This paper studies the low-SNR regime performance of a scalar complex K-user interference channel with the Gaussian noise. The finite bandwidth case is considered, where the low-SNR regime is approached by letting the input power go to zero, while the bandwidth is small and fixed. We show that for all δ > 0, there exists a set of channel coefficients with non-zero measure (probability), in which the wideband slope per user satisfies S0<; 2/K +δ. This is quite contrary to the large bandwidth case, where a slope of 1 per user is achievable with probability 1. We also develop an interference alignment scheme for the finite bandwidth case that shows some gain in wideband slope.

It is well known that minimum received energy per bitEb/N0|minin the interference channel is -1.59 dB as if there were no interference. Thus, the best way to mitigate interference is to operate the interference channel in the low-signal-to-noise-ratio ( SNR) regime. However, when the SNR is small but nonzero,Eb/N0|minalone does not characterize performance. Verdu introduced the wideband slopeS0to characterize the performance in this regime. We show that a wideband slope ofS0/S0, no interference= 1/2 is achievable. This result is similar to recent results on degrees of freedom in the high-SNR regime, and we use a type of interference alignment using delays to obtain the result. We also show that in many cases, the wideband slope is upper bounded byS0/S0, no interference≤ 1/2 for large number of usersK.

In this paper we investigate the wideband slope of a K-user interference channel. We show that delay-based inteference alignment can achieve a wideband slope of S0over S0, no interference = 1 over 2 independent of the number of users K, when the delays are known exactly. This result is similar to recent results on degrees of freedom in the high SNR regime. We also show that in many cases the wideband slope is upper bounded by S0over S0, no interference ≤ 1 over 2 for large number of users K. We then consider delay uncertainty at the transmitter side. We present a modified delay-based interference alignment scheme. Its achievable wideband slope can get arbitrarily close S0over S0, no interference = 1 over 2 -the best achievable wideband slope for the channel without delay uncertainty‥

In this paper, the achievable rate of a K-user interference channel with single antenna at individual node is studied. Interference alignment and zero forcing are applied at the transmitter and receiver, respectively. It is well known from the paper [1] of Cadambe and Jafar that a multiplexing gain (degrees of freedom) of K/2 is achievable. We propose two new pre-coding methods and study how they enhance the achievable rate in terms of the high SNR offset, while maintain the optimality of degree of freedom the Cadambe-Jafar scheme achieved.