## 1 Introduction  
Nowadays, nearly all communication engineers depend on computer simulations to assess the performance of digital communication systems. One of the fundamental parameters used in these simulations is the signal-to-noise ratio (SNR) [1]. SNR, which is the ratio of signal power to noise power, is so commonly understood that many technical papers do not fully explain how this value is derived during simulations. Consider the following simple example in Figure 1. It consists of a transmitter, a channel model, a noise source, and a receiver. To calculate the SNR used in the experiments, it is typically assumed that the mean effective gain of antennas [2] is known. For instance, unity for a single-input single-output (SISO) system. During simulations of a SISO system, even though the gain of the antenna is unity, the simulated channel also incurs a gain, known as channel (power) gain [3]. Please refer to Section 2 for details. In the following,we will use a unity (average) channel gain in the discussion. Under this assumption, the SNR is computed as the ratio of transmitted signal power to noise power (please refer to Section 2 for more details). However, in a standard simulation procedure, the simulated channel is generated multiple times, such as 50 times (trials) [4]. Each time, the generated channel exhibits different behavior, resulting in varying channel gains from one trial to another (see Section 2 for details). Although the channel gain is no longer unity for each trial, the average channel gain remains close to one, provided a sufficient number of trials are conducted. From the perspective of communication theory, performing averaging over various realizations in a random process is an ensemble average. In this case, the calculation of SNR remains the ratio of transmitted signal power to noise power. This is the standard method for computing SNR in almost all research papers. As mentioned previously, the channel gain varies across different trials. In some trials, the channel gain can significantly deviate from unity, such as 0.8 or 1.2. In this situation, there are two possible ways to compute the SNR. The first method is the conventional one, which uses the transmitted signal power as the denominator in the SNR calculation. This method computes the SNR from the viewpoint of the transmitter side, essentially using the ensemble average of received signal power as a basis. The second method uses the average power of the received signal for that specific trial as the denominator, computing the SNR from the receiver's perspective over a short period. Theoretically, if the channel is ergodic [5], then after averaging over a very long period, both SNR values should be equal. Unfortunately, as we will demonstrate through simulations, many orthogonal frequency-division multiplexing (OFDM)-based communication systems [6] do not have sufficiently long codewords for the time average to approach the ensemble average. In the following discussion, we will refer to the transmitter-side SNR as the ensemble-average SNR and the receiver-side SNR as the short-term SNR. Please refer to Section 2 for a complete description. It seems reasonable to assume that using either ensemble-average SNR or short-term SNR would not significantly alter the observed performance. Consequently, most existing literature does not explicitly explain how the SNR is calculated. We initially shared this belief. However, during our simulations on the bit error rate (BER) performance of long-term evolution (LTE) downlink (DL) transmission [7; 8; 9; 10; 11] over three widely used channel models--the Extended Pedestrian A model (EPA), Extended Vehicular A model (EVA), and Extended Typical Urban model (ETU) [12], defined by the European Telecommunications Standards Institute (ETSI) to represent short, medium, and long delay spread environments, respectively--we discovered some intriguing results.