It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.

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An overview of limited feedback in wireless communication systems

Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple-input multiple-output (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector; both are hard to realize. In this article, a quantized maximum signal-to-noise ratio (SNR) beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter. By using the distribution of the optimal beamforming vector in independent and identically distributed Rayleigh fading matrix channels, the codebook design problem is solved and related to the problem of Grassmannian line packing. The proposed design criterion is flexible enough to allow for side constraints on the codebook vectors. Bounds on the codebook size are derived to guarantee full diversity order. Results on the density of Grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or SNR loss. Monte Carlo simulations are presented that compare the probability of error for different quantization strategies.

Grassmannian beamforming for multiple-input multiple-output wireless systems

A multiple-access MIMO WLAN system that employs MIMO, OFDM, and TDD. The system (1) uses a channel structure with a number of configurable transport channels, (2) supports multiple rates and transmission modes, which are configurable based on channel conditions and user terminal capabilities, (3) employs a pilot structure with several types of pilot (e.g., beacon, MIMO, steered reference, and carrier pilots) for different functions, (4) implements rate, timing, and power control loops for proper system operation, and (5) employs random access for system access by the user terminals, fast acknowledgment, and quick resource assignments. Calibration may be performed to account for differences in the frequency responses of transmit/receive chains at the access point and user terminals. The spatial processing may then be simplified by taking advantage of the reciprocal nature of the downlink and uplink and the calibration.

MIMO WLAN system

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.

Antenna selection for spatial multiplexing systems with linear receivers

Multiple-input multiple-output (MIMO) wireless systems provides capacity much larger than that provided by traditional single-input single-output (SISO) wireless systems. Beamforming is a low complexity technique that increases the receive signal-to-noise ratio (SNR), however, it requires channel knowledge. Since in practice channel knowledge at the transmitter is difficult to realize, we propose a technique where the receiver designs the beamforming vector and sends it to the transmitter by transmitting a label in a finite set, or codebook, of beamforming vectors. A codebook design method for quantized versions of maximum ratio transmission, equal gain transmission, and generalized selection diversity with maximum ratio combining at the receiver is presented. The codebook design criterion exploits the quantization problem's relationship with Grassmannian line packing. Systems using the beamforming codebooks are shown to have a diversity order of the product of the number of transmit and the number of receive antennas. Monte Carlo simulations compare the performance of systems using this new codebook method with the performance of systems using previously proposed quantized and unquantized systems.

In this paper, a bit-error-rate (BER) analysis for closed-loop transmit diversity in a time-selective Rayleigh fading channel containing feedback delay is presented. In the absence of feedback delay, closed-loop transmit diversity always outperforms open-loop transmit for a given transmitted signal energy. This is no longer true in the presence of feedback delay. We derive closed-form expressions of the average BER for this case assuming QPSK and BPSK signaling. The results of the analysis are instrumental for comparing closed-loop with open-loop schemes under given operating conditions. In particular, we demonstrate that, for a given transmitted energy and number of transmit antennas, open-loop outperforms closed-loop at sufficiently fast channel fading. We also show that, for a given transmitted signal energy and fading rate, closed-loop outperforms open-loop for sufficiently large numbers of transmit antennas while the total average transmitted signal energy is kept constant. For some special cases, closed-form expressions for the fading rate at which the performance of open-loop is equal to closed-loop are obtained.

Performance analysis of closed-loop transmit diversity in the presence of feedback delay

Multi-mode wireless devices having single-mode or reduced-mode receivers. In one embodiment, a wireless device is provided with a transmitter and a receiver. The transmitter transmits with any one of multiple selectable modulation techniques, the selected modulation technique being selected to correspond to a modulation technique supported by a target wireless device. The receiver receives signals modulated in accordance any one of a subset of the selectable modulation techniques. The subset might include only one modulation technique. Also disclosed is a wireless communications method in a wireless device having a transmitter configurable to transmit in at least one modulation mode other than that receivable by the wireless device.

Multi-mode wireless devices having reduced-mode receivers

A system and method facilitate estimating noise in a received signal. The received signal is formed of a plurality of tones, such as training tones and data tones. Noise is estimated at the training tones, which generally comprise a lesser number of the tones in the received signal than the data tones. The estimated noise at the training tones can be employed to facilitate demodulating and/or decoding data tones in the received signal. In one aspect, the estimated training tone noise can be utilized by a beamformer.

Simplified noise estimation and/or beamforming for wireless communications

The present application discloses an improved mobile communications architecture, in which each base station broadcasts not only data which has been spread by that station's long code word, but also (intermittently) code identification data which has not been spread. The code identification data is a block code which includes multiple symbols, so that multiple intermittent transmissions are required to complete the transmission of the code identification data. This transmission lets the mobile station shorten the search for the base station's long code word in two ways: the code identification data gives at least some information about the long code itself; and the phase of the block code gives at least some information about the phase of the long code word.

Spread-spectrum telephony with accelerated code acquisition

A method for providing closed-loop transmit precoding between a transmitter and a receiver, includes defining a codebook that includes a set of unitary rotation matrices (202). The receiver determines which precoding rotation matrix from the codebook should be used for each sub-carrier that has been received (204). The receiver sends an index to the transmitter (206), where the transmitter reconstructs the precoding rotation matrix using the index, and precodes the symbols to be transmitted using the precoding rotation matrix (208). An apparatus that employs this closed-loop technique is also described.

Srinath Hosur

Papers

Performance analysis of closed-loop transmit diversity in the presence of feedback delay

Multi-mode wireless devices having reduced-mode receivers

Simplified noise estimation and/or beamforming for wireless communications

Spread-spectrum telephony with accelerated code acquisition

Method and apparatus for providing closed-loop transmit precoding