We consider the$K$-user Multiple Input Multiple Output (MIMO) Gaussian interference channel with$M$antennas at each transmitter and$N$antennas at each receiver. It is assumed that channel coefficients are constant real numbers and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the number of Degrees of Freedom (DoF) of this channel. Using the real interference alignment technique introduced in Motahariet al., 2014, we show that$\frac {MN}{M+N} K$degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the DoF of this channel is provided. This upper-bound coincides with our achievable DoF for$K\geq K_{u} \triangleq \frac {M+N}{\gcd (M,N)}$, where$\gcd (M,N)$denotes the greatest common divisor of$M$and$N$. This gives an exact characterization of DoF for$M\times N$MIMO Gaussian interference channel in the case of$K\geq K_{u}$. Since there is no cooperation between transmit (or receive) antennas of each user in our transmission scheme, this result shows that the DoF benefit of joint processing in collocated antennas vanishes when the number of users is greater than a certain threshold.

The Gaussian K-user interference and M × K X channels are investigated with no instantaneous channel state information at transmitters (CSIT). First, it is assumed that the CSI is fed back to all nodes after a finite delay (delayed CSIT), and furthermore, the transmitters operate in full-duplex mode, i.e, they can transmit and receive simultaneously. Achievable results on the degrees of freedom (DoFs) of these channels under the above assumption are obtained. It is observed that, in contrast with no CSIT and full CSIT models, when CSIT is delayed, the achievable DoFs for both channels with the full-duplex transmitter cooperation are greater than the available achievable results on their DoF without transmitter cooperation. Then, K-user interference and K × K X channels are considered with output feedback, wherein the channel output of each receiver is causally fed back to its corresponding transmitter. Our achievable results with output feedback demonstrate strict DoF improvements over those with the full-duplex delayed CSIT when K 5 in the K-user interference channel and K > 2 in the K × K X channel. Next, the combination of delayed CSIT and output feedback, known as Shannon feedback, is studied and strictly higher DoFs compared with the output feedback model are achieved in the K-user interference channel when K = 5 or K 6, and in the K × K X channel when K > 2.

This paper addresses the following question regarding Gaussian networks: Is there an alternative to decoding interference or treating interference as Gaussian noise? To state our result, we study a decentralized network of one primary user (PU) and one secondary user (SU) modeled by a two-user Gaussian interference channel. In one scenario, the primary transmitter is constellation-based and PUs codebook is constructed over its modulation signal set. Assuming SU is aware of the constellation points of PU, the interference plus noise at the secondary receiver is modeled by a mixed Gaussian process. We show that SU can achieve larger rates by matching its decoder to the actual interference plus noise compared with the case where the secondary receiver performs nearest neighbor decoding (NND). In another scenario, we assume that PU utilizes a predetermined point-to-point code. We ask if SU can utilize its knowledge about PUs codebook without decoding PUs codewords. The proposed strategy assumes each transmitted codeword of SU overlaps with infinitely many transmitted codewords of PU, referred to as the unequal codeword-length (UCL) strategy. The secondary receiver views PU as a virtual user that is constellation-based and its modulation signal set is the codebook of the actual PU. UCL is compared with other strategies, namely, interference cancellation (IC), joint decoding, and NND. It is shown that UCL can outperform both IC and NND simultaneously.

The K-user single-input single-output (SISO) additive white Gaussian noise (AWGN) interference channel and 2×K SISO AWGN X channel are considered, where the transmitters have delayed channel state information (CSI) through noiseless feedback links. Multiphase transmission schemes are proposed for both channels which possess novel ingredients, namely, multiphase partial interference nulling, distributed interference management via user scheduling, and distributed higher order symbol generation. The achieved degree-of-freedom (DoF) values are greater than the best previously known DoFs for both channels with delayed CSI at the transmitters.

The Gaussian single-input single-output (SISO) K-user interference and M × K X channels are investigated in i.i.d. fading environment with no instantaneous channel state information (CSI) at transmitters. First, it is assumed that the CSI is fed back to all nodes after some delay (delayed CSIT), and furthermore, the transmitters operate in full-duplex mode. Achievable results on the degrees of freedom (DoF) of these channels under the above assumption are obtained. Then, achievable DoFs are obtained for the K-user interference and K × K X channels with output feedback and also Shannon feedback, which is a combination of output feedback and delayed CSIT, and compared with the achievable DoFs under the full-duplex delayed CSIT assumption.

The multiple-input multiple-output (MIMO) Gaussian X channel in i.i.d. fading environment and with delayed channel state information at transmitters (delayed CSIT) is considered. It is assumed that each transmitter has M antennas and each receiver has N antennas. New achievable results on the sum degrees of freedom (DoF) of this channel are provided and shown to be tight for all possible values of M and N except for 1/2 <; N/M <; 4/3. It is noteworthy that for certain values of M and N, the channel DoF coincides with the DoF of the broadcast channel obtained by assuming perfect transmitter cooperation.

A random access interference channel in which transmitters are active with a certain probability is considered. By adopting the deterministic channel model, the optimum transmission strategy which yields the maximum achievable expected sum-rate, or channel throughput, is characterized for the symmetric case. The optimal transmission strategy achieves the sum-capacity of the deterministic interference channel when both users are active, and opportunistically increases the expected sum-rate when transmitters may not always be active.

We consider a K user Gaussian multiple access system with impulse radio ultra-wideband signaling. The receiver is assumed to treat the Multi-Access Interference (MAI) as additive noise and does not enjoy multiuser detection. It is well known that for such a system the MAI is neither Gaussian nor white. Although, the non-Gaussianity of the MAI has been extensively studied, little attention has been directed to the non-whiteness of it. In this paper, we show that by employing a new front-end filter at the receiver, the non-whiteness of the MAI can be exploited to improve the performance of the single-user detector. We use the signal-to-interference-plus-noise ratio (SINR) as a merit to evaluate the performance improvement brought to the system. The SINR improvement depends on the interference level as well as pulse waveform. The bit error rate of the system is also simulated and compared with that of conventional matched filter receiver.

We investigate the three-user MIMO Gaussian broadcast channel with i.i.d. fading and the same number of antennas at each receiver, and with the delayed channel state information at the transmitter (CSIT). We obtain achievability results on the degrees of freedom (DoF) of this channel and also show that our achievable DoF is tight for some ranges of transmit-receive antenna ratio. It is observed that when the number of antennas at the transmitter is strictly greater than that at each receiver, the DoF with delayed CSIT lies strictly between the DoF with perfect CSIT and DoF with no CSIT.

We consider the X channel and the 3-user X network with independent and identically distributed fading across antennas and channel uses and with the delayed channel state information at the transmitters (CSIT). We provide new results for degrees of freedom of these channels. Specifically, we show that the single antenna X channel with delayed CSIT can achieve 6/5 degrees of freedom while the 3-user X network can achieve 5/4 degrees of freedom.

This paper addresses the following question regarding Gaussian networks: Is there an alternative to decoding interference or treating interference as Gaussian noise? By answering this question we aim to establish a benchmark for practical systems where multiuser decoding is not a common practice. To state our result, we study a decentralized network of one Primary User (PU) and one Secondary User (SU) modeled by a two-user Gaussian interference channel. The primary transmitter is constellation-based, i.e., PU is equipped with a modulator and its code-book is constructed over a modulation signal set. SU utilizes random Gaussian codewords with controlled transmission power that guarantees a certain level of Interference-to-Noise Ratio (INR) at the primary receiver. Both users are unaware of each other's code-book, however, SU is smart in the sense that it is aware of the constellation set of PU. While interference at the primary receiver is modeled as additive Gaussian noise, the secondary receiver can utilize the structure of PU's modulator as side information to decode its message without decoding the message of PU. The instantaneous realizations of symbols in a codeword transmitted by PU are unknown to both ends of SU's direct link, however, the sample space of such symbols is available to SU. This makes the interference plus noise at the secondary receiver be a mixed Gaussian process. Invoking entropy power inequality and an upper bound on the differential entropy of a mixed Gaussian vector, we develop an achievable rate for SU that is robust to the structure of PU's modulation signal set and only depends on its constellation size and the dimension of the euclidean space that the constellation points lie in. Moreover, we obtain an achievable rate for PU using Fano's inequality in conjunction with a Gallager-type upper bound on the probability of error in decoding constellation points at the primary receiver. The developed achievable rates for PU and SU enable us to show that the sum rate can be improved compared to a scenario where both users employ Gaussian codewords and treat each other as Gaussian noise.

We consider the K user Multiple Input Multiple Output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver. It is assumed that channel coefficients are fixed and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the total Degrees Of Freedom (DOF) for this channel. Using a new interference alignment technique which has been recently introduced in, we show that MN/M+N K degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the total DOF for this channel is derived. This upper-bound coincides with our achievable DOF for K ≥ Ku=ΔM+N/gcd(M,N) where gcd(M,N) denotes the greatest common divisor of M and N. This gives an exact characterization of DOF for MIMO Gaussian interference channel in the case of K ≥ Ku.

Ultra-wideband (UWB) is a very promising wireless technology for short ranges, because of its many benefits. A common practice in UWB is time hopping (TH)-PAM impulse radio system, in which a number of extremely short pulses are transmitted for each bit and the polarity of pulses determines the bit. In multi-user environments, the interference from other users [multiple access interference (MAI)] may well dominate the Gaussian noise which makes the matched filter receiver be a suboptimal receiver. A model for the statistical structure of MAI in an additive white Gaussian noise channel is presented. Then, using this model, the authors propose a nonlinear pulse combining scheme for the receiver of TH-PAM systems. The bit error rate (BER) of our receiver is compared with that of matched filter receiver and blinking receiver, via simulations. The simulation results show that our receiver always outperforms the matched filter receiver. Blinking receiver performs better than our receiver only when the probability of collision is low and the energy of interfering users is high. In all other cases, our receiver has a lower BER than the blinking receiver. Furthermore, the blinking receiver needs to know the locations of all the interfering pulses, while in our method such information is not required.

As the UWB systems are designed to operate in environments having dense multipath characteristics (i.e., indoor environments) the channel estimation task is much more involved than the conventional systems. In this paper, we present a new blind channel estimation technique for Time-Hopping Pluse-Position-Modulation (TH-PPM) systems. Our proposed method is based on the Pulse Compression (PC) technique introduced in [1]. In spite of its low complexity, the proposed blind channel estimation method outperforms the Non-Data Aided Maximum Likelihood (NDA-ML) technique. Our simulation results show the promising gain of 4 dB around the Bit Error Rate (BER) of 10-3, compared to NDA-ML. The performance loss, compared to the Perfect Channel Knowledge (PCK) is only 1.5 dB at this BER.