How much feedback is required in MIMO Broadcast Channels?

In this paper, a downlink communication system, in which a Base Station (BS) equipped with M antennas communicates with N users each equipped with K receive antennas ($K \leq M$), is considered. It is assumed that the receivers have perfect Channel State Information (CSI), while the BS only knows the partial CSI, provided by the receivers via feedback. The minimum amount of feedback required at the BS, to achieve the maximum sum-rate capacity in the asymptotic case of $N \to \infty$ and different ranges of SNR is studied. In the fixed and low SNR regimes, it is demonstrated that to achieve the maximum sum-rate, an infinite amount of feedback is required. Moreover, in order to reduce the gap to the optimum sum-rate to zero, in the fixed SNR regime, the minimum amount of feedback scales as $\theta(\ln \ln \ln N)$, which is achievable by the Random Beam-Forming scheme proposed in [14]. In the high SNR regime, two cases are considered; in the case of $K < M$, it is proved that the minimum amount of feedback bits to reduce the gap between the achievable sum-rate and the maximum sum-rate to zero grows logaritmically with SNR, which is achievable by the "Generalized Random Beam-Forming" scheme, proposed in [18]. In the case of $K = M$, it is shown that by using the Random Beam-Forming scheme and the total amount of feedback not growing with SNR, the maximum sum-rate capacity is achieved.Comment: Submitted to IEEE Trans. on Inform. Theor

Rate-Constrained Wireless Networks with Fading Channels: Interference-Limited and Noise-Limited Regimes

A network of $n$ wireless communication links is considered in a Rayleigh fading environment. It is assumed that each link can be active and transmit with a constant power $P$ or remain silent. The objective is to maximize the number of active links such that each active link can transmit with a constant rate $\lambda$. An upper bound is derived that shows the number of active links scales at most like $\frac{1}{\lambda} \log n$. To obtain a lower bound, a decentralized link activation strategy is described and analyzed. It is shown that for small values of $\lambda$, the number of supported links by this strategy meets the upper bound; however, as $\lambda$ grows, this number becomes far below the upper bound. To shrink the gap between the upper bound and the achievability result, a modified link activation strategy is proposed and analyzed based on some results from random graph theory. It is shown that this modified strategy performs very close to the optimum. Specifically, this strategy is \emph{asymptotically almost surely} optimum when $\lambda$ approaches $\infty$ or 0. It turns out the optimality results are obtained in an interference-limited regime. It is demonstrated that, by proper selection of the algorithm parameters, the proposed scheme also allows the network to operate in a noise-limited regime in which the transmission rates can be adjusted by the transmission powers. The price for this flexibility is a decrease in the throughput scaling law by a multiplicative factor of $\log \log n$.Comment: Submitted to IEEE Trans. Information Theor

Media-Based MIMO: A New Frontier in Wireless Communications

The idea of Media-based Modulation (MBM), is based on embedding information in the variations of the transmission media (channel state). This is in contrast to legacy wireless systems where data is embedded in a Radio Frequency (RF) source prior to the transmit antenna. MBM offers several advantages vs. legacy systems, including "additivity of information over multiple receive antennas", and "inherent diversity over a static fading channel". MBM is particularly suitable for transmitting high data rates using a single transmit and multiple receive antennas (Single Input-Multiple Output Media-Based Modulation, or SIMO-MBM). However, complexity issues limit the amount of data that can be embedded in the channel state using a single transmit unit. To address this shortcoming, the current article introduces the idea of Layered Multiple Input-Multiple Output Media-Based Modulation (LMIMO-MBM). Relying on a layered structure, LMIMO-MBM can significantly reduce both hardware and algorithmic complexities, as well as the training overhead, vs. SIMO-MBM. Simulation results show excellent performance in terms of Symbol Error Rate (SER) vs. Signal-to-Noise Ratio (SNR). For example, a $4\times 16$ LMIMO-MBM is capable of transmitting $32$ bits of information per (complex) channel-use, with SER $\simeq 10^{-5}$ at $E_b/N_0\simeq -3.5$dB (or SER $\simeq 10^{-4}$ at $E_b/N_0=-4.5$dB). This performance is achieved using a single transmission and without adding any redundancy for Forward-Error-Correction (FEC). This means, in addition to its excellent SER vs. energy/rate performance, MBM relaxes the need for complex FEC structures, and thereby minimizes the transmission delay. Overall, LMIMO-MBM provides a promising alternative to MIMO and Massive MIMO for the realization of 5G wireless networks.Comment: 26 pages, 11 figures, additional examples are given to further explain the idea of Media-Based Modulation. Capacity figure adde

Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction

A simple scheme for communication over MIMO broadcast channels is introduced which adopts the lattice reduction technique to improve the naive channel inversion method. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. Simulation results show that the proposed scheme performs well, and as compared to the more complex methods (such as the perturbation method) has a negligible loss. Moreover, the proposed method is extended to the case of different rates for different users. The asymptotic behavior of the symbol error rate of the proposed method and the perturbation technique, and also the outage probability for the case of fixed-rate users is analyzed. It is shown that the proposed method, based on LLL lattice reduction, achieves the optimum asymptotic slope of symbol-error-rate (called the precoding diversity). Also, the outage probability for the case of fixed sum-rate is analyzed.Comment: Submitted to IEEE Trans. on Info. Theory (Jan. 15, 2006), Revised (Jun. 12, 2007