Abstract-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-tonoise 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 quasistatic frequency selective MIMO channel is analyzed under zeropadding 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.Index Terms-Diversity, linear receiver, minimum mean square error (MMSE), multiple-input multiple-output (MIMO).

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 givenThis 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.

Linear precoding is a relatively simple method of MIMO signaling that can also be optimal in certain special cases. This paper is dedicated to high-SNR analysis of MIMO linear precoding. The Diversity-Multiplexing Tradeoff (DMT) of a number of linear precoders is analyzed. Furthermore, since the diversity at finite rate (also known as the fixed-rate regime, corresponding to multiplexing gain of zero) does not always follow from the DMT, linear precoders are also analyzed for their diversity at fixed rates. In several cases, the diversity at multiplexing gain of zero is found not to be unique, but rather to depend on spectral efficiency. The analysis includes the zero-forcing (ZF), regularized ZF, matched filtering and Wiener filtering precoders. We calculate the DMT of ZF precoding under two common design approaches, namely maximizing the throughput and minimizing the transmit power. It is shown that regularized ZF (RZF) or Matched filter (MF) suffer from error floors for all positive multiplexing gains. However, in the fixed rate regime, RZF and MF precoding achieve full diversity up to a certain spectral efficiency and zero diversity at rates above it. When the regularization parameter in the RZF is optimized in the MMSE 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.

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