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Previous work on space-frequency coded multipleinput multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) has been restricted to idealistic propagation conditions. In this paper, using a broadband MIMO channel model taking into account Ricean -factor, transmit and receive angle spread, and antenna spacing, we study the impact of the propagation environment on the performance of space-frequency coded MIMO-OFDM. For a given space-frequency code, we quantify the achievable diversity order and coding gain as a function of the propagation parameters. We find that while the presence of spatial receive correlation affects all space-frequency codes equally, spatial fading correlation at the transmit array can result in widely varying performance losses. High-rate space-frequency codes such as spatial multiplexing are typically significantly more affected by transmit correlation than low-rate codes such as space-frequency block codes.We show that in the MIMO Ricean case the presence of frequency-selectivity typically results in improved performance compared to the frequency-flat case.Index Terms-Channel modeling, diversity, multiple-input multiple-output (MIMO), orthogonal frequency-division multiplexing (OFDM), space-frequency coding, spatial multiplexing.

Recently, the use of coherent space-frequency coding in orthogonal frequency-division multiplexing (OFDM)-based frequency-selective multiple-input multiple-output (MIMO) fading channels has been proposed. Acquiring knowledge of the fading coefficients in a MIMO channel is already very challenging in the frequency-flat (fast) fading case. In the frequency-selective case, this task becomes significantly more difficult due to the presence of multiple paths, which results in an increased number of parameters to be estimated. In this paper, we address code design for noncoherent frequency-selective MIMO-OFDM fading links, where neither the transmitter nor the receiver knows the channel. We derive the code design criteria, quantify the maximum achievable diversity gain, and provide explicit constructions of full-diversity (space and frequency) achieving codes along with an analytical and numerical performance assessment. We also demonstrate that unlike in the coherent case, noncoherent space-frequency codes designed to achieve full spatial diversity in the frequency-flat fading case can fail completely to exploit not only frequency diversity but also spatial diversity when used in frequency-selective fading environments. We term such codes "catastrophic." Index Terms-Diversity, frequency-selective fading channels, multiple-input multiple-output (MIMO) systems, noncoherent communications, orthogonal frequency-division multiplexing (OFDM), pairwise error probability (PEP), Rayleigh fading, space-frequency coding. I. INTRODUCTION AND OUTLINE S PACE-TIME coding has emerged as a promising technique for realizing spatial diversity gains in multiple-input-multiple-output (MIMO) wireless systems. The design criteria for space-time codes (STCs) in the coherent case, where the receiver has perfect channel state information (CSI), were derived in [1] and [2]. While the coherent setup is representative for fixed or low mobility wireless systems, future mobile wireless access systems are expected to operate at high vehicle speeds and will, hence, experience fast fading. Estimating the MIMO channel in a fast-fading environment is very challenging and often not possible at all. Addressing this problem, noncoherent communication, where neither the transmitter nor the receiver has CSI, was considered recently for the frequency-flat fading case in [3]-[6]. The design criteria for space-time unitary codebooks were derived in [4]. A simple systematic code construction was given in [5]. Different code designs were proposed, among Manuscript

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