Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well-known zero-forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite-rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signal-to-noise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to point-to-point multiple-input multiple-output (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR

MIMO Broadcast Channels With Finite-Rate Feedback

It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.

/pdf/an-overview-of-limited-feedback-in-wireless-communication-1njp2bb1kz.pdf

An overview of limited feedback in wireless communication systems

Multi-user MIMO (MU-MIMO) networks reveal the unique opportunities arising from a joint optimization of antenna combining techniques with resource allocation protocols. Furthermore, it brings robustness with respect to multipath richness, allowing for compact antenna spacing at the BS and, crucially, yielding the diversity and multiplexing gains without the need for multiple antenna user terminals. To realize these gains, however, the BS should be informed with the user's channel coefficients, which may limit practical application to TDD or low-mobility settings. To circumvent this problem and reduce feedback load, combining MU-MIMO with opportunistic scheduling seems a promising direction. The success for this type of scheduler is strongly traffic and QoS-dependent, however.

Shifting the MIMO Paradigm

Multiple-input multiple-output (MIMO) wireless systems use antenna arrays at both the transmitter and receiver to provide communication links with substantial diversity and capacity. Spatial multiplexing is a common space-time modulation technique for MIMO communication systems where independent information streams are sent over different transmit antennas. Unfortunately, spatial multiplexing is sensitive to ill-conditioning of the channel matrix. Precoding can improve the resilience of spatial multiplexing at the expense of full channel knowledge at the transmitter-which is often not realistic. This correspondence proposes a quantized precoding system where the optimal precoder is chosen from a finite codebook known to both receiver and transmitter. The index of the optimal precoder is conveyed from the receiver to the transmitter over a low-delay feedback link. Criteria are presented for selecting the optimal precoding matrix based on the error rate and mutual information for different receiver designs. Codebook design criteria are proposed for each selection criterion by minimizing a bound on the average distortion assuming a Rayleigh-fading matrix channel. The design criteria are shown to be equivalent to packing subspaces in the Grassmann manifold using the projection two-norm and Fubini-Study distances. Simulation results show that the proposed system outperforms antenna subset selection and performs close to optimal unitary precoding with a minimal amount of feedback.

Limited feedback unitary precoding for spatial multiplexing systems

In this paper, we present space shift keying (SSK) as a new modulation scheme, which is based on spatial modulation (SM) concepts. Fading is exploited for multiple-input multiple-output(MIMO) channels to provide better performance over conventional amplitude/phase modulation (APM) techniques. In SSK, it is the antenna index used during transmission that relays information, rather than the transmitted symbols themselves. This absence of symbol information eliminates the transceiver elements necessary for APM transmission and detection (such as coherent detectors). As well, the simplicity involved in modulation reduces the detection complexity compared to that of SM, while achieving almost identical performance gains. Throughout the paper, we illustrate SSK's strength by studying its interaction with the fading channel. We obtain tight upper bounds on bit error probability, and discuss SSK's performance under some non-ideal channel conditions (estimation error and spatial correlation). Analytical and simulation results show performance gains over APM systems (3 dB at a bit error rate of 10-5), making SSK an interesting candidate for future wireless applications. We then extend SSK concepts to incorporate channel coding, where in particular, we consider a bit interleaved coded modulation (BICM) system using iterative decoding for both convolutional and turbo codes. Capacity results are derived, and improvements over APM are illustrated (up to 1 bits/s/Hz), with performance gains of up to 5 dB.

/pdf/space-shift-keying-modulation-for-mimo-channels-4za6dmyo4w.pdf

Space shift keying modulation for MIMO channels

We consider a point-to-point frequency-selective orthogonal frequency division multiplexing (OFDM) channel. Based on a linear minimum mean square error (MMSE) channel estimates from pilot signals, a receiver determines a set of 'on' or active subchannels that maximizes a lower bound on a sum capacity. The capacity bound optimization is constrained to a fixed total power, which is a sum of total training power and a sum of equal transmission power on activated subchannels. We show that as number of subchannels N increases, the optimal training power converges to a deterministic constant while the optimal number of active subchannels increases at the rate of (log N −2 log log N)2. The associated capacity bound tends to infinity at the rate of log N −2 log log N while that with uniform power allocation of all subchannels converges to a constant.

/pdf/on-the-optimal-sum-capacity-for-ofdm-with-on-off-power-1jr29lqa6y.pdf

On the optimal sum capacity for OFDM with on/off power allocation and imperfect channel estimation

We consider downlink max-based scheduling, in which the base station and each user are equipped with a single antenna. In each time slot, the base station obtains the channel gains of all users and selects the user with the largest squared channel gain. Assuming that channel state information at the transmitter (CSIT), i.e., squared channel gain, can be inaccurate, we derive lower bounds for probability of outage, which occurs when a required data rate is not satisfied under a delay constraint. The bounds are tight for Rayleigh fading and show how required rate and CSIT error affect outage performance.

Outage Bound for Max-Based Downlink Scheduling With Imperfect CSIT and Delay Constraint

We propose a bit-allocation scheme for powerline orthogonal frequency-division multiplexing (OFDM) that minimizes total transmit energy subject to total-bit and delay constraints. Multiple delay requirements stem from different sets of data that a transmitter must time-multiplex and transmit to a receiver. The proposed bit allocation takes into account the channel power-to-noise density ratio of subchannels as well as statistic of narrowband interference and impulsive noise that is pervasive in powerline communication (PLC) channels. The proposed scheme is optimal with 1 or 2 sets of data, and is suboptimal with more than 2 sets of data. However, numerical examples show that the proposed scheme performs close to the optimum. Also, it is less computationally complex than the optimal scheme especially when minimizing total energy over large number of data sets. We also compare the proposed scheme with some existing schemes and find that our scheme requires less total transmit energy when the number of delay constraints is large.

Energy-Minimizing Bit Allocation For Powerline OFDM With Multiple Delay Constraints

We propose binary-search user selection that maximizes sum transmission rate in downlink non-orthogonal multiple access (NOMA). The selected existing user shares a downlink channel with a new cell-edge user and applies successive interference cancellation (SIC) to detect the transmitted symbols. The proposed binary search is shown to be significantly less complex than exhaustive search, especially in a large system. If random shadowing exists in the cell, the base station may not select the optimal user and the rate performance can suffer greatly. Simulation and analytical results for log-normal shadowing are also shown.

Rate-Maximizing User Selection for Downlink NOMA with Effect of Log-Normal Shadowing

The study investigated the allocation of transmission power and bits for a point-to-point orthogonal frequency-division multiplexing channel assuming perfect channel information at the receiver, but imperfect channel information at the transmitter. Channel information was quantized at the receiver and was sent back to the transmitter via a finite-rate feedback channel. Based on limited feedback from the receiver, the corresponding transmitter adapted the power level and/or modulation across subcarriers. To reduce the amount of feedback, subcarriers were partitioned into different clusters and an on/off threshold-based power allocation was applied to subcarrier clusters. In addition, two options were proposed to interpolate a channel frequency response from a set of quantized channel gains and apply the optimal water-filling allocation or a greedy bit allocation based on channel interpolation. Proposed schemes with finite feedback rates were shown to perform close to the optimal allocation without a feedback-rate constraint. In the numerical example, channel capacity decreased about 6% from the optimum when one bit of feedback per subcarrier was used.

Wiroonsak Santipach

Papers

On the optimal sum capacity for OFDM with on/off power allocation and imperfect channel estimation

Outage Bound for Max-Based Downlink Scheduling With Imperfect CSIT and Delay Constraint

Energy-Minimizing Bit Allocation For Powerline OFDM With Multiple Delay Constraints

Rate-Maximizing User Selection for Downlink NOMA with Effect of Log-Normal Shadowing

Power and Bit Allocation for Wireless OFDM Channels with Finite-Rate Feedback and Subcarrier Clustering