Sumeet Sandhu

Antenna selection for spatial multiplexing systems with linear receivers

Future cellular systems will employ spatial multiplexing with multiple antennas at both the transmitter and receiver to take advantage of large capacity gains. In such systems it will be desirable to select a subset of available transmit antennas for link initialization, maintenance or handoff. We present a criterion for selecting the optimal antenna subset when linear, coherent receivers are used over a slowly varying channel. We propose use of the post-processing SNRs (signal to noise ratios) of the multiplexed streams whereby the antenna subset that induces the largest minimum SNR is chosen. Simulations demonstrate that our selection algorithm also provides diversity advantage thus making linear receivers useful over fading channels.

Space-time block codes: a capacity perspective

Space-time block codes are a remarkable modulation scheme discovered recently for the multiple antenna wireless channel. They have an elegant mathematical solution for providing full diversity over the coherent, flat-fading channel. In addition, they require extremely simple encoding and decoding. Although these codes provide full diversity at low computational costs, we show that they incur a loss in capacity because they convert the matrix channel into a scalar AWGN channel whose capacity is smaller than the true channel capacity. In this letter the loss in capacity is quantified as a function of channel rank, code rate, and number of receive antennas.

Near-optimal selection of transmit antennas for a MIMO channel based on Shannon capacity

Current wireless MIMO (multiple transmit and receive antenna) systems are designed with the assumption that the fading channel is estimated perfectly at the receiver while the transmitter has no channel knowledge. If even a small amount of information is fed back to the transmitter, the capacity of the resulting channel increases appreciably. We consider a low-scattering, quasistatic environment where the matrix channel is rank deficient. Previous results (Gore et al. 2000, and Nabar et al. 2000) for such a channel indicate that channel capacity can be increased by a judicious choice of fewer transmit antennas. The optimal subset of transmit antennas is computed by the receiver as the subset that induces the highest Shannon capacity of all subsets of the same cardinality. Here we describe a computationally efficient, near-optimal search technique for the optimal subset based on classical waterpouring. We also provide enhanced search techniques based on partial waterpouring and uniform pourer allocation over the strongest channel modes that outperform waterpouring at high signal to noise ratios.

Cooperation in a Half-Duplex Gaussian Diamond Relay Channel

A half-duplex relay channel consisting of two relays in a diamond topology is studied. In contrast to full-duplex systems, it is shown that time should be optimally allocated among different states. In contrast to the classical three-node relay channel, it is shown that spatial reuse can be utilized to allow communication without interference. Both achievable rate and upper bound on capacity are studied. Several communication schemes such as multihop with spatial reuse, scale-forward, broadcast-multiaccess with common message, compress-forward, as well as hybrid ones are characterized, some of which are novel. It is also shown that simple multihop with spatial reuse achieves the capacity of certain symmetric diamond channels.

Delay diversity codes for frequency selective channels

Space-time coding for the flat fading, quasi-static MIMO wireless channel has received widespread attention. This paper treats space-time code design for frequency selective channels from a single carrier modulation perspective. We present a general framework for analyzing space-time codes for delay spread channels based on PEP analysis. It is shown that as in the flat fading case, diversity gain is driven by the minimum rank of the pairwise codeword difference matrices. Delay spread, however, imposes a block Hankel structure on the codewords which may prevent certain codes designed for the flat fading case from exploiting full spatio-temporal diversity when used over frequency selective channels. We explicitly show this diversity loss for the delay diversity code. We show that a properly generalized delay diversity (GDD) code achieves full diversity over frequency selective channels. Finally we propose an extension to the GDD which fits naturally in a multi-carrier setting.

Space-time block codes versus space-time trellis codes

Two outstanding examples of transmit diversity schemes for the multiple-antenna flat-fading channel are space-time block coding (STBC) and space-time trellis coding (STTC). We compare the performance of STBC and STTC in terms of the frame error rate keeping the transmit power, spectral efficiency and number of trellis states fixed. We discover that a simple concatenation of space-time block codes with traditional AWGN (additive white Gaussian noise) trellis codes outperforms some of the best known space-time trellis codes at SNRs (signal to noise ratios) of interest. Our result holds for a small number of trellis states with one or two receive antennas, and is useful for the design and implementation of multiple-antenna wireless systems.

PHY-layer network coding for broadcast channel with side information

This paper proposes a novel combination of network coding and channel coding for a two-receiver Gaussian broadcast channel under practical modulation. We assume that one receiver may know the message for the other receiver, called the side information (SI). This models relaying in dense wireless networks where destination nodes may have received packets intended for other nodes in previous transmissions. Four cases are considered: i) both receivers have SI; ii) only the weak receiver has SI; iii) only the strong receiver has SI; and iv) neither receiver has SI. We propose a simple adaptive coding scheme that combines channel coding with network coding, which greatly reduces coding/decoding complexity as compared to pure random coding. The scheme first designs channel codes independently for each channel, then combines them with simple network coding. Analysis is also presented showing that the joint design achieves capacity regions for both Cases i) and ii). For Case i), each link achieves the same error probability as that of one-to-one single-link transmission using the constituent code. For Case ii), an embedded coding structure is used, and upper bounds on decoding error probability are characterized. For Cases iii) and iv), the scheme resembles super-position coding.

A Shannon-Theoretic Perspective on Fading Multihop Networks

We consider a frequency-flat fading multihop network with a single active source-destination pair terminals communicating over multiple hops through a set of intermediate relay terminals. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) for a simple communication protocol based on time-division decode-and-forward relaying in meaningful asymptotic regimes of signal-to-noise ratio (SNR) under a system-wide power constraint on source and relay transmissions. The impact of multi-hopping and channel fading on the key performance measures of the high and low SNR regimes is investigated to shed new light on the possible enhancements in power/bandwidth efficiency and link reliability. In contrast to the common belief that in fading environments communicating over multiple hops suffers significantly in performance due to the worst link limitation, our results indicate that hopping could significantly improve the outage behavior over slow-fading networks and stabilize links against the random channel fluctuations. In particular, we prove that there exists an optimal number of hops that minimizes the end-to-end outage probability and characterize the dependence of this optimal number on the fading statistics and target energy and spectral efficiencies.

Union bound on error probability of linear space-time block codes

The design of practical coding techniques for the multiple antenna wireless channel is a challenging problem. A number of interesting solutions have been proposed ranging from block codes to trellis codes for the MIMO (multiple input, multiple output) channel. We consider linear block codes for the quasi-static, flat-fading, coherent MIMO channel. A linear code refers to an encoder that is linear with respect to scalar input symbols. We assume maximum likelihood decoding at the receiver. We provide a cohesive framework for analysis of linear codes in terms of a union bound on the conditional probability of symbol error. The error bound is a function of the instantaneous channel realization and does not make any assumptions on channel statistics. We show that the orthogonal block codes proposed by Tarokh, Jafarkhani and Calderbank, (see IEEE Trans. Information Theory, vol.45, no.5, p.1456-67, 1999) achieve the lowest error bound among all unitary codes and are in fact optimal.

Analog combining of multiple receive antennas with OFDM

Optimal signal processing of M receiver antennas requires digitization of each of the M RF signals. For example, MRC (maximal ratio combining) of M receiver antennas requires M ADCs (analog to digital converters). Since the ADC is a highly power-consumptive component in current receiver chain architectures, we investigate suboptimal signal processing schemes that combine M analog signals before digitization, thus enabling a much cheaper implementation with a single ADC. We focus on IEEE 802.11a like OFDM LAN systems with one transmit and multiple receiver antennas (SIMO - single input multiple output), with perfect channel knowledge at the receiver. Our scheme uses scalar weights to combine the receiver antennas in the time-domain. These weights are a function of the spatio-temporal channel matrix. The results are very promising: 4-antenna linear combining (LC) outperforms 2-antenna selection diversity by 5-7 dB at an uncoded BER of 0.01, and this margin is even wider at lower BERs.