New perspectives for wireless communications have brought new techniques, such as a very large number of antennas at a base station (BS) serving multiple user terminals (UTs) with a single antenna each, known as massive MIMO (M-MIMO). M-MIMO linear detectors, such as maximal-ratio combining (MRC), zero-forcing (ZF) or minimum-mean-square error (MMSE) can achieve excellent performance with low complexity due to the channel hardening property. However, imperfect channel estimation produces a penalty in the performance. An average bit error rate (BER) performance analysis over time-invariant channel is presented for M-MIMO systems under imperfect channel estimation in contrast with most of M-MIMO literature that uses the ergodic capacity approach. Closed-form expressions and bounds to evaluate the average BER are derived for MRC, ZF and MMSE detectors in a unicellular environment considering M -QAM modulation. Furthermore, an expression to evaluate the normalized signal-to-noise ratio (E b /N 0 ) penalty due to the imperfect channel estimation is presented. Montecarlo numerical simulations are used to verify the tightness of the derived equations which are a function of the number of BS antennas, number of users, coherence time interval, number of pilot symbols and the E b /N 0 of pilot and data symbols used for channel estimation and data detection.INDEX TERMS BER, imperfect channel estimation, massive MIMO, maximal-ratio combining, minimummean-square error, zero-forcing.
N e w good high-rate p u n c t u r e d convolutional codes (PCC's) are presented. While any previously k n o w n PCC was derived b y puncturing a low-rate time-invariant m o t h e r code, the n e w PCC's are s h o w n t o be derived b y puncturing a periodically time-varying convolutional code (PTVCC) acting as the mother code. To find the n e w PCC's, w e first show that a n y PTVCC (hence, a n y PCC) is equivalent to a t y p e of time-invariant convolutional code.Focusing on a fixed unit-memory (UM) code, w e also s h o w that under certain conditions there exists a PTVCC along w i t h a p u n c t u r i n g pattern that is equivalent to that WM code. A combinatorial optmization a l g o r i t h m is then used to search for the n e w good WM codes €or which equivalent PCC's do exist. We observe that the n e w PCC's compare favorably to the previously known PCC's in several respects.
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