## Optimizing the Transmit Power for Slow Fading Channels (2000)

Venue: | IEEE Transactions on Information Theory |

Citations: | 8 - 0 self |

### BibTeX

@ARTICLE{Ligdas00optimizingthe,

author = {Paschalis Ligdas and Nariman Farvardin},

title = {Optimizing the Transmit Power for Slow Fading Channels},

journal = {IEEE Transactions on Information Theory},

year = {2000},

volume = {46},

pages = {565--576}

}

### OpenURL

### Abstract

We consider the design of power-adaptive systems for minimizing the average bit-error-rate over flat fading channels. Channel state information, obtained through estimation at the receiver, is sent to the transmitter over a feedback channel, where it is used to optimally adapt the transmit power. We consider finite-state optimal policies to reflect the limitations of the feedback channel. We develop an iterative algorithm that determines the optimal finite-state power control policy given the probability density function of the fading. Next, we present a discretized formulation of the problem and obtain a suboptimal solution via standard dynamic programming techniques. The discretization of the problem enables us to obtain a suboptimal policy for arbitrary fading channels for which the analytic expression of the fading probability density function is not available. Simulation results are used to draw conclusions regarding the effects of limited feedback channel capacity, delay and numb...

### Citations

2856 |
Dynamic Programming
- Bellman
- 1957
(Show Context)
Citation Context ...ies in the Principle of Optimality according to which an optimal policy has the property that at any stage, the remaining decisions also form an optimal policy with respect to the corresponding state =-=[20]-=-. In order to illustrate the procedure of discretizing the original continuous optimization problem and rendering it suitable for dynamic programming approaches, we begin by formulating the simple cas... |

1752 |
Vector Quantization and signal compression
- Gersho, Gray
- 1992
(Show Context)
Citation Context ...quantization cells, and the power levels S i correspond to the quantized outputs. Therefore, the minimization in (11) can be achieved by following the standard approach to designing scalar quantizers =-=[18]-=-. Taking the derivatives of the expression to be minimized with respect to, S i , i = 1; 2; : : : ; K and setting them equal to zero yields the following set of equations 2 = Effle \Gammafl S i jfl 2 ... |

1741 |
Wireless Communications Principles and Practices
- Rappaport
- 2001
(Show Context)
Citation Context ... fluctuations of the received power, known as fading, can be the result of several distinct phenomena that characterize wireless channels, such as multipath transmission, Doppler spread and shadowing =-=[1]-=-. In general, fading manifests itself as distortion in the frequency domain and intersymbol interference at the receiver, in addition to the fluctuations of its amplitude. The simplest form of fading ... |

1553 |
Information theory and reliable communication
- Gallager
- 1968
(Show Context)
Citation Context ...hat time instant. Finally, we assume that the channel is non-anticipatory, i.e. given the current input and the input-output history of the channel, the current output is independent of future inputs =-=[17]. A channel satisfyi-=-ng the above conditions can be described by the conditional distribution p(r t ; �� t+1 js t 0 ; �� t 0 ) = p(r t js t ; �� t )p(�� t+1 j�� t 0 ); (2) where r t is the received sym... |

486 | Iterative decoding of binary block and convolutional codes
- Hagenauer, Offer, et al.
- 1996
(Show Context)
Citation Context ...ing methods designed for memoryless AWGN channels have been proposed. The most promising of these methods are the parallel concatenated codes with iterative decoding, also known as "turbo" c=-=odes [4], [5]. The perf-=-ormances of the above coding schemes depend strongly on the interleaver that is used to decorrelate the fade depths "seen" by successive symbols. In fact, it can be shown [6] that for any tr... |

395 |
Rate compatible punctured convolutional codes (RCPC-codes) and their application
- Hagenauer
(Show Context)
Citation Context ...ated a growing interest in finite-state systems that switch between different modes according to some law determined by the short-term statistical behavior of the channel and/or the source. Hagenauer =-=[13]-=-, [14] introduced the rate-compatible punctured convolutional codes in an attempt to utilize the CSI in the decoding of convolutional codes. In [14] the source significance information (SSI) is being ... |

359 | Variable-rate variable-power MQAM for fading channels
- Goldsmith, Chua
- 1997
(Show Context)
Citation Context ...ffect of feedback delay on the system performance. Optimization of the transmit power for the Rayleigh channel first appeared in the early work of Hayes [8]. More recently, Goldsmith and Varaiya [9], =-=[10]-=- investigated the similar problem of maximizing the capacity of fading channels with CSI at the transmitter, by adapting the power, signalling scheme and rate to the current values of the fading. In [... |

257 | Unveiling turbo codes: some results on parallel concatenated coding schemes
- Benedetto, Montorsi
(Show Context)
Citation Context ...l coding methods designed for memoryless AWGN channels have been proposed. The most promising of these methods are the parallel concatenated codes with iterative decoding, also known as "turbo&qu=-=ot; codes [4], [5]. The-=- performances of the above coding schemes depend strongly on the interleaver that is used to decorrelate the fade depths "seen" by successive symbols. In fact, it can be shown [6] that for a... |

109 |
Introduction to Trellis-Coded Modulation with Applications,Macmillan
- Biglieri, Divsalar, et al.
- 1991
(Show Context)
Citation Context ...rbo" codes [4], [5]. The performances of the above coding schemes depend strongly on the interleaver that is used to decorrelate the fade depths "seen" by successive symbols. In fact, i=-=t can be shown [6]-=- that for any trellis code, if the fading is sufficiently slow, so that it can be assumed constant over a period corresponding to the minimum-distance error event path, the asymptotic rate of descent ... |

61 | Foundations of Mobile Radio Engineering - Yacoub - 1993 |

60 |
Calculus of Variations and Optimal Control Theory
- Hestenes
- 1966
(Show Context)
Citation Context ...subject to the additional constraint S isS max . The solution still satisfies Equations (12) and (13) for those states for which the peak-power constraint is inactive, and is equal to S max otherwise =-=[19]-=-. The Lagrange parametersis adjusted so that the final solution satisfies the average power constraint. Numerical results of the performance of finite-state power control, with and without peak power ... |

55 |
Adaptive feedback communications
- Hayes
- 1968
(Show Context)
Citation Context ...eedback channel capacity requirements and the effect of feedback delay on the system performance. Optimization of the transmit power for the Rayleigh channel first appeared in the early work of Hayes =-=[8]-=-. More recently, Goldsmith and Varaiya [9], [10] investigated the similar problem of maximizing the capacity of fading channels with CSI at the transmitter, by adapting the power, signalling scheme an... |

24 |
The performance of rate-compatible punctured convolutional codes for digital mobile radio
- Hagenauer, Seshadri, et al.
- 1990
(Show Context)
Citation Context ... growing interest in finite-state systems that switch between different modes according to some law determined by the short-term statistical behavior of the channel and/or the source. Hagenauer [13], =-=[14]-=- introduced the rate-compatible punctured convolutional codes in an attempt to utilize the CSI in the decoding of convolutional codes. In [14] the source significance information (SSI) is being utiliz... |

23 |
Minimum duration outage for cellular systems: a level crossing analysis
- Mandayam, Chen, et al.
- 1996
(Show Context)
Citation Context ...elow a certain threshold fl o . The threshold fl o is determined by the given quality of service requirements. Here, we employ a modified version of this definition that was introduced recently [22], =-=[23], termed m-=-inimum duration outage. This definition includes only outages whose duration exceeds a "minimum duration"sm . The rationale behind this definition is that in certain applications, such as vo... |

22 | Adaptive Rate Allocation in a Joint Source-Channel Coding Framework for Wireless Channels
- Jafarkhani, Ligdas, et al.
- 1996
(Show Context)
Citation Context ...e significance information (SSI) is being utilized along with the CSI by an adaptive source/channel coding scheme for speech. Adaptive transmission for finite-state channels (FSC's) was considered in =-=[15]-=-, where the objective was to optimally allocate a fixed bandwidth between the source and channel coders so as to minimize the end-to-end average source distortion. An earlier work [16] attacks the pro... |

16 |
Finite-state Modeling, Capacity, and Joint Source/Channel Coding for Time-Varying Channels
- Wang
- 1992
(Show Context)
Citation Context ...s considered in [15], where the objective was to optimally allocate a fixed bandwidth between the source and channel coders so as to minimize the end-to-end average source distortion. An earlier work =-=[16]-=- attacks the problem of joint source/channel coding for Rayleigh fading channels with state information at the encoder using FSC modeling of the channel, and iteratively optimizing the coder and the F... |

14 |
Increasing Spectral Efficiency through Power Control
- Goldsmith, Varaiya
- 1993
(Show Context)
Citation Context ...the effect of feedback delay on the system performance. Optimization of the transmit power for the Rayleigh channel first appeared in the early work of Hayes [8]. More recently, Goldsmith and Varaiya =-=[9]-=-, [10] investigated the similar problem of maximizing the capacity of fading channels with CSI at the transmitter, by adapting the power, signalling scheme and rate to the current values of the fading... |

12 |
Coded M-DPSK with built-in time diversity for fading channels
- Wei
- 1993
(Show Context)
Citation Context ...ge SNR is at best inverse linear. For cellular channels with fading due to Doppler spread, the depth of interleaving, and hence the delay it introduces, is inversely proportional to the vehicle speed =-=[7]-=-. In several cases the 2 required delay exceeds 100 ms, a value that is unacceptable for many real-time two-way communication applications. This constraint, limits the applications of interleaving-bas... |

11 |
Random Processes: A Mathematical Approach for Engineers
- Gray, Davidson
- 1986
(Show Context)
Citation Context ...the transmitter. The limits in Equations (4) and (5) exist and are equal with probability one to the corresponding expectations on the right-hand side when the process f t g is stationary and ergodic =-=[17]-=-. The design of such a transmission system with feedback consists of selecting a family of transmitters T indexed by u 2 U , determining the mode-selection rule h(\Delta) and designing the channel sta... |

8 |
Minimum duration outage for CDMA cellular systems: A level crossing analysis
- Mandayam, Chen, et al.
- 1998
(Show Context)
Citation Context ...alls below a certain threshold fl o . The threshold fl o is determined by the given quality of service requirements. Here, we employ a modified version of this definition that was introduced recently =-=[22], [23], te-=-rmed minimum duration outage. This definition includes only outages whose duration exceeds a "minimum duration"sm . The rationale behind this definition is that in certain applications, such... |

5 |
Joint source/channel coding for wireless channels
- Goldsmith
- 1995
(Show Context)
Citation Context ...] investigated the similar problem of maximizing the capacity of fading channels with CSI at the transmitter, by adapting the power, signalling scheme and rate to the current values of the fading. In =-=[11]-=- power control was used jointly with variable rate channel codes to minimize the distortion of a binary source. In [12] the authors derive optimal policies for minimizing the BER subject to the additi... |

2 |
Power control schemes for memoryless channels with known variations
- Ligdas, Farvardin
- 1995
(Show Context)
Citation Context ...ng the power, signalling scheme and rate to the current values of the fading. In [11] power control was used jointly with variable rate channel codes to minimize the distortion of a binary source. In =-=[12]-=- the authors derive optimal policies for minimizing the BER subject to the additional peak-power constraint. They also attempt an investigation of the effect of imperfect channel estimation. Most of t... |