The "writing dirty paper" capacity result crucially dependents on the perfect channel knowledge at the transmitter as the presence of even a small uncertainty in the channel realization gravely hampers the ability of the transmitter to pre-code its transmission against the channel state. This is particularly disappointing as it implies that interference pre-coding in practical systems is effective only when the channel estimates at the users have very high precision, a condition which is generally unattainable in wireless environments. In this paper we show that substantial improvements are possible when the state sequence is drawn from a discrete distribution, such as a constrained input constellation, for which state decoding can be approximately optimal. We consider the "writing on dirty paper" channel in which the state sequence is multiplied by a fast fading process and derive conditions on the fading and state distributions for which state decoding closely approaches capacity. These conditions intuitively relate to the ability of the receiver to correctly identify both the input and the state realization despite of the uncertainty introduced by fading.
We investigate the impact of fading correlation on the performance of the doubly dirty fading multiple access channel (MAC) with non-causally known side information at transmitters. Using Copula theory, we derive closed-form expressions for the outage probability and the coverage region under arbitrary dependence conditions. We show that a positive dependence structure between the fading channel coefficients is beneficial for the system performance, as it improves the outage probability and extends the coverage region compared to the case of independent fading. Conversely, a negative dependenc…
The classical writing on dirty paper capacity result establishes that full interference pre-cancellation can be attained in Gelfand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the idealized assumption that perfect channel knowledge is available at both transmitter and receiver. While channel knowledge at the receiver can be obtained through pilot tones, transmitter channel knowledge is harder to acquire. For this reason, we are interested in characterizing the capacity under the more realistic assumption that only partial channel knowledge is …
A multiple-input multiple-output (MIMO) version of the dirty paper channel is studied, where the channel input and the dirt experience the same fading process and the fading channel state is known at the receiver (CSIR). This represents settings where signal and interference sources are co-located, such as in the broadcast channel. First, a variant of Costa's dirty paper coding (DPC) is presented, whose achievable rates are within a constant gap to capacity for all signal and dirt powers. Additionally, a lattice coding and decoding scheme is proposed, whose decision regions are independent of …
The impact of phase fading on the classical Costa dirty paper coding channel is studied. We consider a variation of this channel model in which the amplitude of the interference sequence is known at the transmitter while its phase is known at the receiver. Although the capacity of this channel has already been established, it is expressed using an auxiliary random variable and as the solution of a maximization problem. To circumvent the difficulty evaluating capacity, we derive alternative inner and outer bounds and show that the two expressions are to within a finite distance. This provide an…
This paper studies a variant of the classical problem of ``writing on dirty paper'' in which the sum of the input and the interference, or dirt, is multiplied by a random variable that models resizing, known to the decoder but not to the encoder. The achievable rate of Costa's dirty paper coding (DPC) scheme is calculated and compared to the case of the decoder's also knowing the dirt. In the ergodic case, the corresponding rate loss vanishes asymptotically in the limits of both high and low signal-to-noise ratio (SNR), and is small at all finite SNR for typical distributions like Rayleigh, Ri…
Costa`s "writing on dirty paper" result establishes that full state pre-cancellation can be attained in the Gel`fand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the assumptions that full channel knowledge is available at both the transmitter and the receiver. In this work we consider the scenario in which the state is multiplied by an ergodic fading process which is not known at the encoder. We study both the case in which the receiver has knowledge of the fading and the case in which it does not: for both models we derive inner and outer boun…
The problem of Dirty Paper Coding (DPC) over the Fading Dirty Paper Channel (FDPC) Y = H(X + S)+Z, a more general version of Costa's channel, is studied for the case in which there is partial and perfect knowledge of the fading process H at the transmitter (CSIT) and the receiver (CSIR), respectively. A key step in this problem is to determine the optimal inflation factor (under Costa's choice of auxiliary random variable) when there is only partial CSIT. Towards this end, two iterative numerical algorithms are proposed. Both of these algorithms are seen to yield a good choice for the inflatio…
In this paper, we examine the effects of imperfect channel estimation at the receiver and no channel knowledge at the transmitter on the capacity of the fading Costa's channel with channel state information non-causally known at the transmitter. We derive the optimal Dirty-paper coding (DPC) scheme and its corresponding achievable rates with the assumption of Gaussian inputs. Our results, for uncorrelated Rayleigh fading, provide intuitive insights on the impact of the channel estimate and the channel characteristics (e.g. SNR, fading process, channel training) on the achievable rates. These a…
The problem of dirty paper coding (DPC) over the (multi-antenna) fading dirty paper channel (FDPC) Y = H(X + S) + Z is considered when there is imperfect knowledge of the channel state information H at the transmitter (CSIT). The case of FDPC with positive definite (p.d.) input covariance matrix was studied by the authors in a recent paper, and here the more general case of positive semi-definite (p.s.d.) input covariance is dealt with. Towards this end, the choice of auxiliary random variable is modified. The algorithms for determination of inflation factor proposed in the p.d. case are then …
We characterize the capacity region of a two-user multiple access channel (MAC) in a reconfigurable intelligent surface (RIS)-aided communication system with side information (SI) at the transmitters. We consider two uplink communication scenarios: (i) a double dirty MAC where the interferences are known non-causally to both users; and (ii) a single dirty MAC model where only one of the users knows the interference and the other one is not aware of the interference. Considering that each of the users is assisted by a different RIS with Mi elements, we derive closed-form expressions for the cap…
We consider transmission over the ergodic fading multi-antenna broadcast (MIMO-BC) channel with partial channel state information at the transmitter and full information at the receiver. Over the equivalent {\it non}-fading channel, capacity has recently been shown to be achievable using transmission schemes that were designed for the ``dirty paper'' channel. We focus on a similar ``fading paper'' model. The evaluation of the fading paper capacity is difficult to obtain. We confine ourselves to the {\it linear-assignment} capacity, which we define, and use convex analysis methods to prove that…
Dirty paper codes are a powerful tool for combating known interference. However, there is a significant difference between knowing the transmitted interference sequence and knowing the received interference sequence, especially when the channel modifying the interference is uncertain. We present an upper bound on the capacity of a compound vector dirty paper channel where although an additive Gaussian sequence is known to the transmitter, the channel matrix between the interferer and receiver is uncertain but known to lie within a bounded set. Our bound is tighter than previous bounds in the l…
A wideband fading channel is considered with causal channel state information (CSI) at the transmitter and no receiver CSI. A simple orthogonal code with energy detection rule at the receiver (similar to [6]) is shown to achieve the capacity of this channel in the limit of large bandwidth. This code transmits energy only when the channel gain is large enough. In this limit, this capacity without any receiver CSI is the same as the capacity with full receiver CSI--a phenomenon also true for dirty paper coding. For Rayleigh fading, this capacity (per unit time) is proportional to the logarithm o…
In this paper we consider the State-Dependent Wiretap Channel (SD-WC). As the main idea, we model the SD-WC as a Cognitive Interference Channel (CIC), in which the primary receiver acts as an eavesdropper for the cognitive transmitter's message. By this point of view, the Channel State Information (CSI) in SD-WC plays the role of the primary user's message in CIC which can be decoded at the eavesdropper. This idea enables us to use the main achievability approaches of CIC, i.~e., Gel'fand-Pinsker Coding (GPC) and Superposition Coding (SPC), to find new achievable equivocation-rates for the SD-…
In this paper, the problem of writing on a dirty paper in the presence of jamming is examined. We consider an AWGN channel with an additive white Gaussian state and an additive adversarial jammer. The state is assumed to be known non-causally to the encoder and the jammer but not to the decoder. The capacity of the channel in the presence of a jammer is determined. A surprising result that this capacity is equal to the capacity of a relaxed version of the problem, where the state is also known non-causally to the decoder, is proved.
The "Carbon Copy onto Dirty Paper" (CCDP) channel is the compound "writing on dirty paper" channel in which the channel output is obtained as the sum of the channel input, white Gaussian noise and a Gaussian state sequence randomly selected among a set possible realizations. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output. We study the capacity of the CCDP channel for two scenarios: (i) the state sequences are independent and identically distributed, and (ii) the state sequences are scale…
This paper investigates downlink transmission over a quasi-static fading Gaussian broadcast channel (BC), to model delay-sensitive applications over slowly time-varying fading channels. System performance is characterized by outage achievable rate regions. In contrast to most previous work, here the problem is studied under the key assumption that the transmitter only knows the probability distributions of the fading coefficients, but not their realizations. For scalar-input channels, two coding schemes are proposed. The first scheme is called blind dirty paper coding (B-DPC), which utilizes a…
The additive exponential noise channel with additive exponential interference (AENC-AEI) known non-causally at the transmitter is studied. This channel can be considered as an exponential version of the discrete memoryless channel with state known non-causally at the encoder considered by Gelfand and Pinsker. We make use of Gelfand-Pinsker classic capacity Theorem to derive inner and outer bounds on the capacity of this channel under a non-negative input constraint as well as a constraint on the mean value of the input. First we obtain an outer bound for AENC-AEI. Then by using the input distr…
In this paper, the Two-Way Channel (TWC) with Cannel State Information (CSI) is investigated. First, an achievable rate region is derived for the discrete memoryless channel. Then by extending the result to the Gaussian TWC with additive interference noise, it is shown that the capacity region of the later channel is the same as the capacity when there is no interference, i.e. a two-way version of Costa's writing on dirty paper problem is established.
Recently there has been a lot of success in using the deterministic approach to provide approximate characterization of Gaussian network capacity. In this paper, we take a deterministic view and revisit the problem of wiretap channel with side information. A precise characterization of the secrecy capacity is obtained for a linear deterministic model, which naturally suggests a coding scheme which we show to achieve the secrecy capacity of the degraded Gaussian model (dubbed as "secret writing on dirty paper") to within half a bit.
The dirty paper channel (DPC) under a peak amplitude constraint arises in an optical wireless broadcast channel (BC), where the state at one receiver is the transmitted signal intended for the other receiver(s). This paper studies a class of peak-constrained DPC that is applicable to the optical wireless BC, where the channel state (i.e, `dirt') takes values from some evenly-spaced grid. For the discrete-state DPC studied this paper, a capacity upper bound is obtained from its state-free counterpart. To lower bound its capacity, classical dirty paper coding schemes are revisited, including Cos…
Costa's "writing on dirty paper" capacity result establishes that full state pre-cancellation can be attained in Gelfand-Pinsker channel with additive state and additive Gaussian noise. The "carbon copy onto dirty paper" channel is the extension of Costa's model to the compound setting: M receivers each observe the sum of the channel input, Gaussian noise and one of M Gaussian state sequences and attempt to decode the same common message. The state sequences are all non-causally known at the transmitter which attempts to simultaneously pre-code its transmission against the channel state affect…
We consider the Gaussian Dirty Tape Channel (DTC) Y=X+S+Z, where S is an additive Gaussian interference known causally to the transmitter. The general expression [max]\_top(P_U,f(.),X=f(U,S))I(U;Y) is presented for the capacity of this channel. For linear assignment to f(.), i.e. X=U-βS, this expression leads to the compensation strategy proposed previously by Willems to obtain an achievable rate for the DTC. We show that linear assignment to f(.) is optimal, under the condition that there exists a real number β^* such that the pair (X+β^* S,U) is independent of interference S. Furthermore, by…
A modification is proposed for the formula known from the literature that characterizes the boundary of the capacity region of Gaussian multiaccess fading channels. The modified version takes into account potentially negative arguments of the cumulated density function that would affect the accuracy of the numerical capacity results.
We develop a characterization of fading models, which assigns a number called logarithmic Jensen's gap to a given fading model. We show that as a consequence of a finite logarithmic Jensen's gap, approximate capacity region can be obtained for fast fading interference channels (FF-IC) for several scenarios. We illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic Jensen's gap. Firstly for an FF-IC with neither feedback nor instantaneous channel state information at transmitter (CSIT), if the fading distribution has finite logarithmic Jensen's…
The "Writing onto Fast Fading Dirt" (WFFD) channel is investigated to study the effects of partial channel knowledge on the capacity of the "writing on dirty paper" channel. The WFFD channel is the Gel'fand-Pinsker channel in which the output is obtained as the sum of the input, white Gaussian noise and a fading-times-state term. The fading-times-state term is equal to the element-wise product of the channel state sequence, known only at the transmitter, and a fast fading process, known only at the receiver. We consider the case of Gaussian distributed channel states and derive an approximate …
For delay-limited communication over block-fading channels, the difference between the ergodic capacity and the maximum achievable expected rate for coding over a finite number of coherent blocks represents a fundamental measure of the penalty incurred by the delay constraint. This paper introduces a notion of worst-case expected-capacity loss. Focusing on the slow-fading scenario (one-block delay), the worst-case additive and multiplicative expected-capacity losses are precisely characterized for the point-to-point fading channel. Extension to the problem of writing on fading paper is also co…
The ergodic and outage channel capacity of different optimal and suboptimal combinations of transmit power and modulation rate adaptation strategies over a joint fading and two-path shadowing (JFTS) fading/shadowing channel is studied in this paper. Analytically tractable expressions for channel capacity are obtained, assuming perfect channel side information (CSI) at the receiver and/or the transmitter with negligible feedback delay. Furthermore, the impacts of the JFTS parameters on the channel capacity achieved by these adaptive transmission techniques are determined.
There are currently a plurality of capacity theories of fading channels, including the ergodic capacity for fast fading channels and outage capacity for slow fading channels. However, analyses show that the outage capacity is a misconception. In this paper we use the 1st order Gaussian-Markov process with coherence coefficient $α$ as the unified model for slow and fast fading channels, the capacity of which without channel side information is studied. We demonstrate that the information rate of a fading channel has a structure that the rate of user message is always accompanied by a rate of ch…
A generalization of the problem of writing on dirty paper is considered in which one transmitter sends a common message to multiple receivers. Each receiver experiences on its link an additive interference (in addition to the additive noise), which is known noncausally to the transmitter but not to any of the receivers. Applications range from wireless multi-antenna multicasting to robust dirty paper coding. We develop results for memoryless channels in Gaussian and binary special cases. In most cases, we observe that the availability of side information at the transmitter increases capacity r…
We analyze the impact of arbitrary dependence between the forward and backward links in backscatter communication systems. Specifically, we quantify the effect of positive and negative dependence between these fading links on channel capacity, using Copula theory. The benefits of this approach are highlighted over the classical framework of linear dependence based on Pearson's correlation coefficient, which is also analyzed. Results show that for a fixed transmit power budget, capacity grows with positive dependence as well as with fading severity in the low signal-to-noise ratio (SNR) regime.…
Accurate fading characterization and channel capacity determination are of paramount importance in both conventional and emerging communication systems. The present work addresses the nonlinearity of the propagation medium and its effects on the channel capacity. Such fading conditions are first characterized using information theoretic measures, namely, Shannon entropy, cross entropy and relative entropy. The corresponding effects on the channel capacity with and without power adaptation are then analyzed. Closed-form expressions are derived and validated through comparisons with respective r…
The capacity of non-coherent stationary Gaussian fading channels with memory under a peak-power constraint is studied in the asymptotic weak-signal regime. It is assumed that the fading law is known to both transmitter and receiver but that neither is cognizant of the fading realization. A connection is demonstrated between the asymptotic behavior of channel capacity in this regime and the asymptotic behavior of the prediction error incurred in predicting the fading process from very noisy observations of its past. This connection can be viewed as the low signal-to-noise ratio (SNR) analog of …
Cognitive radio technology is an innovative radio design concept which aims to increase spectrum utilization by exploiting unused spectrum in dynamically changing environments. By extending previous results, we investigate the capacity gains achievable with this dynamic spectrum approach in asymmetric fading channels. More specifically, we allow the secondary-to-primary and secondary-to-secondary user channels to undergo Rayleigh or Rician fading, with arbitrary link power. In order to compute the capacity, we derive the distributions of ratios of Rayleigh and Rician variables. Compared to the…
In slow fading scenarios, cooperation between nodes can increase the amount of diversity for communication. We study the performance limit in such scenarios by analyzing the outage capacity of slow fading relay channels. Our focus is on the low SNR and low outage probability regime, where the adverse impact of fading is greatest but so are the potential gains from cooperation. We showed that while the standard Amplify-Forward protocol performs very poorly in this regime, a modified version we called the Bursty Amplify-Forward protocol is optimal and achieves the outage capacity of the network.…
We characterize the capacity of the general class of noncoherent underspread wide-sense stationary uncorrelated scattering (WSSUS) time-frequency-selective Rayleigh fading channels, under peak constraints in time and frequency and in time only. Capacity upper and lower bounds are found which are explicit in the channel's scattering function and allow to identify the capacity-maximizing bandwidth for a given scattering function and a given peak-to-average power ratio.
The effective capacity of communication systems over generalized $κ$-$μ$ shadowed fading channels is investigated in this letter. A novel and analytical expression for the exact effective capacity is derived in terms of extended generalized bivariate Meijer's-$G$ function. To intuitively reveal the impact of the system and channel parameters on the effective capacity, we also derive closed-form expressions for the effective capacity in the asymptotically high signal-to-noise ratio regime. Our results demonstrate that the effective capacity is a monotonically increasing function of channel fadi…
In this paper, we investigate upper and lower bounds on the capacity of two-user fading broadcast channels where one of the users has a constant (non-fading) channel. We use the Costa entropy power inequality (EPI) along with an optimization framework to derive upper bounds on the sum-capacity and superposition coding to obtain lower bounds on the sum-rate for this channel. For this fading broadcast channel where one channel is constant, we find that the upper and lower bounds meet under special cases, and in general, we show that the achievable sum-rate comes within a constant of the outer bo…
We investigate the problem of common randomness (CR) generation from discrete correlated sources aided by one-way communication over single-user multiple-input multiple-output (MIMO) slow fading channels with additive white Gaussian noise (AWGN), arbitrary state distribution and with channel state information available at the receiver side (CSIR). We completely solve the problem by first characterizing the channel outage capacity of MIMO slow fading channels for arbitrary state distribution. For this purpose, we also provide an achievable rate for a specific compound MIMO Gaussian channel. Sec…
The ergodic capacity of underlay cognitive (secondary) dual-hop relaying systems is analytically investigated. Specifically, the amplify-and-forward transmission protocol is considered, while the received signals undergo multipath fading and shadowing with non-identical statistics. To efficiently describe this composite type of fading, the well-known generalized-$K$ fading model is used. New analytical expressions and quite accurate closed-form approximations regarding the ergodic capacity of the end-to-end communication are obtained, in terms of finite sum series of the Meijer's-$G$ function.…
The covert capacity is characterized for a non-coherent fast Rayleigh-fading wireless channel, in which a legitimate user wishes to communicate reliably with a legitimate receiver while escaping detection from a warden. It is shown that the covert capacity is achieved with an amplitude-constrained input distribution that consists of a finite number of mass points including one at zero and numerically tractable bounds are provided. It is also conjectured that distributions with two mass points in fixed locations are optimal.
A discrete-time single-user scalar channel with temporally correlated Rayleigh fading is analyzed. There is no side information at the transmitter or the receiver. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The simple formula of Verdu for capacity per unit cost is adapted to a channel with memory, and is used in the proof. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity. The results are ext…
In this letter, we study the ergodic capacity of a maximum ratio combining (MRC) Rician fading channel with full channel state information (CSI) at the transmitter and at the receiver. We focus on the low Signal-to-Noise Ratio (SNR) regime and we show that the capacity scales as (L Omega/(K+L)) SNR log(1/SNR), where Omega is the expected channel gain per branch, K is the Rician fading factor, and L is the number of diversity branches. We show that one-bit CSI feedback at the transmitter is enough to achieve this capacity using an on-off power control scheme. Our framework can be seen as a gene…
Discrete-time Rayleigh fading multiple-input multiple-output (MIMO) channels are considered, with no channel state information at the transmitter and receiver. The fading is assumed to be correlated in time and independent from antenna to antenna. Peak and average transmit power constraints are imposed, either on the sum over antennas, or on each individual antenna. In both cases, an upper bound and an asymptotic lower bound, as the signal-to-noise ratio approaches zero, on the channel capacity are presented. The limit of normalized capacity is identified under the sum power constraints, and, …
The effect of Rician-ness on the capacity of multiple antenna systems is investigated under the assumption that channel state information (CSI) is available only at the receiver. The average-power-constrained capacity of such systems is considered under two different assumptions on the knowledge about the fading available at the transmitter: the case in which the transmitter has no knowledge of fading at all, and the case in which the transmitter has knowledge of the distribution of the fading process but not the instantaneous CSI. The exact capacity is given for the former case while capacity…
This paper deals with fading and/or near-far effects with or without power control on the evaluation of the sum capacity of finite dimensional Code Division Multiple Access (CDMA) systems for binary and finite nonbinary inputs and signature matrices. Important results of this paper are that the knowledge of the received power variations due to input power differences, fading and/or near-far effects can significantly improve the sum capacity. Also traditional power controls can not improve the sum capacity; for the asymptotic case, any type of power control on the near-far effects is equivalent…
We study the throughput capacity region of the Gaussian multi-access (MAC) fading channel with perfect channel state information (CSI) at the receiver and at the transmitters, at low power regime. We show that it has a multidimensional rectangle structure and thus is simply characterized by single user capacity points. More specifically, we show that at low power regime, the boundary surface of the capacity region shrinks to a single point corresponding to the sum rate maximizer and that the coordinates of this point coincide with single user capacity bounds. Inspired by this result, we propos…
The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The secrecy capacity region is first established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived…
This paper investigates the limits of information transfer over a fast Rayleigh fading MIMO channel, where neither the transmitter nor the receiver has the knowledge of the channel state information (CSI) except the fading statistics. We develop a scalar channel model due to absence of the phase information in non-coherent Rayleigh fading and derive a capacity supremum with the number of receive antennas at any signal to noise ratio (SNR) using Lagrange optimisation. Also, we conceptualise the discrete nature of the optimal input distribution by posing the optimisation on the channel mutual in…
A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna. It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signal-to-noise (SNR) throughput is greatly reduced if, rather than knowing the fading realization \emph{precisely}, the trasmitter only knows the fading realization \emph{approximately}. The results are general and are not limited to memoryless Gaussian fading.
We establish an upper bound on the noncoherent capacity pre-log of temporally correlated block-fading single-input multiple-output (SIMO) channels. The upper bound matches the lower bound recently reported in Riegler et al. (2011), and, hence, yields a complete characterization of the SIMO noncoherent capacity pre-log, provided that the channel covariance matrix satisfies a mild technical condition. This result allows one to determine the optimal number of receive antennas to be used to maximize the capacity pre-log for a given block-length and a given rank of the channel covariance matrix.
This paper investigates the Gaussian state-dependent interference channel (IC) and Z-IC, in which two receivers are corrupted respectively by two different but correlated states that are noncausally known to two transmitters but are unknown to the receivers. Three interference regimes are studied, and the capacity region boundary or the sum capacity boundary is characterized either fully or partially under various channel pa- rameters. In particular, the impact of the correlation between states on cancellation of state and interference as well as achievability of capacity is explored with nume…
The sum-capacity for specific sub-classes of ergodic fading Gaussian two-user interference channels (IFCs) is developed under the assumption of perfect channel state information at all transmitters and receivers. For the sub-classes of uniformly strong (every fading state is strong) and ergodic very strong two-sided IFCs (a mix of strong and weak fading states satisfying specific fading averaged conditions) the optimality of completely decoding the interference, i.e., converting the IFC to a compound multiple access channel (C-MAC), is proved. It is also shown that this capacity-achieving sche…
In this paper we consider the capacity of the cognitive radio channel in different fading environments under a low interference regime. First we derive the probability that the low interference regime holds under shadow fading as well as Rayleigh and Rician fast fading conditions. We demonstrate that this is the dominant case, especially in practical cognitive radio deployment scenarios. The capacity of the cognitive radio channel depends critically on a power loss parameter, $α$, which governs how much transmit power the cognitive radio dedicates to relaying the primary message. We derive a s…
We investigate the problem of message transmission over time-varying single-user multiple-input multiple-output (MIMO) Rayleigh fading channels with average power constraint and with complete channel state information available at the receiver side (CSIR). To describe the channel variations over the time, we consider a first-order Gauss-Markov model. We completely solve the problem by giving a single-letter characterization of the channel capacity in closed form and by providing a rigorous proof of it.
The capacity of peak-power limited, single-antenna, non-coherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log.
