Ahmed Hesham Mehana

Diversity of MMSE MIMO Receivers

In most multiple-input multiple-output (MIMO) systems, the family of waterfall error curves, calculated at different spectral efficiencies, are asymptotically parallel at high signal-to-noise ratio. In other words, most MIMO systems exhibit a single diversity value for all fixed rates. The MIMO minimum mean square error (MMSE) receiver does not follow this pattern and exhibits a varying diversity in its family of error curves. This paper analyzes this interesting behavior of the MMSE MIMO receiver and produces the MMSE MIMO diversity at all rates. The diversity of the quasi-static flat-fading MIMO channel consisting of any arbitrary number of transmit and receive antennas is fully characterized, showing that full spatial diversity is possible if and only if the rate is within a certain bound which is a function of the number of antennas. For other rates, the available diversity is fully characterized. At sufficiently low rates, the MMSE receiver has a diversity similar to the maximum likelihood receiver (maximal diversity), while at high rates, it performs similarly to the zero-forcing receiver (minimal diversity). Linear receivers are also studied in the context of the MIMO multiple-access channel. Then, the quasi-static frequency selective MIMO channel is analyzed under zero-padding and cyclic-prefix (CP) block transmissions and MMSE reception, and lower and upper bounds on diversity are derived. For the special case of SIMO under CP, it is shown that the aforementioned bounds are tight.

Diversity of MMSE MIMO receivers

This work settles a long-standing open problem by providing a complete characterization of the diversity of the MMSE MIMO receiver for all fixed rates (spectral efficiencies). The MMSE MIMO receivers exhibit a complicated behavior in the fixed-rate regime that cannot be obtained via DMT analysis. Specifically, we show that in a system with M transmit antennas, N receive antennas, and rate R, the diversity is given by d = ⌈M2−R over M⌉2 + (N − M)⌈M2−R over M⌉. This verifies and refines earlier results that were obtained only for two extremal operating points: diversity MN at very low rates and diversity N − M + 1 at very high rates.

Diversity of MIMO Linear Precoding

This paper studies multiple-input multiple-output linear precoding in the high-signal-to-noise-ratio regime under flat fading. The diversity at all fixed rates is analyzed for a number of linear precoders. The diversity-multiplexing tradeoffs (DMTs) are also obtained, discovering that for many linear precoders the DMT gives no direct insight into the intricate behavior of fixed-rate diversity. The zero-forcing (ZF), regularized ZF, matched filtering, and Wiener filtering precoders are analyzed. It is shown that regularized ZF (RZF) or matched filter (MF) suffers from error floors for all positive multiplexing gains. However, in the fixed rate regime, RZF and MF precoding achieve full diversity for spectral efficiencies up to a certain threshold and zero diversity at rates above it. When the regularization parameter in the RZF is optimized in the minimum mean square error sense, the structure is known as the Wiener precoder, which in the fixed-rate regime is shown to have diversity that depends not only on the number of antennas, but also on the spectral efficiency. The diversity in the presence of both precoding and equalization is also analyzed.

Single-Carrier Frequency-Domain Equalizer with Multi-Antenna Transmit Diversity

Single-carrier (SC) block transmission with cyclic prefix (CP) is a method with several advantages that has been incorporated into standards. This paper investigates the performance of multi-antenna SC-FDE under cyclic-delay diversity (CDD) and Alamouti signaling. Our analysis fully characterizes the diversity, showing that it depends not only on the antenna configuration and channel memory, but also on data block length and data transmission rate. Below a certain rate threshold, full diversity is available to both CDD and Alamouti signaling, while at higher rates their diversity diminishes, albeit not quite in the same way. Our analysis shows that at high rates the CDD diversity degenerates to the diversity of the SISO SC-FDE, while Alamouti signaling provides twice the diversity of SISO SC-FDE.

The diversity of MMSE receiver over frequency-selective MIMO channel

This paper analyzes the MMSE receiver in MIMO frequency-selective channels. This expands our understanding of the MMSE MIMO channel, whose diversity was only recently characterized in the MIMO flat-fading regime. Specifically, in this paper lower and upper bounds on the diversity of the MMSE receiver operating over frequency selective MIMO channel under block transmission with zero-padding (ZP) or cyclic-prefix (CP) are produced. The tightness of the bounds is demonstrated for both ZP/CP for the special case of SIMO channel.

Performance of Linear Receivers in Frequency-Selective MIMO Channels

This paper investigates the performance of the zero-forcing (ZF) and minimum mean-square error (MMSE) equalizers in MIMO frequency selective channels under zero-padding (ZP) transmission. It was previously known that the SISO zero-forcing ZP receiver achieves full diversity; this paper shows that the MIMO version of this receiver is suboptimal in diversity. The MMSE ZP is also investigated, showing that it exhibits an intricate error behavior that depends not only on channel memory and antenna configuration, but also on transmission rate. This behavior is fully characterized in closed form, revealing that the MMSE ZP receiver attains the (optimal) diversity of a ML receiver but only at small spectral efficiencies. Thus MMSE ZP works better than ZF ZP, but not quite as well as ML. To further improve the performance, lattice-reduction aided equalization in the frequency-selective channel is investigated. It is shown that lattice-reduction-aided zero forcing equalizer as well as MMSE equalizer achieve the maximum spatial and temporal diversity at all spectral efficiencies.

High-SNR analysis of MIMO linear precoders

For linear MIMO precoders, the diversity is an important parameter affecting broad tradeoffs in system design, however, the diversity of many MIMO precoders has not been available in the open literature. This paper analyzes the diversity of the following MIMO precoders: the zero-forcing (ZF), regularized ZF, matched filtering and Wiener filtering. Several interesting properties of these precoders are revealed by this analysis. It is shown that regularized ZF (RZF) and the matched filter (MF) exhibit two-mode diversity: full diversity at low rates R and error floor at high rates. The rate threshold of this two-mode behavior is analytically determined. The Wiener precoder is also shown to produce a diversity that depends on the spectral efficiency and can be as small as one and as large as the product of the number of transmit and receive antennas.

Performance of MMSE MIMO receivers in frequency-selective channels

This paper investigates the performance of the minimum mean-square error (MMSE) equalizers in MIMO frequency selective channels under zero-padding (ZP) transmission. It was previously known that the SISO linear ZP receiver achieves full diversity; this paper shows that the MIMO version of this receiver is suboptimal in diversity. It is shown that the MMSE MIMO receiver exhibits an intricate error behavior that depends not only on channel memory and antenna configuration, but also on transmission rate. This behavior is fully characterized in closed form, revealing that the MMSE ZP receiver attains the (optimal) diversity of a ML receiver but only at small spectral efficiencies.

Performance of MIMO single-carrier frequency domain zero-forcing equalizer

Single-carrier frequency domain equalization (SC-FDE) has many advantages, but in the MIMO frequency selective channel its performance has not been fully characterized and several important open questions remain. This paper analyzes the diversity of zero-forcing MIMO SC-FDE. It is shown that the diversity of the ZF receiver over this channel is the same as that of the ZF receiver in the frequency-flat channel. To improve the performance, a lattice-reduction (LR) aided ZF equalization is proposed and analyzed. It is shown that the full spatial and temporal diversity is achieved by he LR-aided ZF receiver for the uncoded transmission. This is the first analytical proof for the LR-aided equalization for MIMO frequency selective channel.

Cyclic delay transmission achieves full diversity without (Pre)coding

Cyclic Delay Diversity (CDD) is a simple method that converts transmit antenna diversity into frequency selectivity, thus allowing simple operation and use of conventional receivers to capture the diversity. This paper shows that single-carrier CDD methods are capable of producing diversity without channel coding or linear precoding, and that this is made possible via the appropriate design and use of linear equalizers. At the heart of our result is the establishment of a functional equivalence between effective channels seen by the CDD MISO system and the cyclic-prefix SISO ISI system. Specifically, we show that in an M×1 CDD MSIO system, the MMSE receiver achieves maximum diversity for rate values R ≤ log L/M(ν+1)-1, where L is the data block length, R the spectral efficiency in b/s/Hz, and ν is the channel memory. The equivalence between the delay diversity (DD) system and a zero-padding single-carrier system can be also established (as long as the DD delay taps are carefully chosen) for which linear equalizers can achieve maximum diversity with no constraint on rate.