast codebook search and indexing algorithm. We show that such codebooks perform superior or comparable to other codebooks, with much lower implementation complexity.

This paper considers the problem of beamforming in multiple-input multiple-output (MIMO) wireless systems. Assuming perfect channel state information at the receiver, the choice of the beamforming vector is made possible through a noiseless limited-rate feedback of one or more bits per coefficient to the transmitter. This paper proposes the use of beamforming codebooks based on quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations, which essentially eliminates the need for storage of the codebook. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the beamforming codebook search problem with that of noncoherent sequence detection. Based on this we propose fast beamforming vector search algorithms. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

This paper considers the multiuser multiple-input multiple-output (MIMO) Rayleigh fading broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via a multiuser technique known as vector perturbation. We propose lattice-theoretic and rate-distortion based approaches to analyze the performance of these systems, taking into account the practical restrictions imposed by limited feedback and training. We show that performance is primarily determined by the ratio between the number of users and the number of transmit antennas. We then propose a new practical low-complexity low-rate feedback scheme, and show that the performance approaches the ideal rate-distortion based scheme.

This paper considers the use of multiple transmit antennas to deliver independent data streams to multiple users. In particular, we examine a multi-user technique known as vector perturbation. We provide a new lattice-theoretic approach to analyze its performance in the presence of Rayleigh fading. Vector perturbation is based on performing a channel inversion, with the additional step of perturbing the data signal prior to linear preceding to significantly reduce the required transmit power. To analyze such systems it is necessary to calculate the resulting average energy of the sphere-encoded signal vector, as this determines the signal-to-noise ratio (SNR) at the output of the demodulator. Previous results presented in the literature were partially analytic, requiring further numerical evaluation. Here, we derive a concise approximation to the output SNR. We also provide tight upper and lower bounds on the bit error rate for the reception of QAM symbols using the required modulo demodulator, as a function of the average energy of the sphere- encoded signal vector.

This paper proposes a new QAM based codebook for beamforming in multiple-input multiple-output (MIMO) wireless systems with a limited-rate feedback channel. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the problems of beamforming codebook search and noncoherent sequence detection. Based on this we propose a fast beamforming vector search algorithm. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

We consider the optimal performance of noncoherent channel estimation, that is, where the codebook is known to the receiver but the actual transmitted data is not. It is well known that when training data is known to the receiver, the minimum variance of the channel estimation error for unbiased channel estimation is bounded by the Cramer-Rao lower bound. However, in the noncoherent case, where joint estimation of both a continuous channel and discrete data is required, the Cramer- Rao bound is not applicable. We derive a new bound for this mixed multiple parameter estimation problem for flat fading channels, based on the Hammersley-Chapman-Robbins bound for restricted parameters. We show that the new noncoherent bound asymptotically approaches the Cramer-Rao bound with increasing SNR and sequence length. As an example we consider channel estimation for BPSK over a positive real-valued channel. We show that the noncoherent ML detector is asymptotically unbiased and achieves the lower bound with increasing SNR. We also observe that for moderate SNR the noncoherent ML estimator can actually outperform the optimal coherent ML estimator.

We present a novel, maximum-likelihood (ML), lattice-decoding algorithm for noncoherent block detection of QAM signals. The computational complexity is polynomial in the block length; making it feasible for implementation compared with the exhaustive search ML detector. The algorithm works by enumerating the nearest neighbor regions for a plane defined by the received vector; in a conceptually similar manner to sphere decoding. Simulations show that the new algorithm significantly outperforms existing approaches.

In this paper we present a novel maximum-likklihood polynomial-time algorithm for noncoherent detection of PAM over fading channels. The algorithm is based on a geometric interpretation of the noncoherent detection metric. This interpretation leads to a novel low complexity decoder based on an angular criterion, rather than the usual Euclidean distance sense. We prove that the ML estimate of the data must lie in a reduced search space which is of log-linear complexity with the block length. We then provide an algorithm that enumerates the codewords and their corresponding metrics in an efficient, recursive manner. We also consider detection of ASK, by combining the maximum-likelihood algorithm with a simple phase estimator.

This correspondence considers block detection for blind wireless digital transmission. At high signal-to-noise ratio (SNR), block detection errors are primarily due to the received sequence having multiple possible decoded sequences with the same likelihood. We derive analytic expressions for the probability of detection ambiguity written in terms of a Dedekind zeta function, in the zero noise case with large constellations. Expressions are also provided for finite constellations, which can be evaluated efficiently, independent of the block length. Simulations demonstrate that the analytically derived error floors exist at high SNR

This paper presents performance bounds for block-based detection of PAM and QAM transmitted over non-coherent channels. Such channels give rise to inherent detection ambiguities since multiple possible transmit sequences can have the same likelihood. The number of ambiguous sequences is a function of the block length. In this paper, we derive the probability of detection error in terms of a Dedekind zeta function of the block length, for infinite-sized constellations and zero noise. We also provide expressions for finite constellations which can be evaluated in polynomial time with the constellation size, as opposed to checking all possible sequences