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This paper addresses the problem of transmit beamforming (BF) design for cyclic prefixed transmissions over MISO frequency selective channels. Unlike  which is based on convex optimization tools, we here give two more computationally effective solutions in close-form to minimize the arithmetic mean of the effective error probabilities (ARITH-EEP) under the per-antenna power constraint (PPC). Moreover, limited-rate feedback methods needed for transmit BF is considered and a simple codebook design method for frequency selective channels is proposed. Unlike the conventional method where the codebook is designed for the BF vectors directly, we construct codebooks for the amplitude and phase of the time domain channel state information (CSI) to reduce the rate of feedback. The simulation results show that the proposed suboptimal solutions not only have lower complexities but also outperform the PPC solutions given in  in terms of BER. The effectiveness of the proposed limited-rate feedback method is also demonstrated in the simulation.