Communications using the millimeter wave (mmWave) spectrum are a mainstream technology of the next generation systems due to their huge available bandwidth. However, the mmWave band will experience much more propagation loss than a low-frequency band. Conventional precoding techniques are impractical in mmWave scenarios due to manufacturing costs and power consumption. Hybrid alternatives have been considered as a promising technology to provide a compromise between hardware complexity and system performance by reducing the number of radio-frequency (RF) chains. In this paper, a hybrid processing design for downlink in mmWave scenarios is proposed, where the number of RF chains is reduced to the number of data streams. The precodification process is made by a three-stage-based hybrid precoder, whereas in the terminals, the equalization process only requires a low complex analog combiner. The three stages of the hybrid precoder are designed by a hierarchical strategy. The first stage addresses the phase shifters aiming to maximize the sum-rate system, whereas the second and third stages are dedicated to mitigating the inter-user interference effects. The proposed methodology gets a robust signal processing that can greatly mitigate the side effects of hardware reduction. Numerical results in terms of bit error rate (BER) and sum-rate evidence that the proposed method not only overcomes other hybrid precoders/combiners but also reaches the same performance as a fully digital technique in some scenarios.