Channel State Information At The Receiver Research Articles

Cutoff Rate of MIMO Systems in Rayleigh Fading Channels With Imperfect CSIR and Finite Frame Error Probability

Using the random coding argument, in this paper, we derive the effective cutoff rate R E of multiple-input-multiple-output (MIMO) space-time (ST) codes in Rayleigh fast-fading channels with imperfect channel state information at the receiver (CSIR). In contrast to conventional cutoff rate analysis, where the codeword length N is infinity and the frame error probability Pf is implicitly zero, we loosen the definition to include the more realistic case of finite N and finite P f. Using the tight upper and lower bounds on the pairwise error probability (PEP) in the work of Li and Kam, we are able to derive in turn tight lower and upper bounds on the cutoff rate of MIMO ST coding systems. The results are very general and can be applied to any linear modulation scheme, like M-ary phase-shift keying (MPSK) and M-ary quadrature-amplitude modulation (MQAM). Numerically, we found that for the two-transmit and two-receive antenna configuration, the nonasymptotic segments of our cutoff rate upper bounds for four, 16, and 64 MQAM actually coincide with the ergodic capacity curve. Furthermore, we found that the performance of the Smart-Greedy codes proposed in the seminal work of Tarokh falls within the range predicted by our cutoff rate bounds. Finally, we show in this paper that for MIMO systems employing pilot-symbol-assisted channel estimation, the asymptotic cutoff rate no longer linearly increases with the number of transmit antennas. Instead, for a normalized fade rate of fD and a signal constellation of size M, the maximum effective cutoff rate is (8f D)-1log2 M, which is achieved when the number of transmit antennas is the integer closest to 1/(4f D) . The result suggests that with a large antenna array and high user mobility, a more bandwidth-efficient channel-estimation strategy is desired.

Energy-efficient multiuser SIMO: achieving probabilistic robustness with gaussian channel uncertainty

This paper addresses the joint optimization of power control and receive beamforming vectors for a multiuser singleinput multiple-output (SIMO) antenna system in the uplink in which mobile users are single-antenna transmitters and the base station receiver has multiple antennas. Channel state information at the receiver (CSIR) is exploited but the CSIR is imperfect with its uncertainty being modeled as a random Gaussian matrix. Our objective is to devise an energy-efficient solution to minimize the individual users' transmit power while meeting the users' signal-to-interference plus noise ratio (SINR) constraints, under the consideration of CSIR and its error characteristics. This is achieved by solving a sum-power minimization problem, subject to a collection of users' outage probability constraints on their target SINRs. Regarding the signal power minus the sum of inter-user interferences (SMI) power as Gaussian, an iterative and convergent algorithm which is proved to reach the global optimum for the joint power allocation and receive beamforming solution, is proposed, though the optimization problem is indeed non-convex. A systematic scheme to detect feasibility and find a feasible initial solution, if there exists any, is also devised. Simulation results verify the use of Gaussian approximation and robustness of the proposed algorithm in terms of users' probability constraints, and indicate a significant performance gain as compared to the zero-forcing (ZF) and minimum mean square- error (MMSE) beamforming systems.

The impact of CSI and power allocation on relay channel capacity and cooperation strategies

Capacity gains from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. Under quasi-static phase fading, when all nodes have equal average transmit power along with full channel state information (CSI), it is shown that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the cooperating nodes but only CSI at the receiver (CSIR) is available. When the nodes have equal power with CSIR only, cooperative schemes are shown to offer no capacity improvement over non-cooperation under the same network power constraint. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Under fast Rayleigh fading in the high SNR regime, similar conclusions follow. Cooperative systems provide resilience to fading in channel magnitudes; however, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together for the decode-and-forward scheme to be capacity-achieving. Moreover, to realize capacity improvement, full CSI is necessary in transmitter cooperation, while in receiver cooperation optimal power allocation is essential.

Robust Linear MIMO in the Downlink: A Worst-Case Optimization with Ellipsoidal Uncertainty Regions

This paper addresses the joint robust power control and beamforming design of a linear multiuser multiple-input multiple-output (MIMO) antenna system in the downlink where users are subjected to individual signal-to-interference-plus-noise ratio (SINR) requirements, and the channel state information at the transmitter (CSIT) with its uncertainty characterized by an ellipsoidal region. The objective is to minimize the overall transmit power while guaranteeing the users' SINR constraints for every channel instantiation by designing the joint transmitreceive beamforming vectors robust to the channel uncertainty. This paper first investigates a multiuser MISO system (i.e., MIMO with single-antenna receivers) and by imposing the constraints on an SINR lower bound, a robust solution is obtained in a way similar to that with perfect CSI. We then present a reformulation of the robust optimization problem using S-Procedure which enables us to obtain the globally optimal robust power control with fixed transmit beamforming. Further, we propose to find the optimal robust MISO beamforming via convex optimization and rank relaxation. A convergent iterative algorithm is presented to extend the robust solution for multiuser MIMO systems with both perfect and imperfect channel state information at the receiver (CSIR) to guarantee the worst-case SINR. Simulation results illustrate that the proposed joint robust power and beamforming optimization significantly outperforms the optimal robust power allocation with zeroforcing (ZF) beamformers, and more importantly enlarges the feasibility regions of a multiuser MIMO system.

Channel Coherence in the Low-SNR Regime

Channel capacity in the limit of vanishing signal-to-noise ratio (SNR) per degree of freedom is known to be linear in SNR for fading and nonfading channels, regardless of channel state information at the receiver (CSIR). It has recently been shown that the significant engineering difference between the coherent and the noncoherent fading channels, including the requirement of peaky signaling and the resulting spectral efficiency, is determined by how the capacity limit is approached as SNR tends to zero, or in other words, the sublinear term in the capacity expression. In this paper, we show that this sublinear term is determined by the channel coherence level, which we define to quantify the relation between the SNR and the channel coherence time. This allows us to trace a continuum between the case with perfect CSIR and the case with no CSIR at all. Using this approach, we also evaluate the performance of suboptimal training schemes

On Channels With Partial Channel State Information at the Transmitter

We consider an independent and identically distributed (i.i.d.) state-dependent channel with partial (rate-limited) channel state information (CSI) at the transmitter (CSIT) and full CSI at the receiver (CSIR). The CSIT comprises two parts, both subject to a rate constraint, and communicated over noiseless way-side channels. The first part is coded CSI, provided by a third party (a genie), and the second part is the output of a deterministic scalar quantizer of the state. A single-letter expression for the capacity of the channel is given. In case the CSIT comprises only the coded part, we show that the capacity previously suggested in the literature is too optimistic, and suggest a correction as part of our expression for the information capacity. For the general setting, an optimal coding scheme based upon multiplexing of several codebooks is presented. It is proved that the capacity of the channel is the same whether the quantizer's output is observed causally or noncausally by the encoder. In the rest of the correspondence, we focus on the special case where the system employs a stationary quantizer. Using a rate distortion approach we bound the alphabet's size of the auxiliary random variable (RV) of the information capacity. Next, we turn to the additive white Gaussian noise (AWGN) channel with fading, and show that the determination of the capacity region reduces to finding the optimal genie strategies and the optimal power allocation distribution along the product alphabet of the auxiliary RV and the quantizer's output alphabets. The suggested model can be applied, for example, to an orthogonal frequency-division multiplexing (OFDM) communication system. Here the fading across frequencies comprises the channel state sequence. Coded fading information is provided to the channel encoder via a way-side, rate-limited channel. In addition, since coding operation is expensive, a simpler scheme provides the channel encoder with quantized fading information, e.g., whether each coefficient is above/below a threshold.