JPL's Wireless Communication Reference WebsiteChapter: Wireless Channels

Rice and Nakagami fading are two generalisations of the model for Rayleigh fading. In literature, often a Nakagami model is used for analytical simplicity in cases where Rician fading would be a more appropriate model. In contrast to common belief, the Nakagami model is not an appropriate approximation for Rician fading. It has an essentially different behaviour for deep fades, such that results on outage probabilities or error rates can differ by orders of magnitude.
Rician ModelsTo describe microcellular propagation, the Rayleigh model lacked the effect of a dominant lineofsight component, and Rician model appeared to be more appropriate. For analytical and numerical evaluation of system performance, the expressions for Rician fading are less convenient, mainly due to the occurrence of a Bessel function in the Rician probability density function of received signal amplitude. Approximations by a Nakagami distribution, with simpler mathematical expressions have become popular. 
Nakagami ModelsThe Nakagami fading model was initially proposed because it matched empirical results for short wave ionospheric propagation. In current wireless communication, the main role of the Nakagami model can be summarized as follows

In the analysis of outage probabilities or error rates, it is the behavior of the model for signals in deep fades that has the determining effect. As the behavior of the probability density functions for amplitudes near zero differ significantly, approximations based on behavior near the mean are inappropriate.
Rician and Nakagami models have a fundamentally different density for deep fades. Modeling a Rician fading signal by a Nakagami distribution of the amplitude leads to overly optimistic results, and discrepancies can be many orders of magnitude. That is, we challenge the accuracy of the last application of the model in the above list.
A typical radio channel exhibits multipath reception, which causes fading. The mathematical evaluation of this paper addresses narrowband systems, in which the channel transfer function is sufficiently constant over the signal bandwidth. This corresponds to the assumption that Intersymbol Interference does not play a major role in the performance of the radio links. However, the models also play a role in wideband systems, in which each resolvable bin of reflected waves can be modeled to exhibit flat fading.
In the special case that the dominant component is zero (K = 0) or m = 1, Rayleigh fading occurs, with an exponentially distributed power, viz.,
The Nakagami model is sometimes used to approximate the pdf of the power of a Rician fading signal. Matching the first and second moments of the Rician and Nakagami pdfs gives
which tends to m = K/2 for large K.
For Rician fading, the probability distribution at small powers is  For Nakagami fading, we have 
Here denotes the probability that p_{i} < p_{th} .
The results are strikingly different for m larger than one. As the relation between K and m was based merely on the first and second moments, it is likely to be most accurate for values close to the mean. Outage probabilities however highly depend on the tail of the pdf for small power of the wanted signal. The probability of deep fades (small p_{i}) differs for these two models, so an approximation the pdf of a Ricianfading wanted signal by a Nakagami pdf can be highly inaccurate: Results differ even in firstorder behavior. For Rician fading, the slope of the outage probability versus C/I is the same as for Rayleigh fading. For Nakagami fading, the slope is steeper, similar to that of mbranch diversity reception of a Rayleigh fading signal.
The nakagami approximation appeared less suitable to approximate a Rician channel. Nevertheless other methods are available to make reasonable approximations in numerical evaluations of the outage probability in interferencelimited situations, while restricting the complexity of calculations.