Finite signal-set capacity of two-user Gaussian Multiple Access Channel

Abstract

Abstract-The capacity region of a two-user Gaussian Multiple Access Channel (GMAC) with complex finite input alphabets and continuous output alphabet is studied. When both the users are equipped with the same code alphabet, it is shown that, rotation of one of the user's alphabets by an appropriate angle can make the new pair of alphabets not only uniquely decodable, but will result in enlargement of the capacity region. For this set-up, we identify the primary problem to be finding appropriate angle(s) of rotation between the alphabets such that the capacity region is maximally enlarged. It is shown that the angle of rotation which provides maximum enlargement of the capacity region also minimizes the union bound on the probability of error of the sumalphabet and vice-verse. The optimum angle(s) of rotation varies with the SNR. Through simulations, optimal angle(s) of rotation that gives maximum enlargement of the capacity region of GMAC with some well known alphabets such as M -QAM and M -PSK for some M are presented for several values of SNR. It is shown that for large number of points in the alphabets, capacity gains due to rotations progressively reduce. As the number of points N tends to infinity, our results match the results in the literature wherein the capacity region of the Gaussian code alphabet doesn't change with rotation for any SNR.

On the Capacity of Quantized Gaussian MAC Channels with Finite Input Alphabet

“…With finite input alphabets and an unquantized receiver, the two-user Gaussian MAC rate region has been studied in [5]. In [5], in terms of the achievable rate region, it was shown that, compared to having both the users transmit using the same finite signal set, it is better to have the second user transmit using a rotated version of the first user's signal set.…”

“…In [5], in terms of the achievable rate region, it was shown that, compared to having both the users transmit using the same finite signal set, it is better to have the second user transmit using a rotated version of the first user's signal set. We refer to the two-user Gaussian MAC system model in [5] (with finite input alphabet and no output quantization) as constellation constrained MAC (CCMAC).…”

“…In this paper, as in [5], we consider the rotation scheme, wherein one user transmits using a rotated version of the other user's signal set. However, instead of assuming an unquantized receiver as was done in [5], here we consider quantized receivers.…”

“…In this paper, we first derive the expressions for the achievable rate region of a two-user Gaussian MAC with finite input alphabet and quantized output. We show that, with finite input alphabet, the achievable rate region with the commonly used uniform receiver quantizer has a significant loss in the rate region compared to that in [5]. It is observed that this degradation is due to the fact that the received analog signal is densely distributed around the origin, and is therefore not efficiently quantized with a uniform quantizer which has equally spaced quantization intervals.…”

“…With finite input alphabet and an unquantized receiver, the two-user Gaussian MAC rate region was studied in [5]. In most high throughput communication systems based on digital signal processing, the analog received signal is quantized using a low precision quantizer.…”