Mahesh K. Varanasi

Near-optimum detection in synchronous code-division multiple-access systems

Communication networks using code division multiple access (CDMA) include applications where several packets of information are transmitted synchronously and simultaneously over a common channel. Consideration is given to the problem of simultaneously demodulating every packet from such a transmission. A nonlinear detection scheme based on a linear complexity multistage multiple-access interference rejection algorithm is studied. A class of linear detectors is considered as constituting the first stage for the multistage detector. A bit-error probability comparison of the linear and multistage detectors is undertaken. It is shown that the multistage detectors are capable of achieving considerable improvements over the linear detectors, particularly in near-far situations, i.e., in the demodulation of weak signals in the presence of strong interfering signals. This problem has been of primary concern for currently operational CDMA systems. >

Optimum decision feedback multiuser equalization with successive decoding achieves the total capacity of the Gaussian multiple-access channel

The complex Gaussian multiple-access channel (GMAC) Y_=AX_+N_ is considered. The transmitters send information independently with a power constraint so that X_ has a product distribution with E[|X/sub k/|/sup 2/]/spl les/P/sub k/. It is known that multiuser codes exist that will achieve any rate-tuple in the capacity region of the GMAC provided that an optimum joint decoder is used. However, little progress has been made in multiuser coding, and moreover, optimum joint decoding would be too complex. We restrict the decoder to be of a successive decoding type with equalization. Such a decoder is parameterized by feedforward and feedback equalization vectors. The optimum successive decoder (OSD) is obtained by maximizing the mutual information for each user over those vectors. The key result of this paper is that the OSD achieves the total capacity of the GMAC at any vertex of the capacity region. With the OSD, each transmitter can use a single-user code independently of the other users. The complexity of equalization is also only linear in the number of users. For the conventional GMAC, Y=/spl Sigma//sub i=1//sup M/ X/sub i/+N, where A is a row vector with unit elements, the OSD is degenerate and involves no equalization. It reduces to the well-known successive decoder for that channel as described by Wynter (1974) and Cover (1975). Furthermore, for the particular case of the uncoded channel, the OSD reduces to a new decision feedback multiuser detector. This detector is optimum in the sense that it maximizes signal-to-interference ratio for each user.

Parametric generalized Gaussian density estimation

The primary objective of this paper is to compare the large‐sample as well as the small‐sample properties of different methods for estimating the parameters of a three‐parameter generalized Gaussian distribution. Three estimators, namely, the moment method (MM), the maximum‐likelihood (ML), and the moment/Newton‐step (MNS) estimators, are considered. The applicability of general asymptotic optimality results of the efficient ML and MNS estimation techniques is studied in the generalized Gaussian context. The asymptotic normal distributions of the estimators are obtained. The asymptotic relative superiority of the ML estimator or its variant, the MNS estimator, over the moment method is studied in terms of asymptotic relative efficiency. Based on this study, it is concluded that deviations from normality in the underlying distribution of the data necessitate the use of the efficient ML or MNS methods. In the small‐sample case, a detailed comparative study of the estimators is made possible by extensive Mon...

Group detection for synchronous Gaussian code-division multiple-access channels

The concept of group detection Is introduced to address the design of suboptimum multiuser detectors for code-division multiple-access (CDMA) channels. A group detection scheme consists of a bank of P group detectors, one each for detecting the information symbols of users in each group of a P group partition of the K simultaneously transmitting users. In a parallel group detection scheme, these group detectors operate independently, whereas in a sequential scheme, each group detector. Uses the decisions of the previous group detectors to successively cancel the interference from those users. Group detectors based on the generalized likelihood ratio test (GLRT) are obtained for the synchronous Gaussian CDMA channel. The complexity of these detectors is exponential in the group size, whereas that of the optimum detector is exponential in K. Since the partition of users is a design parameter, group sizes can be chosen to satisfy a wide range of complexity constraints. A key performance result is that the GLRT group detectors are optimally group near-far resistant. Furthermore, upper and lower bounds on the asymptotic efficiency of the sequential group detectors are derived. These bounds reveal that the sequential group detectors can, under certain conditions, perform as well as GLRT group detectors of much larger group sizes. Group detection provides a unifying approach to multiuser detection. When the users are partitioned into K single-user groups, the GLRT, a modified form of GLRT, and the sequential group detectors reduce to previously proposed suboptimal detectors; namely, the decorrelator, the two-stage detector, and the decorrelating decision-feedback detector, respectively. For the other nontrivial partitions, the group detectors are new and have a performance that is commensurate with their complexity. >

Performance Analysis of ZF and MMSE Equalizers for MIMO Systems: An In-Depth Study of the High SNR Regime

This paper presents an in-depth analysis of the zero forcing (ZF) and minimum mean squared error (MMSE) equalizers applied to wireless multiinput multioutput (MIMO) systems with no fewer receive than transmit antennas. In spite of much prior work on this subject, we reveal several new and surprising analytical results in terms of output signal-to-noise ratio (SNR), uncoded error and outage probabilities, diversity-multiplexing (D-M) gain tradeoff and coding gain. Contrary to the common perception that ZF and MMSE are asymptotically equivalent at high SNR, we show that the output SNR of the MMSE equalizer (conditioned on the channel realization) is ρ_mmse = ρ_zf+η_\ssr<i>snr</i>, where ρ_zf is the output SNR of the ZF equalizer and that the gap η_\ssr<i>snr</i> is statistically independent of ρ_zf and is a nondecreasing function of input SNR. Furthermore, as \ssr <i>snr</i>\ura ∞, η_\ssr<i>snr</i> converges with probability one to a scaled <i>F</i> random variable. It is also shown that at the output of the MMSE equalizer, the interference-to-noise ratio (INR) is tightly upper bounded by [(η_\ssr<i>snr</i>)/(ρ_zf)]. Using the decomposition of the output SNR of MMSE, we can approximate its uncoded error, as well as outage probabilities through a numerical integral which accurately reflects the respective SNR gains of the MMSE equalizer relative to its ZF counterpart. The ε-outage capacities of the two equalizers, however, coincide in the asymptotically high SNR regime. We also provide the solution to a long-standing open problem: applying optimal detection ordering does not improve the D-M tradeoff of the vertical Bell Labs layered Space-Time (V-BLAST) architecture. It is shown that optimal ordering yields a SNR gain of 10log₁₀<i>N</i> dB in the ZF-V-BLAST architecture (where <i>N</i> is the number of transmit antennas) whereas for the MMSE-V-BLAST architecture, the SNR gain due to ordered detection is even better and significantly so.

Asymptotic error probability analysis of quadratic receivers in Rayleigh-fading channels with applications to a unified analysis of coherent and noncoherent space-time receivers

A general, asymptotic (high signal-to-noise (SNR)) error analysis is introduced for quadratic receivers in frequency-flat and multipath Rayleigh-fading channels with multiple transmit and receive antennas. Asymptotically tight expressions for the pairwise error probabilities are obtained for coherent, noncoherent, and differentially coherent space-time receivers. Not only is our unified analysis applicable to more general modulation schemes and/or channel models than previously considered, but it also reveals a hitherto unrecognized eigenvalue structure that is common to all of these problems. In addition to providing an easy recipe for computing the asymptotic pairwise error rates, we make some conclusions regarding criteria for the design of signal constellations and codes such as (a) the same design criteria apply for both correlated and independent and identically distributed (i.i.d.) fading processes and (b) for noncoherent communications, unitary signals are optimal in the sense that they minimize the asymptotic union bound.

The Degree-of-Freedom Regions of MIMO Broadcast, Interference, and Cognitive Radio Channels With No CSIT

The degree-of-freedom (DoF) regions are characterized for the multiple-input multiple-output (MIMO) broadcast channel (BC), interference channels (ICs), including X and multihop ICs, and the cognitive radio channel (CRC), when there is no channel state information at the transmitter(s) (CSIT) and for fading distributions in which transmit directions are statistically indistinguishable. For the K-user MIMO BC, the exact DoF region is obtained, which shows that time division is DoF-region optimal. For the two-user MIMO IC and CRC, inner and outer bounds are obtained that coincide for a vast majority of the relative numbers of antennas at the four terminals. Finally, the DoF of the K-user MIMO IC, the CRC, and X networks are obtained for certain classes of these networks. The results herein are derived for fading distributions and additive noises that are more general than those considered in other simultaneous related works. The DoF with and without CSIT are compared and conditions under which a lack of CSIT does, or does not, result in the loss of DoF are identified, thereby 1) providing robust no-CSIT schemes that have the same DoF as their previously found CSIT counterparts and 2) identifying situations where CSI feedback to transmitters would provide gains that are significant enough that even the DoF could be improved.

Decision feedback multiuser detection: a systematic approach

A systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of K simultaneously transmitting users of a synchronous correlated waveform multiple-access (CWMA) channel with Gaussian noise. A new performance criterion called symmetric energy is defined which is a low-noise indicator of the joint error rate that at least one user is detected erroneously. Even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum-likelihood detector. A general class of decision feedback detectors (DFDs) is defined with O(K) implementational complexity per user. The symmetric energy of arbitrary DFD and bounds on their asymptotic effective energy (AEE) performance are obtained along with an exact bit-error rate and AEE analysis for the decorrelating DFD. The optimum DFD that maximizes symmetric energy is obtained. Each one of the K! optimum, decorrelating, and conventional DFDs, that correspond to the K! orders in which the users can be detected, are shown to outperform the linear optimum, decorrelating, and conventional detectors, respectively, in terms of symmetric energy. Moreover, algorithms are obtained for determining the choice of order of detection for the three DFDs which guarantee that they uniformly (user-wise) outperform their linear counterparts. In addition to optimality in symmetric energy, it is also shown that under certain conditions, the optimum DFD achieves the AEE performance of the exponentially complex maximum-likelihood detector for all users simultaneously. None of the results of this paper make the perfect feedback assumption. The implications of our work on power control for multiuser detection are also discussed.

The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel With Delayed CSIT

The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel (IC) is studied under the assumptions of fast fading and delayed channel state information (CSI) at the transmitters (CSIT). Under our fast fading assumption, the channel matrices vary independently across time, so that delayed CSIT is equivalent to outdated CSIT. In particular, the DoF region under delayed CSIT is established for the general MIMO IC with an arbitrary numbers of antennas at each of the four terminals. Toward this end, a set of outer bounds to the DoF region of the general MIMO IC is derived. These bounds are then shown to be tight by developing DoF-region-optimal interference alignment schemes. A comparison of the DoF region of the MIMO IC under the delayed CSIT assumption with those under the two extremes of instantaneous CSIT and no CSIT assumptions is made. This comparison reveals that there are nonempty classes of MIMO ICs, defined by certain relationships between the numbers of antennas at the four terminals, that correspond to each of the following four scenarios: the no CSIT DoF region is strictly contained by, or is equal to, the delayed CSIT DoF region, which in turn is strictly contained by, or is equal to, the instantaneous CSIT DoF region. It is notable that within the class of MIMO ICs for which the delayed CSIT DoF region is strictly larger than the no CSIT DoF region, there is a subclass for which the interference alignment scheme which uses just delayed CSIT achieves the entire DoF region previously known to be achievable only with instantaneous CSIT.

Interference alignment under limited feedback for MIMO interference channels

This paper analyzes multiple-input, multiple-output interference channels where each receiver knows its channels from all the transmitters and feeds back this information using a limited number of bits to all the other terminals. It is shown that as long as the feedback bit rate scales sufficiently fast with the signal-to-noise ratio, the transmitters can use an interference alignment strategy by treating the quantized channel estimates as being perfect to achieve the sum degrees of freedom of the interference channel attainable with perfect and global channel state information. A tradeoff between the feedback rate and the achievable degrees of freedom is established by showing that a slower scaling of feedback rate for any one user leads to commensurately fewer degrees of freedom for that user alone. It is then shown that under the same fixed transmission strategy but with random quantization, the above mentioned sufficient condition on the feedback scaling rate to attain a given sum degrees of freedom (up to the maximum attainable) is also necessary in this setting.