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In this paper, we characterize the degrees of freedom (DoF) for $K $-user $M\times 1 $ multiple-input single-output interference channels withreconfigurable antennas which have multiple preset modes at the receivers,assuming linear coding strategies in the absence of channel state informationat the transmitters, i.e., blind interference alignment. Our linear DoFconverse builds on the lemma that if a set of transmit symbols is aligned attheir common unintended receivers, those symbols must have independent signalsubspace at their corresponding receivers. This lemma arises from the inherentfeature that channel state's changing patterns of the links towards the samereceiver are always identical, assuming that the coherence time of the channelis long enough. We derive an upper bound for the linear sum DoF, and propose anachievable scheme that exactly achieves the linear sum DoF upper-bound whenboth of the $\frac{n^{*}}{M}=R_{1} $ and $\frac{MK}{n^{*}}=R_{2} $ areintegers. For the other cases, where either $R_1 $ or $R_2 $ is not an integer,we only give some guidelines how the interfering signals are aligned at thereceivers to achieve the upper-bound. As an extension, we also show the linearsum DoF upper-bound for downlink/uplink cellular networks.

Linear Degrees of Freedom for $K $-user MISO Interference Channels with Blind Interference Alignment