Krishnan Padmanabhan

The Sampling Theorem With Constant Amplitude Variable Width Pulses

This paper proves a novel sampling theorem with constant amplitude and variable width pulses. The theorem states that any bandlimited baseband signal within ±0.637 can be represented by a pulsewidth modulation (PWM) waveform with unit amplitude. The number of pulses in the waveform is equal to the number of Nyquist samples and the peak constraint is independent of whether the waveform is two-level or three-level. The proof of the sampling theorem uses a simple iterative technique that is guaranteed to converge to the exact PWM representation whenever it exists. The paper goes on to develop a practical matrix based iterative technique to generate the PWM waveform that is guaranteed to converge exponentially. The peak constraint in the theorem is only a sufficient condition. In fact, many signals with higher peaks, e.g., lower than Nyquist frequency sinusoids, can be accurately represented by a PWM waveform.

Calculating and Achieving Capacity on the Unknown Fading MIMO Channel

This paper calculates both an upper bound and a constructive lower bound on the capacity of an N transmitter, K receiver MIMO fading network. The channel between the transmitters and the receivers is Rayleigh flat fading with fading coefficients unknown to both transmitters and receivers. The lower bound is derived from a practicable successive decoding scheme, and when N is significantly larger than K, it approaches the upper bound with increasing coherence length of the fading process. Obviously, in the limit of large coherence lengths, the system becomes coherent and so is trivial. However, the lower and upper bounds of this paper are close to the MIMO capacity even when the system is highly non-coherent. For example, with N = 50, K = 15 and a coherence length of 200, the achievable rate of the successive decoding scheme diverges from the upper bound by just 6%, even when it is only 40% of coherent capacity. At this design point, the scheme achieves a rate of 13 bits/sec/Hz, significantly greater than any current cellular standards

The Constrained Capacity of Single and Multiuser Channels with Unknown Fading

This work presents a general technique to compute tight upper and lower bounds on the constrained capacity of both the point to point and multiuser Rayleigh flat fading channel with no channel state information (CSI) at the transmitter or the receiver. The paper begins by proving that the optimal input distribution for the point-to-point fading channel must have uniform i.i.d phase and therefore, for constant envelope transmitters, the only design parameter is the density of the driving constellation. The paper then presents plots of the (essentially coincident) upper and lower bounds on the constrained capacity for BPSK,QPSK and 8-PSK inputs as a function of SNR for the point to point channel. These allow the designer to judge the benefits of different channel alphabet choices and to compare the efficiency of the final coding system with the capacity of this channel and modulation alphabet combination. The paper then goes on to extend these methods to multiuser fading channels.

Tight upper and lower bounds on the constrained capacity of non-coherent multi-antenna channels

This paper first presents an optimal receiver and coding scheme for a multi-user, multi-receiver, non-coherent Rayleigh flat fading channel which achieves the channels constrained capacity (i.e., the capacity for a fixed input distribution). The paper then goes on to analyze the optimal receiver and uses it to generate tight upper and lower bounds on the constrained capacity. Knowing this constrained capacity is essential to judge the efficiency of coding schemes for the channel; it performs the same function as BPSK capacity for the AWGN channel in judging LDPC codes. The paper then goes on to present a practicable correlation based receiver that uses a novel iterative channel estimation technique. The performance of this receiver remains close to the constrained capacity as long as the per-user SNR is low; there is no requirement on the aggregate SNR. With 50 users, 50 receivers and a brickwall fading channel with a coherence length of 200 symbols, for example, the correlation based receiver achieves a sum rate of 36 bits/sec/Hz, significantly greater than any current cellular standards.

Exact PWM representation of bandlimited signals

This paper proves that any bandlimited signal within ±0.637V can be represented by a PWM waveform with amplitude V. The number of the pulses in the waveform is equal to the number of the Nyquist samples. This paper also provides a practical iterative procedure to generate the PWM waveform for a given bandlimited signal. The error of this procedure decreases exponentially with the number of iterations.

Information rates of the noncoherent frequency selective fading channel

This paper examines ways of improving channel estimation using successive decoding for the time varying frequency selective fading channel in a point to point wireless communication system. The channel state information (CSI) is not known a priori at either the transmitter or the receiver. The paper first presents the conventional pilot-symbol aided channel estimation (PACE) scheme and then the sequential successive decoding scheme. The conventional PACE scheme involves a big loss in achievable rates, while the sequential successive decoding scheme has a large delay. Finally, these two schemes are compared with three interleaved pilot schemes, in which interleaved codewords are decoded successively. These interleaved pilot schemes have significantly reduced delays, but still maintain good achievable rates.

Interleaver Structures for Channel Estimation and Decoding on the Frequency Selective Fading Channel

This paper examines different designs for combined channel estimation and decoding for a point to point time varying frequency selective fading channel. The channel state information (CSI) is not known a priori at either the transmitter or the receiver. Channel estimation is performed through a combination of conventional pilots and manufactured pilots from previously decoded data. The paper examines how different interleaver structures affect the tradeoff between achievable rates, delay and complexity. When there is no delay constraint at all, the conventional pilots can be eliminated completely and a proper interleaving scheme can convert half the symbols into manufactured pilots. When there is a delay constraint, the paper explores various interleaver structures that combine the conventional pilots with the manufactured pilots in different ways to get much better achievable rates than conventional pilot-symbol aided channel estimation.

Information Rates for Multiantenna Systems With Unknown Fading

This paper presents analytical upper and lower bounds on the information rate of a multiuser Rayleigh fading channel with no channel state information (CSI) at the transmitters or the receivers. These bounds are shown to converge whenever an individual users data rate is small compared with the bandwidth, e.g., when users can employ CDMA. The amount of spreading required for a given degree of convergence depends on the number of receive antennas. The number of users can be sufficient for the aggregate spectral density to be large. The paper presents exact analytical expressions for the information rates of both the block fading and the continuous correlated fading channel models in this regime. Finally, the results are extended to more general channel models.

Large wireless systems with unknown fading

This paper presents results on the capacity of large wireless systems with unknown fading. The system model consists of many independent transmitters who have to communicate with a large number of receivers via wireless links. The receivers in the system are connected to a wired backbone. The paper presents an upper bound on the per user capacity of the large network which allows for full cooperation among the receivers. The paper also presents constructive lower bounds on per user capacity which meet the upper bounds. Sometimes, the lower bounds require no receiver cooperation and sometimes they require medium distance receiver cooperation. The results of this paper are fundamental and result from the randomness of the fading present in the network rather than any peculiarities in the system model.

Achievable rates for the noncoherent frequency selective fading channel

This paper investigates achievable rates for the time varying frequency selective fading channel in a single-input and single-output (SISO) system. The channel state information (CSI) is not known a priori at either the transmitter or the receiver. The paper begins by presenting a general simulation based technique to compute lower and upper bounds on the achievable rates. The paper also derives an analytical lower bound. Finally, the paper computes the loss associated with pilot based schemes by comparing their achievable rates with the bounds.